{"id":104,"date":"2021-04-16T13:46:39","date_gmt":"2021-04-16T05:46:39","guid":{"rendered":"http:\/\/18.141.9.105\/?p=104"},"modified":"2021-12-10T14:53:29","modified_gmt":"2021-12-10T06:53:29","slug":"algsum","status":"publish","type":"post","link":"https:\/\/yunpeng.site\/index.php\/2021\/04\/16\/algsum\/","title":{"rendered":"\u7b97\u6cd5\u5bfc\u8bba\u603b\u7ed3"},"content":{"rendered":"\t\t
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\n\t\t\t\n\n\n\n\u7b97\u6cd5\u57fa\u7840\u671f\u672b\u603b\u7ed3<\/title><link href='https:\/\/fonts.loli.net\/css?family=Open+Sans:400italic,700italic,700,400&subset=latin,latin-ext' rel='stylesheet' type='text\/css' \/><style type='text\/css'>html {overflow-x: initial !important;}:root { --bg-color: #ffffff; --text-color: #333333; --select-text-bg-color: #B5D6FC; --select-text-font-color: auto; --monospace: \"Lucida Console\",Consolas,\"Courier\",monospace; --title-bar-height: 20px; }\n.mac-os-11 { --title-bar-height: 28px; }\nhtml { font-size: 14px; background-color: var(--bg-color); color: var(--text-color); font-family: \"Helvetica Neue\", Helvetica, Arial, sans-serif; -webkit-font-smoothing: antialiased; }\nbody { margin: 0px; padding: 0px; height: auto; bottom: 0px; top: 0px; left: 0px; right: 0px; font-size: 1rem; line-height: 1.42857143; overflow-x: hidden; background-image: inherit; background-size: inherit; background-attachment: inherit; background-origin: inherit; 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1;\n}\n\n.md-toc { \n margin-top:20px;\n padding-bottom:20px;\n}\n\n.sidebar-tabs {\n border-bottom: none;\n}\n\n#typora-quick-open {\n border: 1px solid #ddd;\n background-color: #f8f8f8;\n}\n\n#typora-quick-open-item {\n background-color: #FAFAFA;\n border-color: #FEFEFE #e5e5e5 #e5e5e5 #eee;\n border-style: solid;\n border-width: 1px;\n}\n\n\/** focus mode *\/\n.on-focus-mode blockquote {\n border-left-color: rgba(85, 85, 85, 0.12);\n}\n\nheader, .context-menu, .megamenu-content, footer{\n font-family: \"Segoe UI\", \"Arial\", sans-serif;\n}\n\n.file-node-content:hover .file-node-icon,\n.file-node-content:hover .file-node-open-state{\n visibility: visible;\n}\n\n.mac-seamless-mode #typora-sidebar {\n background-color: #fafafa;\n background-color: var(--side-bar-bg-color);\n}\n\n.md-lang {\n color: #b4654d;\n}\n\n.html-for-mac .context-menu {\n --item-hover-bg-color: #E6F0FE;\n}\n\n#md-notification .btn {\n border: 0;\n}\n\n.dropdown-menu .divider {\n border-color: #e5e5e5;\n}\n\n.ty-preferences .window-content {\n background-color: #fafafa;\n}\n\n.ty-preferences .nav-group-item.active {\n color: white;\n background: #999;\n}\n\n :root {--mermaid-font-zoom:1em ;} .typora-export li, .typora-export p, .typora-export, .footnote-line {white-space: normal;} \n<\/style>\n<\/head>\n<body class='typora-export'>\n<div id='write' class=''><h1><a name=\"\u7b97\u6cd5\u57fa\u7840\u671f\u672b\u603b\u7ed3\" class=\"md-header-anchor\"><\/a><span>\u7b97\u6cd5\u57fa\u7840\u671f\u672b\u603b\u7ed3<\/span><\/h1><h3><a name=\"\u7b97\u6cd5\u5206\u6790\" class=\"md-header-anchor\"><\/a><span>\u7b97\u6cd5\u5206\u6790<\/span><\/h3><h4><a name=\"\u4e00\u6392\u5e8f\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u4e00\u3001\u6392\u5e8f\u7b97\u6cd5<\/span><\/h4><p><strong><span>1\u3001\u63d2\u5165\u6392\u5e8f\uff1a<\/span><\/strong><\/p><p><span>\u6700\u574f\u60c5\u51b5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"6.061ex\" height=\"2.811ex\" viewBox=\"0 -906.7 2609.6 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E1-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E1-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E1-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E1-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E1-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E1-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E1-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><g transform=\"translate(1167,0)\"><use xlink:href=\"#E1-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E1-MJMAIN-32\" x=\"848\" y=\"513\"><\/use><\/g><use xlink:href=\"#E1-MJMAIN-29\" x=\"2220\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta (n^2)<\/script><span> \u5f53\u6570\u7ec4\u9006\u5e8f\u65f6\u53d1\u751f<\/span><\/p><p><span>\u6700\u597d\u60c5\u51b5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E188-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E188-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(n)<\/script><span> \u5f53\u6570\u7ec4\u987a\u5e8f\u65f6\u53d1\u751f<\/span><\/p><p><span>\u7b97\u6cd5\u65f6\u95f4\u590d\u6742\u5ea6\u4e3b\u8981\u6765\u81ea\u5bf9\u6570\u7ec4\u7684\u904d\u5386\u4ee5\u53ca\u5143\u7d20\u7684\u79fb\u52a8\uff0c\u4fee\u6539\u641c\u7d22\u7b97\u6cd5\u5e76\u4e0d\u80fd\u6539\u8fdb\u65f6\u95f4\u590d\u6742\u5ea6<\/span><\/p><p><span>\u7a33\u5b9a<\/span><\/p><p><strong><span>2\u3001\u5f52\u5e76\u6392\u5e8f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.334ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4019 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E3-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E3-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E3-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E3-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E3-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E3-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E3-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E3-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E3-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E3-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E3-MJMATHI-6C\" x=\"1767\" y=\"0\"><\/use><use xlink:href=\"#E3-MJMATHI-6F\" x=\"2065\" y=\"0\"><\/use><use xlink:href=\"#E3-MJMATHI-67\" x=\"2550\" y=\"0\"><\/use><use xlink:href=\"#E3-MJMATHI-6E\" x=\"3030\" y=\"0\"><\/use><use xlink:href=\"#E3-MJMAIN-29\" x=\"3630\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta (nlogn)<\/script><\/strong><\/p><p><span>\u9012\u5f52\u5f0f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"22.205ex\" height=\"2.928ex\" viewBox=\"0 -806.1 9560.3 1260.5\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.055ex;\"><defs><path stroke-width=\"0\" id=\"E4-MJMATHI-54\" d=\"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z\"><\/path><path stroke-width=\"0\" id=\"E4-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E4-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E4-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E4-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path stroke-width=\"0\" id=\"E4-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E4-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E4-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E4-MJMATHI-54\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-28\" x=\"704\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMATHI-6E\" x=\"1093\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-29\" x=\"1693\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-3D\" x=\"2359\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-32\" x=\"3415\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMATHI-54\" x=\"3915\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-28\" x=\"4619\" y=\"0\"><\/use><g transform=\"translate(5008,0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"544\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E4-MJMATHI-6E\" x=\"84\" y=\"582\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E4-MJMAIN-32\" x=\"134\" y=\"-531\"><\/use><\/g><\/g><use xlink:href=\"#E4-MJMAIN-29\" x=\"5792\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-2B\" x=\"6404\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-398\" x=\"7404\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-28\" x=\"8182\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMATHI-6E\" x=\"8571\" y=\"0\"><\/use><use xlink:href=\"#E4-MJMAIN-29\" x=\"9171\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">T(n) = 2T(\\frac{n}{2}) + \\Theta(n)<\/script><\/p><p><span>\u7a33\u5b9a<\/span><\/p><p><strong><span>3\u3001\u5806\u6392\u5e8f\uff1a <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.3ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4004 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E50-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E50-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6C\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6F\" x=\"2050\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-67\" x=\"2535\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6E\" x=\"3015\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMAIN-29\" x=\"3615\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (nlogn)<\/script><\/strong><\/p><p><span>\u4e0e\u5806\u6392\u5e8f\u76f8\u5173\u7684\u8fc7\u7a0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff1a<\/span><\/p><p><span>MAX-HEAPIFY: <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E201-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E201-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(logn)<\/script><\/p><p><span>BUILD-MAX-HEAP: <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E34-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E34-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n)<\/script><\/p><p><span>MAX-HEAP-INSERT, HEAP-EXTRACT-MAX, HEAP-INCREASE-KEY: <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E201-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E201-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(logn)<\/script><\/p><p><span>HEAP-MAXIMUM\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.74ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2041 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E200-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E200-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E200-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E200-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E200-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E200-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E200-MJMAIN-31\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E200-MJMAIN-29\" x=\"1652\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(1)<\/script><\/p><p><span>\u5728\u4e00\u4e2a\u5305\u542bn\u4e2a\u5143\u7d20\u7684\u5806\u4e2d\uff0c\u6240\u6709\u4f18\u5148\u961f\u5217\u7684\u64cd\u4f5c\u90fd\u53ef\u4ee5\u5728<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E201-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E201-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(logn)<\/script><span>\u65f6\u95f4\u5185\u5b8c\u6210<\/span><\/p><p><span>\u4e0d\u7a33\u5b9a<\/span><\/p><p><strong><span>4\u3001\u5feb\u901f\u6392\u5e8f\uff1a<\/span><\/strong><\/p><p><span>\u6700\u574f\u60c5\u51b5\uff1a <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"6.026ex\" height=\"2.811ex\" viewBox=\"0 -906.7 2594.6 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E228-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E228-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E228-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><g transform=\"translate(1152,0)\"><use xlink:href=\"#E228-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E228-MJMAIN-32\" x=\"848\" y=\"513\"><\/use><\/g><use xlink:href=\"#E228-MJMAIN-29\" x=\"2205\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n^2)<\/script><span> \u5f53\u6bcf\u6b21\u90fd\u5c06\u6570\u7ec4\u5212\u5206\u4e3an-1\u548c0\u4e2a\u5143\u7d20\u7684\u65f6\u5019\u53d1\u751f<\/span><\/p><p><span>\u6700\u597d\u60c5\u51b5\uff1a <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.3ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4004 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E14-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E14-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6C\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6F\" x=\"2050\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-67\" x=\"2535\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6E\" x=\"3015\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMAIN-29\" x=\"3615\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(nlogn)<\/script><span> \u5f53\u6bcf\u6b21\u5212\u5206\u90fd\u5c06\u6570\u7ec4\u5747\u5206\u65f6\u4ea7\u751f<\/span><\/p><p><span>\u5e73\u5747\u60c5\u51b5\uff1a <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.3ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4004 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E14-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E14-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6C\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6F\" x=\"2050\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-67\" x=\"2535\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6E\" x=\"3015\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMAIN-29\" x=\"3615\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(nlogn)<\/script><span> \u5f53\u5212\u5206\u662f\u5e38\u6570\u6bd4\u4f8b\u6216\u8005\u597d\u5212\u5206\u548c\u5dee\u5212\u5206\u540c\u65f6\u51fa\u73b0\u65f6\u4ea7\u751f<\/span><\/p><p><span>\u968f\u673a\u5feb\u901f\u6392\u5e8f\u7b97\u6cd5\u671f\u671b\u8fd0\u884c\u65f6\u95f4\uff1a <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.3ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4004 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E14-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E14-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E14-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6C\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6F\" x=\"2050\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-67\" x=\"2535\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMATHI-6E\" x=\"3015\" y=\"0\"><\/use><use xlink:href=\"#E14-MJMAIN-29\" x=\"3615\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(nlogn)<\/script><span> <\/span><\/p><p><span>\u4e3b\u8981\u770bpartition\u8fc7\u7a0b\u4e2d\u6bd4\u8f83\u5143\u7d20\u65f6\u6709\u6ca1\u6709\u52a0\u7b49\u53f7\u6765\u786e\u5b9a\u7a33\u5b9a\u6027\uff0c\u52a0\u4e86\u7b49\u53f7\u5373\u7a33\u5b9a(\u7b97\u6cd5\u5bfc\u8bba\u4e2d\u7684\u7b97\u6cd5\u7a33\u5b9a)<\/span><\/p><p><strong><span>5\u3001\u8ba1\u6570\u6392\u5e8f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.057ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3899.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E15-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E15-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E15-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path stroke-width=\"0\" id=\"E15-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E15-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E15-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E15-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E15-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E15-MJMATHI-6B\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E15-MJMAIN-2B\" x=\"1910\" y=\"0\"><\/use><use xlink:href=\"#E15-MJMATHI-6E\" x=\"2910\" y=\"0\"><\/use><use xlink:href=\"#E15-MJMAIN-29\" x=\"3510\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(k+n)<\/script><\/strong><\/p><p><span>\u7a33\u5b9a<\/span><\/p><p><span>k\u8868\u793a\u6570\u7684\u4e0a\u754c\uff0c\u82e5<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.315ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4010.6 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E18-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E18-MJMATHI-6B\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-3D\" x=\"798\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-398\" x=\"1854\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-28\" x=\"2632\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMATHI-6E\" x=\"3021\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-29\" x=\"3621\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">k=\\Theta(n)<\/script><span>\uff0c\u5219\u8ba1\u6570\u6392\u5e8f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E17-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E17-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E17-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E17-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E17-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E17-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E17-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E17-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta ( n)<\/script><\/p><p><span>\u9002\u7528\u4e8e<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.315ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4010.6 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E18-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E18-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E18-MJMATHI-6B\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-3D\" x=\"798\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-398\" x=\"1854\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-28\" x=\"2632\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMATHI-6E\" x=\"3021\" y=\"0\"><\/use><use xlink:href=\"#E18-MJMAIN-29\" x=\"3621\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">k=\\Theta(n)<\/script><span>\u7684\u6574\u6570\u6392\u5e8f<\/span><\/p><p><strong><span>6\u3001\u57fa\u6570\u6392\u5e8f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"12.078ex\" height=\"2.577ex\" viewBox=\"0 -806.1 5200.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E19-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E19-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E19-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 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477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path stroke-width=\"0\" id=\"E19-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E19-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMATHI-64\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMAIN-28\" x=\"1690\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMATHI-6E\" x=\"2079\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMAIN-2B\" x=\"2901\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMATHI-6B\" x=\"3901\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMAIN-29\" x=\"4422\" y=\"0\"><\/use><use xlink:href=\"#E19-MJMAIN-29\" x=\"4811\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\"> \\Theta (d(n+k) ) <\/script><\/strong><\/p><p><span>\u5b50\u8fc7\u7a0b\u5fc5\u987b\u4f7f\u7528\u7a33\u5b9a\u7684\u6392\u5e8f\u7b97\u6cd5<\/span><\/p><p><span>\u6309r\u4f4d\u4e00\u8d77\u6392\u5e8f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"15.29ex\" height=\"3.278ex\" viewBox=\"0 -956.9 6583.2 1411.3\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.055ex;\"><defs><path stroke-width=\"0\" id=\"E20-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E20-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E20-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><path stroke-width=\"0\" id=\"E20-MJMATHI-72\" d=\"M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E20-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E20-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E20-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E20-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E20-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E20-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E20-MJMAIN-28\" x=\"1167\" y=\"0\"><\/use><g transform=\"translate(1556,0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"489\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E20-MJMATHI-64\" x=\"84\" y=\"581\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E20-MJMATHI-72\" x=\"120\" y=\"-488\"><\/use><\/g><\/g><use xlink:href=\"#E20-MJMAIN-29\" x=\"2285\" y=\"0\"><\/use><use xlink:href=\"#E20-MJMAIN-28\" x=\"2674\" y=\"0\"><\/use><use xlink:href=\"#E20-MJMATHI-6E\" x=\"3063\" y=\"0\"><\/use><use xlink:href=\"#E20-MJMAIN-2B\" x=\"3886\" y=\"0\"><\/use><g transform=\"translate(4886,0)\"><use xlink:href=\"#E20-MJMAIN-32\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E20-MJMATHI-72\" x=\"707\" y=\"555\"><\/use><\/g><use xlink:href=\"#E20-MJMAIN-29\" x=\"5805\" y=\"0\"><\/use><use xlink:href=\"#E20-MJMAIN-29\" x=\"6194\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta((\\frac{d}{r})(n+2^r))<\/script><\/p><p><span>\u5e76\u4e0d\u4e00\u5b9a\u6bd4\u57fa\u4e8e\u6bd4\u8f83\u7684\u6392\u5e8f\u7b97\u6cd5\u597d\uff0c\u56e0\u4e3a\u57fa\u6570\u6392\u5e8f\u5e76\u975e\u539f\u5740\u6392\u5e8f\u4e14\u5e38\u6570\u9879\u56e0\u5b50\u5927\u5c0f\u4e0d\u540c<\/span><\/p><p><span>\u7a33\u5b9a<\/span><\/p><p><strong><span>7\u3001\u6876\u6392\u5e8f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E34-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E34-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n)<\/script><\/strong><\/p><p><span>\u5047\u8bbe\u6570\u636e\u670d\u4ece\u5747\u5300\u5206\u5e03<\/span><\/p><p><span>\u5e73\u5747\u60c5\u51b5\u4e0b\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E22-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E22-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E22-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E22-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E22-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E22-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E22-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E22-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O( n)<\/script><\/p><p><span>\u7b97\u6cd5\u5bfc\u8bba\u4e2d\u63cf\u8ff0\u7684\u6876\u6392\u5e8f\u7a33\u5b9a<\/span><\/p><p><strong><span>\u5728\u6700\u574f\u60c5\u51b5\u4e0b\uff0c\u4efb\u4f55\u6392\u5e8f\u7b97\u6cd5\u90fd\u9700\u8981\u505a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.204ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3963 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E24-MJMAIN-3A9\" d=\"M55 454Q55 503 75 546T127 617T197 665T272 695T337 704H352Q396 704 404 703Q527 687 596 615T666 454Q666 392 635 330T559 200T499 83V80H543Q589 81 600 83T617 93Q622 102 629 135T636 172L637 177H677V175L660 89Q645 3 644 2V0H552H488Q461 0 456 3T451 20Q451 89 499 235T548 455Q548 512 530 555T483 622T424 656T361 668Q332 668 303 658T243 626T193 560T174 456Q174 380 222 233T270 20Q270 7 263 0H77V2Q76 3 61 89L44 175V177H84L85 172Q85 171 88 155T96 119T104 93Q109 86 120 84T178 80H222V83Q206 132 162 199T87 329T55 454Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E24-MJMAIN-3A9\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMAIN-28\" x=\"722\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6E\" x=\"1111\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6C\" x=\"1711\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6F\" x=\"2009\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-67\" x=\"2494\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6E\" x=\"2974\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMAIN-29\" x=\"3574\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Omega(nlogn)<\/script><span>\u6b21\u6bd4\u8f83<\/span><\/strong><\/p><p><strong><span>\u5806\u6392\u5e8f\u548c\u5f52\u5e76\u6392\u5e8f\u662f\u6e10\u8fdb\u6700\u4f18\u7684\u6bd4\u8f83\u6392\u5e8f\u7b97\u6cd5\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u65f6\u95f4\u4e0a\u754c\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.204ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3963 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E24-MJMAIN-3A9\" d=\"M55 454Q55 503 75 546T127 617T197 665T272 695T337 704H352Q396 704 404 703Q527 687 596 615T666 454Q666 392 635 330T559 200T499 83V80H543Q589 81 600 83T617 93Q622 102 629 135T636 172L637 177H677V175L660 89Q645 3 644 2V0H552H488Q461 0 456 3T451 20Q451 89 499 235T548 455Q548 512 530 555T483 622T424 656T361 668Q332 668 303 658T243 626T193 560T174 456Q174 380 222 233T270 20Q270 7 263 0H77V2Q76 3 61 89L44 175V177H84L85 172Q85 171 88 155T96 119T104 93Q109 86 120 84T178 80H222V83Q206 132 162 199T87 329T55 454Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E24-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E24-MJMAIN-3A9\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMAIN-28\" x=\"722\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6E\" x=\"1111\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6C\" x=\"1711\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6F\" x=\"2009\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-67\" x=\"2494\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMATHI-6E\" x=\"2974\" y=\"0\"><\/use><use xlink:href=\"#E24-MJMAIN-29\" x=\"3574\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Omega(nlogn)<\/script><\/strong><\/p><h4><a name=\"\u4e8c\u9012\u5f52\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u4e8c\u3001\u9012\u5f52\u7b97\u6cd5<\/span><\/h4><p><strong><span>1\u3001\u6c42Fibonacci\u6570<\/span><\/strong><\/p><p><span>\u4e00\u822c\u9012\u5f52\u7b97\u6cd5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"8.166ex\" height=\"3.278ex\" viewBox=\"0 -956.9 3515.8 1411.3\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.055ex;\"><defs><path stroke-width=\"0\" id=\"E25-MJMAIN-3A9\" d=\"M55 454Q55 503 75 546T127 617T197 665T272 695T337 704H352Q396 704 404 703Q527 687 596 615T666 454Q666 392 635 330T559 200T499 83V80H543Q589 81 600 83T617 93Q622 102 629 135T636 172L637 177H677V175L660 89Q645 3 644 2V0H552H488Q461 0 456 3T451 20Q451 89 499 235T548 455Q548 512 530 555T483 622T424 656T361 668Q332 668 303 658T243 626T193 560T174 456Q174 380 222 233T270 20Q270 7 263 0H77V2Q76 3 61 89L44 175V177H84L85 172Q85 171 88 155T96 119T104 93Q109 86 120 84T178 80H222V83Q206 132 162 199T87 329T55 454Z\"><\/path><path stroke-width=\"0\" id=\"E25-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E25-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path stroke-width=\"0\" id=\"E25-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E25-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E25-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E25-MJMAIN-3A9\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E25-MJMAIN-28\" x=\"722\" y=\"0\"><\/use><use xlink:href=\"#E25-MJMAIN-28\" x=\"1111\" y=\"0\"><\/use><g transform=\"translate(1500,0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"473\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E25-MJMAIN-33\" x=\"84\" y=\"593\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E25-MJMAIN-32\" x=\"84\" y=\"-531\"><\/use><\/g><\/g><g transform=\"translate(2213,0)\"><use xlink:href=\"#E25-MJMAIN-29\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E25-MJMATHI-6E\" x=\"550\" y=\"513\"><\/use><\/g><use xlink:href=\"#E25-MJMAIN-29\" x=\"3126\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Omega ((\\frac{3}{2})^n)<\/script><\/p><p><span>\u6539\u8fdb\u540e\u7684\u9012\u5f52\u7b97\u6cd5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E26-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E26-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E26-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E26-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E26-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E26-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E26-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E26-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta (n)<\/script><\/p><p><strong><span>2\u3001\u4e8c\u5206\u67e5\u627e <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E27-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E27-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E27-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E27-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E27-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E27-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E27-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E27-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E27-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E27-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E27-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E27-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E27-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E27-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (logn)<\/script><\/strong><\/p><p><strong><span>3\u3001\u5168\u6392\u5217\u751f\u6210 <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.618ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2419 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E28-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E28-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E28-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E28-MJMAIN-21\" d=\"M78 661Q78 682 96 699T138 716T180 700T199 661Q199 654 179 432T158 206Q156 198 139 198Q121 198 119 206Q118 209 98 431T78 661ZM79 61Q79 89 97 105T141 121Q164 119 181 104T198 61Q198 31 181 16T139 1Q114 1 97 16T79 61Z\"><\/path><path stroke-width=\"0\" id=\"E28-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E28-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E28-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E28-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E28-MJMAIN-21\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E28-MJMAIN-29\" x=\"2030\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n!)<\/script><span> <\/span><\/strong><\/p><p><strong><span>4\u3001Strassen\u77e9\u9635\u4e58\u6cd5 <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"8.135ex\" height=\"2.811ex\" viewBox=\"0 -906.7 3502.6 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E29-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E29-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E29-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E29-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E29-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E29-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E29-MJMAIN-37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><path stroke-width=\"0\" id=\"E29-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E29-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E29-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><g transform=\"translate(1167,0)\"><use xlink:href=\"#E29-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(600,362)\"><use transform=\"scale(0.707)\" xlink:href=\"#E29-MJMATHI-6C\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E29-MJMATHI-6F\" x=\"298\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E29-MJMATHI-67\" x=\"783\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E29-MJMAIN-37\" x=\"1263\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E29-MJMAIN-29\" x=\"3113\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(n^{log7})<\/script><\/strong><\/p><h4><a name=\"\u4e09\u9009\u62e9\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u4e09\u3001\u9009\u62e9\u7b97\u6cd5<\/span><\/h4><p><strong><span>1\u3001\u6700\u5927\u6700\u5c0f\u503c\u7b97\u6cd5<\/span><\/strong><\/p><p><span>\u5355\u72ec\u627e\u6700\u5927\u6700\u5c0f\u503c\uff0c\u9700\u8981\u6bd4\u8f83n-1\u6b21<\/span><\/p><p><span>\u4e00\u8d77\u627e\u6700\u5927\u6700\u5c0f\u503c\uff0c\u9700\u8981\u6bd4\u8f83<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.045ex\" height=\"2.928ex\" viewBox=\"0 -806.1 2172.3 1260.5\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.055ex;\"><defs><path stroke-width=\"0\" id=\"E30-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path stroke-width=\"0\" id=\"E30-MJMAIN-230A\" d=\"M174 734Q174 735 175 737T177 740T180 744T184 747T189 749T196 750Q206 748 214 735V-210H310H373Q401 -210 411 -213T422 -230T411 -247T369 -251Q362 -251 338 -251T298 -250H190Q178 -246 174 -234V734Z\"><\/path><path stroke-width=\"0\" id=\"E30-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E30-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E30-MJMAIN-230B\" d=\"M229 734Q229 735 230 737T232 740T235 744T239 747T244 749T251 750Q262 748 269 735V-235Q266 -240 256 -249L147 -250H77Q43 -250 32 -247T21 -230T32 -213T72 -209Q79 -209 99 -209T133 -210H229V734Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E30-MJMAIN-33\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E30-MJMAIN-230A\" x=\"500\" y=\"0\"><\/use><g transform=\"translate(944,0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"544\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E30-MJMATHI-6E\" x=\"84\" y=\"582\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E30-MJMAIN-32\" x=\"134\" y=\"-531\"><\/use><\/g><\/g><use xlink:href=\"#E30-MJMAIN-230B\" x=\"1728\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">3\\lfloor \\frac{n}{2} \\rfloor<\/script><span>\u6b21<\/span><\/p><p><span>\u4e00\u8d77\u627e\u6700\u5927\u503c\u548c\u6b21\u5927\u503c\u6216\u8005\u4e00\u8d77\u627e\u6700\u5c0f\u503c\u548c\u6b21\u5c0f\u503c\uff0c\u9700\u8981\u6bd4\u8f83<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"14.623ex\" height=\"2.577ex\" viewBox=\"0 -806.1 6295.9 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E31-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMAIN-2308\" d=\"M174 734Q178 746 190 750H298H369Q400 750 411 747T422 730T411 713T372 709Q365 709 345 709T310 710H214V-235Q206 -248 196 -250Q192 -250 189 -249T184 -247T180 -244T178 -241T176 -237T174 -234V734Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMAIN-2309\" d=\"M21 717T21 730T32 746T75 750H147H256Q266 742 269 735V-235Q262 -248 251 -250Q247 -250 244 -249T239 -247T235 -244T233 -241T231 -237T229 -234V710H133Q119 710 99 710T71 709Q43 709 32 713Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E31-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E31-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMAIN-2B\" x=\"822\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMAIN-2308\" x=\"1822\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMATHI-6C\" x=\"2266\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMATHI-6F\" x=\"2564\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMATHI-67\" x=\"3049\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMATHI-6E\" x=\"3529\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMAIN-2309\" x=\"4129\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMAIN-2212\" x=\"4795\" y=\"0\"><\/use><use xlink:href=\"#E31-MJMAIN-32\" x=\"5795\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">n+\\lceil logn \\rceil - 2<\/script><span>\u6b21<\/span><\/p><p><strong><span>2\u3001\u5bfb\u627e\u6570\u7ec4\u4e2d\u7b2ci\u5c0f\u5143\u7d20\u7684\u7b97\u6cd5<\/span><\/strong><\/p><p><span>RANDOMIZED-SELECT:<\/span><\/p><p><span>\u671f\u671b\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E34-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E34-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n)<\/script><\/p><p><span>\u6700\u574f\u60c5\u51b5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"6.061ex\" height=\"2.811ex\" viewBox=\"0 -906.7 2609.6 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E33-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E33-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E33-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E33-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E33-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E33-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E33-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><g transform=\"translate(1167,0)\"><use xlink:href=\"#E33-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E33-MJMAIN-32\" x=\"848\" y=\"513\"><\/use><\/g><use xlink:href=\"#E33-MJMAIN-29\" x=\"2220\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(n^2)<\/script><span> \u5f53\u5212\u5206\u4e0e\u5feb\u901f\u6392\u5e8f\u4e2d\u6700\u574f\u60c5\u51b5\u5212\u5206\u4e00\u81f4\u65f6<\/span><\/p><p><span>SELECT:<\/span><\/p><p><span>\u6700\u574f\u60c5\u51b5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E34-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E34-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E34-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E34-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n)<\/script><\/p><p><span>\u9012\u5f52\u5f0f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"35.995ex\" height=\"3.278ex\" viewBox=\"0 -956.9 15498 1411.3\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.055ex;\"><defs><path stroke-width=\"0\" id=\"E35-MJMATHI-54\" d=\"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-2264\" d=\"M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-2308\" d=\"M174 734Q178 746 190 750H298H369Q400 750 411 747T422 730T411 713T372 709Q365 709 345 709T310 710H214V-235Q206 -248 196 -250Q192 -250 189 -249T184 -247T180 -244T178 -241T176 -237T174 -234V734Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-2309\" d=\"M21 717T21 730T32 746T75 750H147H256Q266 742 269 735V-235Q262 -248 251 -250Q247 -250 244 -249T239 -247T235 -244T233 -241T231 -237T229 -234V710H133Q119 710 99 710T71 709Q43 709 32 713Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-37\" d=\"M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMAIN-36\" d=\"M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z\"><\/path><path stroke-width=\"0\" id=\"E35-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E35-MJMATHI-54\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-28\" x=\"704\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMATHI-6E\" x=\"1093\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-29\" x=\"1693\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-2264\" x=\"2359\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMATHI-54\" x=\"3415\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-28\" x=\"4119\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-2308\" x=\"4508\" y=\"0\"><\/use><g transform=\"translate(4952,0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"544\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E35-MJMATHI-6E\" x=\"84\" y=\"582\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E35-MJMAIN-35\" x=\"134\" y=\"-531\"><\/use><\/g><\/g><use xlink:href=\"#E35-MJMAIN-2309\" x=\"5736\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-29\" x=\"6180\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-2B\" x=\"6792\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMATHI-54\" x=\"7792\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-28\" x=\"8496\" y=\"0\"><\/use><g transform=\"translate(8885,0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"897\" height=\"60\" x=\"0\" y=\"220\"><\/rect><g transform=\"translate(60,419)\"><use transform=\"scale(0.707)\" xlink:href=\"#E35-MJMAIN-37\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E35-MJMATHI-6E\" x=\"500\" y=\"0\"><\/use><\/g><g transform=\"translate(95,-376)\"><use transform=\"scale(0.707)\" xlink:href=\"#E35-MJMAIN-31\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E35-MJMAIN-30\" x=\"500\" y=\"0\"><\/use><\/g><\/g><\/g><use xlink:href=\"#E35-MJMAIN-2B\" x=\"10245\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-36\" x=\"11245\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-29\" x=\"11745\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-2B\" x=\"12356\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMATHI-4F\" x=\"13356\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-28\" x=\"14119\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMATHI-6E\" x=\"14508\" y=\"0\"><\/use><use xlink:href=\"#E35-MJMAIN-29\" x=\"15108\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">T(n) \\leq T(\\lceil \\frac{n}{5} \\rceil) + T(\\frac{7n}{10} + 6) + O(n)<\/script><\/p><p><span>\u5143\u7d20\u5fc5\u987b\u4e92\u5f02<\/span><\/p><h4><a name=\"\u56db\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u56db\u3001\u52a8\u6001\u89c4\u5212\u7b97\u6cd5<\/span><\/h4><p><span>\u9002\u7528\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\u7684\u95ee\u9898\u9700\u5177\u5907\u7684\u6027\u8d28\uff1a\u2460\u3001\u6700\u4f18\u5b50\u7ed3\u6784 \u2461\u3001\u91cd\u53e0\u5b50\u95ee\u9898<\/span><\/p><p><span>\u5206\u6cbb\u6cd5\u9002\u7528\u4e8e\u6bcf\u4e00\u6b65\u751f\u6210\u7684\u5b50\u95ee\u9898\u90fd\u4e0d\u540c\u7684\u95ee\u9898<\/span><\/p><p><span>\u6700\u4f18\u5b50\u7ed3\u6784\uff1a\u539f\u95ee\u9898\u7684\u6700\u4f18\u89e3\u5305\u542b\u5b50\u95ee\u9898\u7684\u6700\u4f18\u89e3\uff0c\u5b50\u95ee\u9898\u95f4\u7684\u89e3\u65e0\u5173<\/span><\/p><p><span>\u91cd\u53e0\u5b50\u95ee\u9898\uff1a\u6709\u4e9b\u5b50\u95ee\u9898\u4e0d\u6b62\u88ab\u6c42\u89e3\u4e00\u6b21<\/span><\/p><p><strong><span>1\u3001\u591a\u6bb5\u56fe\u89c4\u5212\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"8.894ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3829.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E36-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E36-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E36-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 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xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E52-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E52-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E52-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 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y=\"0\"><\/use><use xlink:href=\"#E52-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E52-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (n)<\/script><\/strong><\/p><p><span>\u9012\u5f52\u5f0f\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"27.677ex\" height=\"2.694ex\" viewBox=\"0 -806.1 11916.4 1160\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E41-MJMATHI-62\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 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x=\"8051\" y=\"0\"><\/use><use xlink:href=\"#E41-MJMAIN-2B\" x=\"8551\" y=\"0\"><\/use><g transform=\"translate(9551,0)\"><use xlink:href=\"#E41-MJMATHI-61\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E41-MJMATHI-6A\" x=\"748\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E41-MJMAIN-2C\" x=\"10471\" y=\"0\"><\/use><use xlink:href=\"#E41-MJMAIN-30\" x=\"10916\" y=\"0\"><\/use><use xlink:href=\"#E41-MJMAIN-7D\" x=\"11416\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">b[j] = max\\{b[j-1]+a_j,0\\}<\/script><\/p><p><strong><span>4\u3001\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.012ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3019 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E42-MJMATHI-4F\" d=\"M740 435Q740 320 676 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font-family=\"STIXGeneral, 'PingFang SC', serif\" stroke=\"none\" transform=\"scale(50.259) matrix(1 0 0 -1 0 0)\">\u6216<\/text><\/g><use xlink:href=\"#E45-MJMATHI-6A\" x=\"7318\" y=\"0\"><\/use><use xlink:href=\"#E45-MJMAIN-3D\" x=\"8007\" y=\"0\"><\/use><use xlink:href=\"#E45-MJMAIN-30\" x=\"9063\" y=\"0\"><\/use><use xlink:href=\"#E45-MJMAIN-29\" x=\"9563\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">c[i,j] = 0 (i = 0 \u6216 j = 0)<\/script><\/p><h4><a name=\"\u4e94\u8d2a\u5fc3\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u4e94\u3001\u8d2a\u5fc3\u7b97\u6cd5<\/span><\/h4><p><span>\u9002\u7528\u4e8e\u8d2a\u5fc3\u7b97\u6cd5\u7684\u95ee\u9898\u9700\u5177\u5907\u7684\u6027\u8d28\uff1a\u2460\u3001\u6700\u4f18\u5b50\u7ed3\u6784 \u2461\u3001\u8d2a\u5fc3\u9009\u62e9\u6027\u8d28<\/span><\/p><p><span>\u8d2a\u5fc3\u9009\u62e9\u6027\u8d28\uff1a\u76f4\u63a5\u4f5c\u51fa\u5728\u5f53\u524d\u95ee\u9898\u770b\u6765\u6700\u4f18\u7684\u89e3\uff0c\u4e0d\u8003\u8651\u5b50\u95ee\u9898\u7684\u89e3<\/span><\/p><p><span>\u4e0e\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\u7684\u6bd4\u8f83\uff1a<\/span><\/p><p><span>\u2460\u3001\u5728\u6bcf\u4e00\u6b65\u4e2d\uff0c\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\u5728\u5f97\u77e5\u5b50\u95ee\u9898\u7684\u89e3\u540e\u505a\u51fa\u9009\u62e9\uff0c\u800c\u8d2a\u5fc3\u7b97\u6cd5\u5148\u505a\u51fa\u5c40\u90e8\u6700\u4f18\u7684\u9009\u62e9\u800c\u4e0d\u8003\u8651\u5b50\u95ee\u9898\u7684\u89e3<\/span><\/p><p><span>\u2461\u3001\u52a8\u6001\u89c4\u5212\u81ea\u5e95\u5411\u4e0a\uff0c\u8d2a\u5fc3\u7b97\u6cd5\u81ea\u9876\u5411\u4e0b<\/span><\/p><p><span>\u2462\u3001\u52a8\u6001\u89c4\u5212\u6bd4\u8d2a\u5fc3\u7b97\u6cd5\u66f4\u590d\u6742\uff0c\u6548\u7387\u66f4\u4f4e<\/span><\/p><p><strong><span>0-1\u80cc\u5305\u95ee\u9898\u4e0d\u6ee1\u8db3\u8d2a\u5fc3\u9009\u62e9\u6027\u8d28\uff0c\u5c0f\u6570\u80cc\u5305\u95ee\u9898\u6ee1\u8db3<\/span><\/strong><\/p><p><strong><span>1\u3001\u5c0f\u6570\u80cc\u5305\u95ee\u9898\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.3ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4004 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E50-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6E\" d=\"M21 287Q22 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y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (nlogn)<\/script><\/strong><\/p><p><span>\u6309\u4ef7\u503c\u7387\u6700\u5927\u8d2a\u5fc3\uff0c\u4e3b\u8981\u8fd0\u884c\u65f6\u95f4\u6765\u81ea\u4ef7\u503c\u7387\u7684\u6392\u5e8f\uff0c\u82e5\u4e0d\u9700\u8981\u6392\u5e8f\uff0c\u5219\u8fd0\u884c\u65f6\u95f4\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E47-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 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stroke-width=\"0\" id=\"E47-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E47-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E47-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E47-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E47-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta (n )<\/script><\/p><p><strong><span>2\u3001\u6d3b\u52a8\u9009\u62e9\u95ee\u9898\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.3ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4004 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E50-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E50-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6C\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6F\" x=\"2050\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-67\" x=\"2535\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6E\" x=\"3015\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMAIN-29\" x=\"3615\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (nlogn)<\/script><\/strong><\/p><p><span>\u6309\u6d3b\u52a8\u7ed3\u675f\u65f6\u95f4\u8d2a\u5fc3\uff0c\u4e3b\u8981\u8fd0\u884c\u65f6\u95f4\u6765\u81ea\u6392\u5e8f\uff0c\u82e5\u4e0d\u9700\u8981\u6392\u5e8f\uff0c\u5219\u8fd0\u884c\u65f6\u95f4\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E188-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E188-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(n)<\/script><\/p><p><strong><span>3\u3001\u6700\u4f18\u88c5\u8f7d\u95ee\u9898\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.3ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4004 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E50-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E50-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E50-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6C\" x=\"1752\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6F\" x=\"2050\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-67\" x=\"2535\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMATHI-6E\" x=\"3015\" y=\"0\"><\/use><use xlink:href=\"#E50-MJMAIN-29\" x=\"3615\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (nlogn)<\/script><\/strong><\/p><p><span>\u6309\u8d27\u7269\u91cd\u91cf\u8d2a\u5fc3\uff0c\u4e3b\u8981\u8fd0\u884c\u65f6\u95f4\u6765\u81ea\u6392\u5e8f\uff0c\u82e5\u4e0d\u9700\u8981\u6392\u5e8f\uff0c\u5219\u8fd0\u884c\u65f6\u95f4\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E188-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E188-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(n)<\/script><\/p><p><strong><span>4\u3001\u627e\u94b1\u95ee\u9898\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E52-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E52-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E52-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E52-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E52-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E52-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E52-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E52-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (n)<\/script><span> (n\u4e3a\u9762\u989d\u79cd\u7c7b)<\/span><\/strong><\/p><p><span>\u5148\u6309\u6700\u5927\u9762\u989d\u627e\uff0c\u4e0d\u80fd\u6ee1\u8db3\u518d\u6362\u5c0f\u4e00\u70b9\u7684\u9762\u989d\uff0c\u5982\u6b64\u5faa\u73af<\/span><\/p><h4><a name=\"\u516d\u56de\u6eaf\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u516d\u3001\u56de\u6eaf\u7b97\u6cd5<\/span><\/h4><p><span>\u56de\u6eaf\u6cd5\u662f\u4e00\u79cd\u6df1\u5ea6\u4f18\u5148\u7684\u5e26\u6709\u8df3\u8dc3\u6027\u7b97\u6cd5<\/span><\/p><p><span>\u9002\u7528\u4e8e\u6c42\u89e3\u7ec4\u5408\u6570\u8f83\u5927\u7684\u95ee\u9898<\/span><\/p><p><span>\u4f18\u5316\u65b9\u6cd5\uff1a<\/span><\/p><p><span>\u2460\u3001\u7528\u7ea6\u675f\u51fd\u6570\u526a\u53bb\u4e0d\u6ee1\u8db3\u7ea6\u675f\u7684\u5b50\u6811<\/span><\/p><p><span>\u2461\u3001\u7528\u9650\u754c\u51fd\u6570\u526a\u53bb\u4e0d\u80fd\u5f97\u5230\u6700\u4f18\u89e3\u7684\u5b50\u6811<\/span><\/p><p><strong><span>\u5b50\u96c6\u6811\u6846\u67b6\uff1a(\u53ef\u4ee5\u9009\u62e9\u67d0\u4e00\u4e2a\u503c\u53d6\u6216\u8005\u4e0d\u53d6)<\/span><\/strong><\/p><p><span>\u5faa\u73af\uff1a<\/span><\/p><p><span>\u8bd5\u63a2\u5f53\u524d\u5c42\u7684\u6240\u6709\u53d6\u503c\uff0c\u68c0\u67e5\u662f\u5426\u5408\u6cd5\uff0c\u5408\u6cd5\u5373\u8fdb\u5165\u4e0b\u4e00\u5c42\u8bd5\u63a2<\/span><\/p><p><strong><span>\u6392\u5217\u6811\u6846\u67b6\uff1a(\u6240\u6709\u503c\u5fc5\u987b\u53d6\uff0c\u4e14\u53ea\u80fd\u53d6\u4e00\u6b21)<\/span><\/strong><\/p><p><span>\u5faa\u73af\uff1a<\/span><\/p><p><span>\u4ea4\u6362\u5f53\u524d\u5c42\u7684\u503c\u4e0e\u5176\u5b83\u5c42\u7684\u503c\uff0c\u68c0\u67e5\u662f\u5426\u5408\u6cd5\uff0c\u5408\u6cd5\u8fdb\u5165\u4e0b\u4e00\u5c42\u8bd5\u63a2\uff0c\u6062\u590d\u4ea4\u6362<\/span><\/p><p><span>\u9700\u8981\u6709\u4e00\u4e2a\u521d\u59cb\u7684\u89e3<\/span><\/p><p><strong><span>1\u3001n\u7687\u540e\u95ee\u9898<\/span><\/strong><\/p><p><span>\u5b50\u96c6\u6811\u6846\u67b6<\/span><\/p><p><strong><span>2\u3001\u6392\u5217\u751f\u6210\u95ee\u9898<\/span><\/strong><\/p><p><span>\u6392\u5217\u6811\u6846\u67b6<\/span><\/p><p><strong><span>3\u3001TSP\u95ee\u9898<\/span><\/strong><\/p><p><span>\u6392\u5217\u6811\u6846\u67b6<\/span><\/p><p><strong><span>4\u30010-1\u80cc\u5305\u95ee\u9898<\/span><\/strong><\/p><p><span>\u5b50\u96c6\u6811\u6846\u67b6<\/span><\/p><h4><a name=\"\u4e03\u644a\u8fd8\u5206\u6790\" class=\"md-header-anchor\"><\/a><span>\u4e03\u3001\u644a\u8fd8\u5206\u6790<\/span><\/h4><p><span>\u5206\u6790\u4e00\u4e2an\u4e2a\u64cd\u4f5c\u7684\u5e8f\u5217\u7684\u5e73\u5747\u4ee3\u4ef7\uff0c\u5f97\u5230\u66f4\u52a0\u7d27\u786e\u7684\u65f6\u95f4\u4e0a\u754c(\u867d\u7136\u6709\u4e9b\u64cd\u4f5c\u4ee3\u4ef7\u5f88\u9ad8\uff0c\u4f46\u662f\u5927\u90e8\u5206\u64cd\u4f5c\u4ee3\u4ef7\u5f88\u4f4e\u7684\u60c5\u51b5\u5c24\u4e3a\u9002\u7528)<\/span><\/p><p><strong><span>1\u3001\u805a\u5408\u5206\u6790<\/span><\/strong><\/p><p><span>\u8ba1\u7b97\u6574\u4e2a\u64cd\u4f5c\u5e8f\u5217\u7684\u603b\u4ee3\u4ef7\uff0c\u9664\u4ee5n\uff0c\u5373<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.39ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3182 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E53-MJMATHI-54\" d=\"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z\"><\/path><path stroke-width=\"0\" id=\"E53-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E53-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E53-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E53-MJMAIN-2F\" d=\"M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E53-MJMATHI-54\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E53-MJMAIN-28\" x=\"704\" y=\"0\"><\/use><use xlink:href=\"#E53-MJMATHI-6E\" x=\"1093\" y=\"0\"><\/use><use xlink:href=\"#E53-MJMAIN-29\" x=\"1693\" y=\"0\"><\/use><use xlink:href=\"#E53-MJMAIN-2F\" x=\"2082\" y=\"0\"><\/use><use xlink:href=\"#E53-MJMATHI-6E\" x=\"2582\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">T(n)\/n<\/script><\/p><p><strong><span>2\u3001\u8bb0\u8d26\/\u6838\u7b97\u6cd5<\/span><\/strong><\/p><p><span>\u7ed9\u6bcf\u4e2a\u64cd\u4f5c\u8d4b\u4e88\u4e00\u4e2a\u4ee3\u4ef7<\/span><\/p><p><strong><span>3\u3001\u52bf\u80fd\u6cd5<\/span><\/strong><\/p><p><span>\u4e0d\u5c06\u9884\u4ed8\u4ee3\u4ef7\u8868\u793a\u4e3a\u4fe1\u7528\uff0c\u800c\u8868\u793a\u4e3a\u52bf\u80fd\uff0c\u901a\u8fc7\u52bf\u80fd\u7684\u91ca\u653e\u6765\u652f\u4ed8\u4ee3\u4ef7<\/span><\/p><p><span>\u52bf\u51fd\u6570\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.677ex\" height=\"1.877ex\" viewBox=\"0 -755.9 722 808.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.121ex;\"><defs><path stroke-width=\"0\" id=\"E54-MJMAIN-3A6\" d=\"M312 622Q310 623 307 625T303 629T297 631T286 634T270 635T246 636T211 637H184V683H196Q220 680 361 680T526 683H538V637H511Q468 637 447 635T422 631T411 622V533L425 531Q525 519 595 466T665 342Q665 301 642 267T583 209T506 172T425 152L411 150V61Q417 55 421 53T447 48T511 46H538V0H526Q502 3 361 3T196 0H184V46H211Q231 46 245 46T270 47T286 48T297 51T303 54T307 57T312 61V150H310Q309 151 289 153T232 166T160 195Q149 201 136 210T103 238T69 284T56 342Q56 414 128 467T294 530Q309 532 310 533H312V622ZM170 342Q170 207 307 188H312V495H309Q301 495 282 491T231 469T186 423Q170 389 170 342ZM415 188Q487 199 519 236T551 342Q551 384 539 414T507 459T470 481T434 491T415 495H410V188H415Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E54-MJMAIN-3A6\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Phi<\/script><span>(<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"16.182ex\" height=\"2.577ex\" viewBox=\"0 -806.1 6967.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E55-MJMAIN-3A6\" d=\"M312 622Q310 623 307 625T303 629T297 631T286 634T270 635T246 636T211 637H184V683H196Q220 680 361 680T526 683H538V637H511Q468 637 447 635T422 631T411 622V533L425 531Q525 519 595 466T665 342Q665 301 642 267T583 209T506 172T425 152L411 150V61Q417 55 421 53T447 48T511 46H538V0H526Q502 3 361 3T196 0H184V46H211Q231 46 245 46T270 47T286 48T297 51T303 54T307 57T312 61V150H310Q309 151 289 153T232 166T160 195Q149 201 136 210T103 238T69 284T56 342Q56 414 128 467T294 530Q309 532 310 533H312V622ZM170 342Q170 207 307 188H312V495H309Q301 495 282 491T231 469T186 423Q170 389 170 342ZM415 188Q487 199 519 236T551 342Q551 384 539 414T507 459T470 481T434 491T415 495H410V188H415Z\"><\/path><path stroke-width=\"0\" id=\"E55-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E55-MJMATHI-44\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><path stroke-width=\"0\" id=\"E55-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E55-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E55-MJMAIN-2265\" d=\"M83 616Q83 624 89 630T99 636Q107 636 253 568T543 431T687 361Q694 356 694 346T687 331Q685 329 395 192L107 56H101Q83 58 83 76Q83 77 83 79Q82 86 98 95Q117 105 248 167Q326 204 378 228L626 346L360 472Q291 505 200 548Q112 589 98 597T83 616ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"><\/path><path stroke-width=\"0\" id=\"E55-MJMAIN-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E55-MJMAIN-3A6\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E55-MJMAIN-28\" x=\"722\" y=\"0\"><\/use><g transform=\"translate(1111,0)\"><use xlink:href=\"#E55-MJMATHI-44\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E55-MJMATHI-6E\" x=\"1170\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E55-MJMAIN-29\" x=\"2463\" y=\"0\"><\/use><use xlink:href=\"#E55-MJMAIN-2265\" x=\"3130\" y=\"0\"><\/use><use xlink:href=\"#E55-MJMAIN-3A6\" x=\"4185\" y=\"0\"><\/use><use xlink:href=\"#E55-MJMAIN-28\" x=\"4907\" y=\"0\"><\/use><g transform=\"translate(5296,0)\"><use xlink:href=\"#E55-MJMATHI-44\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E55-MJMAIN-30\" x=\"1170\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E55-MJMAIN-29\" x=\"6578\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Phi(D_n) \\geq \\Phi(D_0)<\/script><span>)\uff0c\u6bcf\u4e2a\u64cd\u4f5c\u7684\u644a\u8fd8\u4ee3\u4ef7\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.29ex\" height=\"1.994ex\" viewBox=\"0 -755.9 555.6 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.028ex; margin-bottom: -0.21ex;\"><defs><path stroke-width=\"0\" id=\"E56-MJMATHI-63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><path stroke-width=\"0\" id=\"E56-MJMAIN-5E\" d=\"M112 560L249 694L257 686Q387 562 387 560L361 531Q359 532 303 581L250 627L195 580Q182 569 169 557T148 538L140 532Q138 530 125 546L112 560Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E56-MJMATHI-63\" x=\"33\" y=\"0\"><\/use><use xlink:href=\"#E56-MJMAIN-5E\" x=\"55\" y=\"-14\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\hat{c}<\/script><span>\uff0c\u5b9e\u9645\u4ee3\u4ef7\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.006ex\" height=\"1.41ex\" viewBox=\"0 -504.6 433 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E57-MJMATHI-63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E57-MJMATHI-63\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">c<\/script><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"27.15ex\" height=\"2.577ex\" viewBox=\"0 -806.1 11689.5 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E58-MJMATHI-63\" d=\"M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z\"><\/path><path stroke-width=\"0\" id=\"E58-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E58-MJMAIN-5E\" d=\"M112 560L249 694L257 686Q387 562 387 560L361 531Q359 532 303 581L250 627L195 580Q182 569 169 557T148 538L140 532Q138 530 125 546L112 560Z\"><\/path><path stroke-width=\"0\" id=\"E58-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path stroke-width=\"0\" id=\"E58-MJMATHI-69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E58-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path 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xlink:href=\"#E58-MJMAIN-29\" x=\"6502\" y=\"0\"><\/use><use xlink:href=\"#E58-MJMAIN-2212\" x=\"7113\" y=\"0\"><\/use><use xlink:href=\"#E58-MJMAIN-3A6\" x=\"8113\" y=\"0\"><\/use><use xlink:href=\"#E58-MJMAIN-28\" x=\"8835\" y=\"0\"><\/use><g transform=\"translate(9224,0)\"><use xlink:href=\"#E58-MJMATHI-44\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(828,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E58-MJMATHI-69\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E58-MJMAIN-2212\" x=\"345\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E58-MJMAIN-31\" x=\"1123\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E58-MJMAIN-29\" x=\"11300\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\hat{c_1} = c_i + \\Phi(D_i) - \\Phi(D_{i-1})<\/script><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"35.632ex\" height=\"2.811ex\" viewBox=\"0 -856.4 15341.5 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E59-MJSZ1-2211\" d=\"M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z\"><\/path><path stroke-width=\"0\" id=\"E59-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 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560Z\"><\/path><path stroke-width=\"0\" id=\"E59-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E59-MJMAIN-3A6\" d=\"M312 622Q310 623 307 625T303 629T297 631T286 634T270 635T246 636T211 637H184V683H196Q220 680 361 680T526 683H538V637H511Q468 637 447 635T422 631T411 622V533L425 531Q525 519 595 466T665 342Q665 301 642 267T583 209T506 172T425 152L411 150V61Q417 55 421 53T447 48T511 46H538V0H526Q502 3 361 3T196 0H184V46H211Q231 46 245 46T270 47T286 48T297 51T303 54T307 57T312 61V150H310Q309 151 289 153T232 166T160 195Q149 201 136 210T103 238T69 284T56 342Q56 414 128 467T294 530Q309 532 310 533H312V622ZM170 342Q170 207 307 188H312V495H309Q301 495 282 491T231 469T186 423Q170 389 170 342ZM415 188Q487 199 519 236T551 342Q551 384 539 414T507 459T470 481T434 491T415 495H410V188H415Z\"><\/path><path stroke-width=\"0\" 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transform=\"scale(0.707)\" xlink:href=\"#E59-MJMATHI-69\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMAIN-3D\" x=\"345\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMAIN-31\" x=\"1123\" y=\"0\"><\/use><\/g><g transform=\"translate(2470,0)\"><use xlink:href=\"#E59-MJMATHI-63\" x=\"33\" y=\"0\"><\/use><use xlink:href=\"#E59-MJMAIN-5E\" x=\"55\" y=\"-14\"><\/use><\/g><use xlink:href=\"#E59-MJMAIN-3D\" x=\"3303\" y=\"0\"><\/use><g transform=\"translate(4359,0)\"><use xlink:href=\"#E59-MJSZ1-2211\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMATHI-6E\" x=\"1493\" y=\"674\"><\/use><g transform=\"translate(1056,-286)\"><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMATHI-69\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMAIN-3D\" x=\"345\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMAIN-31\" x=\"1123\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E59-MJMATHI-63\" x=\"6829\" y=\"0\"><\/use><use xlink:href=\"#E59-MJMAIN-2B\" x=\"7484\" y=\"0\"><\/use><use xlink:href=\"#E59-MJMAIN-3A6\" x=\"8485\" y=\"0\"><\/use><use xlink:href=\"#E59-MJMAIN-28\" x=\"9207\" y=\"0\"><\/use><g transform=\"translate(9596,0)\"><use xlink:href=\"#E59-MJMATHI-44\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMATHI-6E\" x=\"1170\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E59-MJMAIN-29\" x=\"10948\" y=\"0\"><\/use><use xlink:href=\"#E59-MJMAIN-2212\" x=\"11559\" y=\"0\"><\/use><use xlink:href=\"#E59-MJMAIN-3A6\" x=\"12559\" y=\"0\"><\/use><use xlink:href=\"#E59-MJMAIN-28\" x=\"13281\" y=\"0\"><\/use><g transform=\"translate(13670,0)\"><use xlink:href=\"#E59-MJMATHI-44\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E59-MJMAIN-30\" x=\"1170\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E59-MJMAIN-29\" x=\"14952\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\sum ^n _{i=1} \\hat{c} = \\sum ^n _{i=1} c + \\Phi(D_n) - \\Phi(D_0)<\/script><\/p><h4><a name=\"\u516b\u56fe\u8bba\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u516b\u3001\u56fe\u8bba\u7b97\u6cd5<\/span><\/h4><p><strong><span>1\u3001BFS\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.979ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4296.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E60-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E60-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E60-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E60-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 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251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E60-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E60-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E60-MJMATHI-56\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E60-MJMAIN-2B\" x=\"2143\" y=\"0\"><\/use><use xlink:href=\"#E60-MJMATHI-45\" x=\"3143\" y=\"0\"><\/use><use xlink:href=\"#E60-MJMAIN-29\" x=\"3907\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O( V+E )<\/script><\/strong><\/p><p><span>\u9ed1\u8272\u7ed3\u70b9\uff1a\u5df2\u7ecf\u8bbf\u95ee\u8fc7\u7684\u7ed3\u70b9<\/span><\/p><p><span>\u7070\u8272\u7ed3\u70b9\uff1a\u8fd8\u6ca1\u8bbf\u95ee\u8fc7\u4f46\u662f\u5df2\u7ecf\u53d1\u73b0\u7684\u7ed3\u70b9<\/span><\/p><p><span>\u767d\u8272\u7ed3\u70b9\uff1a\u5c1a\u672a\u53d1\u73b0\u7684\u7ed3\u70b9<\/span><\/p><p><span>\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7531\u4e00\u5f00\u59cb\u7684\u7ed3\u70b9\u521d\u59cb\u5316\u548c\u540e\u9762\u7684\u5bf9\u8fb9\u7684\u626b\u63cf\u4ea7\u751f<\/span><\/p><p><span>\u524d\u9a71\u5b50\u56fe\u662f\u4e00\u68f5\u5e7f\u5ea6\u4f18\u5148\u6811<\/span><\/p><p><strong><span>2\u3001DFS\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.014ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4311.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E86-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E86-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMATHI-56\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMAIN-2B\" x=\"2158\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMATHI-45\" x=\"3158\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMAIN-29\" x=\"3922\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(V+E)<\/script><\/strong><\/p><p><span>\u4e24\u4e2a\u65f6\u95f4\u6233\uff1a<\/span><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"3.374ex\" height=\"1.994ex\" viewBox=\"0 -755.9 1452.7 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E62-MJMATHI-76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><path stroke-width=\"0\" id=\"E62-MJMAIN-2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><path stroke-width=\"0\" id=\"E62-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E62-MJMATHI-76\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E62-MJMAIN-2E\" x=\"485\" y=\"0\"><\/use><use xlink:href=\"#E62-MJMATHI-64\" x=\"929\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">v.d<\/script><span>\u8868\u793a\u88ab\u4fee\u6539\u4e3a\u7070\u8272\u7684\u65f6\u95f4<\/span><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"3.437ex\" height=\"2.577ex\" viewBox=\"0 -806.1 1479.7 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E63-MJMATHI-76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><path stroke-width=\"0\" id=\"E63-MJMAIN-2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><path stroke-width=\"0\" id=\"E63-MJMATHI-66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E63-MJMATHI-76\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E63-MJMAIN-2E\" x=\"485\" y=\"0\"><\/use><use xlink:href=\"#E63-MJMATHI-66\" x=\"929\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">v.f<\/script><span>\u8868\u793a\u88ab\u4fee\u6539\u4e3a\u9ed1\u8272\u7684\u65f6\u95f4<\/span><\/p><p><span>\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u7531\u4e00\u5f00\u59cb\u7684\u7ed3\u70b9\u521d\u59cb\u5316\u548c\u540e\u9762\u7684\u5bf9\u70b9\u7684\u626b\u63cf\u4ea7\u751f<\/span><\/p><p><span>\u524d\u9a71\u5b50\u56fe\u5f62\u6210\u4e00\u4e2a\u7531\u591a\u68f5\u6df1\u5ea6\u4f18\u5148\u6811\u6784\u6210\u7684\u6df1\u5ea6\u4f18\u5148\u68ee\u6797<\/span><\/p><p><span>\u5728\u6df1\u5ea6\u4f18\u5148\u68ee\u6797\u4e2d\uff0c<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.126ex\" height=\"1.41ex\" viewBox=\"0 -504.6 485 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E75-MJMATHI-76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E75-MJMATHI-76\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">v<\/script><span>\u662f<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.329ex\" height=\"1.41ex\" viewBox=\"0 -504.6 572 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E68-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E68-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">u<\/script><span>\u7684\u540e\u4ee3\u5f53\u4e14\u4ec5\u5f53\u5728\u53d1\u73b0\u7ed3\u70b9<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.329ex\" height=\"1.41ex\" viewBox=\"0 -504.6 572 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E68-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E68-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">u<\/script><span>\u7684\u65f6\u95f4<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"3.576ex\" height=\"1.994ex\" viewBox=\"0 -755.9 1539.7 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E67-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E67-MJMAIN-2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><path stroke-width=\"0\" id=\"E67-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E67-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E67-MJMAIN-2E\" x=\"572\" y=\"0\"><\/use><use xlink:href=\"#E67-MJMATHI-64\" x=\"1016\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">u.d<\/script><span>\uff0c\u5b58\u5728\u4e00\u6761\u4ece\u7ed3\u70b9<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.329ex\" height=\"1.41ex\" viewBox=\"0 -504.6 572 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E68-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E68-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">u<\/script><span>\u5230\u7ed3\u70b9<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.126ex\" height=\"1.41ex\" viewBox=\"0 -504.6 485 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E75-MJMATHI-76\" d=\"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E75-MJMATHI-76\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">v<\/script><span>\u7684\u5168\u90e8\u7531\u767d\u8272\u7ed3\u70b9\u6784\u6210\u7684\u8def\u5f84<\/span><\/p><p><span>\u8fb9\u7684\u5206\u7c7b\uff1a<\/span><\/p><p><span>\u6811\u8fb9\uff1a\u6df1\u5ea6\u4f18\u5148\u68ee\u6797\u91cc\u7684\u8fb9<\/span><\/p><p><span>\u540e\u5411\u8fb9\uff1a\u4ece\u4e00\u4e2a\u8282\u70b9\u8fde\u63a5\u5230\u5b83\u5728\u6df1\u5ea6\u4f18\u5148\u6811\u4e0a\u7684\u4e00\u4e2a\u7956\u5148\u7684\u8fb9<\/span><\/p><p><span>\u524d\u5411\u8fb9\uff1a\u4ece\u4e00\u4e2a\u8282\u70b9\u8fde\u63a5\u5230\u5b83\u5728\u6df1\u5ea6\u4f18\u5148\u6811\u4e0a\u7684\u4e00\u4e2a\u540e\u4ee3\u7684\u8fb9<\/span><\/p><p><span>\u6a2a\u5411\u8fb9\uff1a\u5176\u4ed6\u6240\u6709\u7684\u8fb9<\/span><\/p><p><span>\u7b2c\u4e00\u6b21\u63a2\u7d22<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.295ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2279.7 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E76-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E76-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 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width=\"5.295ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2279.7 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E76-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E76-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 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xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.295ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2279.7 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E76-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E76-MJMATHI-75\" d=\"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 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type=\"math\/tex\">(u,v)<\/script><span>\u4e3a\u524d\u5411\u8fb9\u6216\u6a2a\u5411\u8fb9<\/span><\/p><p><span>\u65e0\u5411\u56fe\u8fdb\u884c\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u65f6\uff0c\u6bcf\u6761\u8fb9\u8981\u4e48\u662f\u6811\u8fb9\uff0c\u8981\u4e48\u662f\u540e\u5411\u8fb9<\/span><\/p><p><strong><span>3\u3001\u6700\u5c0f\u751f\u6210\u6811\u7b97\u6cd5<\/span><\/strong><\/p><p><strong><span>\u2460\u3001Kruskal\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.073ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4337 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E78-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 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637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E78-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E78-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E78-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E78-MJMATHI-45\" x=\"1152\" y=\"0\"><\/use><use 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ElogV)<\/script><\/strong><\/p><p><span>\u5728\u8fde\u63a5\u96c6\u5408A\u4e2d\u7684\u70b9\u548c\u96c6\u5408A\u4ee5\u5916\u7684\u70b9\u7684\u8fb9\u4e2d\uff0c\u627e\u5230\u6743\u91cd\u6700\u5c0f\u7684\u8fb9<\/span><\/p><p><span>\u5728\u4f7f\u7528\u4e8c\u53c9\u5806\u4f5c\u4e3a\u4f18\u5148\u961f\u5217\u7684\u5b9e\u73b0\u65b9\u5f0f\u65f6\uff1a<\/span><\/p><p><span>EXTRACT-MIN\u603b\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.085ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4342 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E79-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 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xlink:href=\"#E80-MJMATHI-79\" x=\"1916\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">v.key<\/script><span>\u4e4b\u540e\u7ef4\u62a4\u4f18\u5148\u961f\u5217\u603b\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.073ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4337 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E81-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E81-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 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stroke-width=\"0\" id=\"E81-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E81-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E81-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E81-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E81-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E81-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E81-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E81-MJMATHI-45\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E81-MJMATHI-6C\" x=\"1916\" y=\"0\"><\/use><use xlink:href=\"#E81-MJMATHI-6F\" x=\"2214\" y=\"0\"><\/use><use xlink:href=\"#E81-MJMATHI-67\" x=\"2699\" y=\"0\"><\/use><use xlink:href=\"#E81-MJMATHI-56\" x=\"3179\" y=\"0\"><\/use><use xlink:href=\"#E81-MJMAIN-29\" x=\"3948\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(ElogV)<\/script><\/p><p><span>\u521d\u59cb\u5316\u7ed3\u70b9\u603b\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.365ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2310 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E82-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E82-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E82-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E82-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E82-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E82-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E82-MJMATHI-56\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E82-MJMAIN-29\" x=\"1921\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(V)<\/script><\/p><p><span>\u4e09\u8005\u76f8\u52a0\u5373\u662f\u603b\u65f6\u95f4<\/span><\/p><p><span>\u82e5\u7528Fibonacci\u5806\u4f5c\u4e3a\u6709\u9650\u961f\u5217\u7684\u5b9e\u73b0\u65b9\u5f0f\uff0c\u5219\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"14.698ex\" height=\"2.577ex\" viewBox=\"0 -806.1 6328.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E83-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E83-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E83-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMATHI-45\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMAIN-2B\" x=\"2138\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMATHI-56\" x=\"3138\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMATHI-6C\" x=\"3907\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMATHI-6F\" x=\"4205\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMATHI-67\" x=\"4690\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMATHI-56\" x=\"5170\" y=\"0\"><\/use><use xlink:href=\"#E83-MJMAIN-29\" x=\"5939\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(E + VlogV)<\/script><\/p><p><strong><span>Kruskal\u7b97\u6cd5\u9002\u7528\u4e8e\u8fb9\u6570\u4e0d\u591a\u7684\u7a00\u758f\u56fe\uff0cPrim\u7b97\u6cd5\u9002\u7528\u4e8e\u8fb9\u6570\u5f88\u591a\u7684\u7a20\u5bc6\u56fe<\/span><\/strong><\/p><p><strong><span>3\u3001\u5355\u6e90\u6700\u77ed\u8def\u5f84\u7b97\u6cd5<\/span><\/strong><\/p><p><strong><span>\u2460\u3001Bellman-Ford\u7b97\u6cd5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.14ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3074 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E84-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E84-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E84-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E84-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path stroke-width=\"0\" id=\"E84-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E84-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E84-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E84-MJMATHI-56\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E84-MJMATHI-45\" x=\"1921\" y=\"0\"><\/use><use xlink:href=\"#E84-MJMAIN-29\" x=\"2685\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(VE)<\/script><\/strong><\/p><p><span>\u628a\u6bcf\u4e00\u6761\u8fb9\u677e\u5f1b<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.078ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3047.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E85-MJMAIN-7C\" d=\"M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z\"><\/path><path stroke-width=\"0\" id=\"E85-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E85-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E85-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E85-MJMAIN-7C\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E85-MJMATHI-56\" x=\"278\" y=\"0\"><\/use><use xlink:href=\"#E85-MJMAIN-7C\" x=\"1047\" y=\"0\"><\/use><use xlink:href=\"#E85-MJMAIN-2212\" x=\"1547\" y=\"0\"><\/use><use xlink:href=\"#E85-MJMAIN-31\" x=\"2547\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">|V|-1<\/script><span>\u6b21<\/span><\/p><p><span>\u5141\u8bb8\u73af\u7684\u5b58\u5728\uff0c\u5b58\u5728\u6709\u8d1f\u503c\u7684\u56de\u8def\u65f6\u4f1a\u8fd4\u56deFALSE<\/span><\/p><p><strong><span>\u2461\u3001DAG\u7b97\u6cd5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.014ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4311.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E86-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMAIN-2B\" d=\"M56 237T56 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213Z\"><\/path><path stroke-width=\"0\" id=\"E86-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E86-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMATHI-56\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMAIN-2B\" x=\"2158\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMATHI-45\" x=\"3158\" y=\"0\"><\/use><use xlink:href=\"#E86-MJMAIN-29\" x=\"3922\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(V+E)<\/script><\/strong><\/p><p><span>\u5c06\u7ed3\u70b9\u62d3\u6251\u6392\u5e8f\uff0c\u6309\u62d3\u6251\u5e8f\u677e\u5f1b\u7ed3\u70b9<\/span><\/p><p><span>\u7b97\u6cd5\u65f6\u95f4\u590d\u6742\u5ea6\u4e3b\u8981\u6765\u81ea\u4e8e\u62d3\u6251\u6392\u5e8f\u548cfor\u5faa\u73af<\/span><\/p><p><span>\u62d3\u6251\u6392\u5e8f\uff1a\u4f7f\u7528\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff0c\u5c06\u7ed3\u70b9\u6309\u5b8c\u6210\u65f6\u95f4\u4ece\u5927\u5230\u5c0f\u6392\u5e8f<\/span><\/p><p><span>\u5141\u8bb8\u8d1f\u6743\u503c\u7684\u8fb9\u5b58\u5728\uff0c\u4f46\u662f\u4e0d\u5141\u8bb8\u8d1f\u503c\u56de\u8def<\/span><\/p><p><strong><span>\u2462\u3001Dijkstra\u7b97\u6cd5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.073ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4337 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E87-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E87-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E87-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path stroke-width=\"0\" id=\"E87-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E87-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E87-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E87-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E87-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E87-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E87-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E87-MJMATHI-45\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E87-MJMATHI-6C\" x=\"1916\" y=\"0\"><\/use><use xlink:href=\"#E87-MJMATHI-6F\" x=\"2214\" y=\"0\"><\/use><use xlink:href=\"#E87-MJMATHI-67\" x=\"2699\" y=\"0\"><\/use><use xlink:href=\"#E87-MJMATHI-56\" x=\"3179\" y=\"0\"><\/use><use xlink:href=\"#E87-MJMAIN-29\" x=\"3948\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O (ElogV) <\/script><\/strong><\/p><p><span>\u4f7f\u7528\u6700\u5c0f\u4f18\u5148\u961f\u5217\uff0c\u4e00\u5f00\u59cb\u5c06\u6240\u6709\u8282\u70b9\u52a0\u5165\u6700\u5c0f\u4f18\u5148\u961f\u5217\uff0c\u6bcf\u6b21\u53d6\u51fa\u6700\u5c0f\u7684\u7ed3\u70b9\uff0c\u677e\u5f1b\u8fd9\u4e00\u8282\u70b9\u76f8\u90bb\u7684\u7ed3\u70b9\uff0c\u76f4\u5230\u4f18\u5148\u961f\u5217\u4e3a\u7a7a<\/span><\/p><p><span>EXTRACT-MIN\u603b\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.085ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4342 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E88-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E88-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E88-MJMATHI-56\" d=\"M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z\"><\/path><path stroke-width=\"0\" id=\"E88-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E88-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E88-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E88-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E88-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E88-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E88-MJMATHI-56\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E88-MJMATHI-6C\" x=\"1921\" y=\"0\"><\/use><use xlink:href=\"#E88-MJMATHI-6F\" x=\"2219\" y=\"0\"><\/use><use xlink:href=\"#E88-MJMATHI-67\" x=\"2704\" y=\"0\"><\/use><use xlink:href=\"#E88-MJMATHI-56\" x=\"3184\" y=\"0\"><\/use><use xlink:href=\"#E88-MJMAIN-29\" x=\"3953\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(VlogV )<\/script><\/p><p><span>RELAX\u603b\u65f6\u95f4(\u52a0\u4e0a\u7ef4\u62a4\u4f18\u5148\u961f\u5217)\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.073ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4337 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E89-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E89-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E89-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 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xlink:href=\"#E89-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E89-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E89-MJMATHI-45\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E89-MJMATHI-6C\" x=\"1916\" y=\"0\"><\/use><use xlink:href=\"#E89-MJMATHI-6F\" x=\"2214\" y=\"0\"><\/use><use xlink:href=\"#E89-MJMATHI-67\" x=\"2699\" y=\"0\"><\/use><use xlink:href=\"#E89-MJMATHI-56\" x=\"3179\" y=\"0\"><\/use><use xlink:href=\"#E89-MJMAIN-29\" x=\"3948\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(Elog V)<\/script><\/p><p><span>\u82e5\u4f7f\u7528Fibonacci\u5806\u4f5c\u4e3a\u6700\u5c0f\u4f18\u5148\u961f\u5217\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"14.698ex\" height=\"2.577ex\" viewBox=\"0 -806.1 6328.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path 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119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E90-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMATHI-56\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMATHI-6C\" x=\"1921\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMATHI-6F\" x=\"2219\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMATHI-67\" x=\"2704\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMATHI-56\" x=\"3184\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMAIN-2B\" x=\"4175\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMATHI-45\" x=\"5175\" y=\"0\"><\/use><use xlink:href=\"#E90-MJMAIN-29\" x=\"5939\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(VlogV+E)<\/script><\/p><p><span>\u8be5\u7b97\u6cd5\u89e3\u51b3\u6709\u5411\u65e0\u73af\u56fe\u7684\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff0c\u8981\u6c42\u6743\u91cd\u4e3a\u975e\u8d1f\u503c<\/span><\/p><p><strong><span>4\u3001\u6240\u6709\u7ed3\u70b9\u5bf9\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5<\/span><\/strong><\/p><p><strong><span>\u2460\u3001\u77e9\u9635\u7b97\u6cd5\uff1a<\/span><\/strong><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"3.644ex\" height=\"3.745ex\" viewBox=\"0 -1107.7 1569 1612.3\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.172ex;\"><defs><path stroke-width=\"0\" id=\"E91-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 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style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E209-MJMATHI-69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E209-MJMATHI-69\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">i<\/script><span>\u5230\u7ed3\u70b9<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"0.985ex\" height=\"2.461ex\" viewBox=\"-12 -755.9 424 1059.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex; margin-left: -0.028ex;\"><defs><path stroke-width=\"0\" id=\"E93-MJMATHI-6A\" d=\"M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E93-MJMATHI-6A\" x=\"0\" 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57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E98-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><path stroke-width=\"0\" id=\"E98-MJMAIN-2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><path stroke-width=\"0\" id=\"E98-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E98-MJMATHI-4C\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E98-MJMAIN-31\" x=\"963\" y=\"-213\"><\/use><use xlink:href=\"#E98-MJMAIN-2C\" x=\"1134\" y=\"0\"><\/use><use xlink:href=\"#E98-MJMAIN-2E\" x=\"1579\" y=\"0\"><\/use><use xlink:href=\"#E98-MJMAIN-2E\" x=\"2023\" y=\"0\"><\/use><use xlink:href=\"#E98-MJMAIN-2E\" x=\"2468\" y=\"0\"><\/use><use xlink:href=\"#E98-MJMAIN-2C\" x=\"2913\" y=\"0\"><\/use><g transform=\"translate(3357,0)\"><use xlink:href=\"#E98-MJMATHI-4C\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E98-MJMATHI-6E\" x=\"963\" y=\"-213\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">L_1,...,L_n<\/script><span>)\u603b\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"6.026ex\" height=\"2.811ex\" viewBox=\"0 -906.7 2594.6 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E99-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E99-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E99-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 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-249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E99-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E99-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><g transform=\"translate(1152,0)\"><use xlink:href=\"#E99-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E99-MJMAIN-34\" x=\"848\" y=\"513\"><\/use><\/g><use xlink:href=\"#E99-MJMAIN-29\" x=\"2205\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n^4)<\/script><\/p><p><span>\u6539\u8fdb\u7b97\u6cd5(\u8ba1\u7b97<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"17.934ex\" height=\"2.344ex\" viewBox=\"0 -755.9 7721.6 1009.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.588ex;\"><defs><path stroke-width=\"0\" id=\"E100-MJMATHI-4C\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 217 683Q271 680 344 680Q485 680 506 683H518Q524 677 524 674T522 656Q517 641 513 637H475Q406 636 394 628Q387 624 380 600T313 336Q297 271 279 198T252 88L243 52Q243 48 252 48T311 46H328Q360 46 379 47T428 54T478 72T522 106T564 161Q580 191 594 228T611 270Q616 273 628 273H641Q647 264 647 262T627 203T583 83T557 9Q555 4 553 3T537 0T494 -1Q483 -1 418 -1T294 0H116Q32 0 32 10Q32 17 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><path stroke-width=\"0\" id=\"E100-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" 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x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E100-MJMAIN-31\" x=\"963\" y=\"-213\"><\/use><use xlink:href=\"#E100-MJMAIN-2C\" x=\"1134\" y=\"0\"><\/use><g transform=\"translate(1579,0)\"><use xlink:href=\"#E100-MJMATHI-4C\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E100-MJMAIN-32\" x=\"963\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E100-MJMAIN-2C\" x=\"2713\" y=\"0\"><\/use><g transform=\"translate(3158,0)\"><use xlink:href=\"#E100-MJMATHI-4C\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E100-MJMAIN-34\" x=\"963\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E100-MJMAIN-2C\" x=\"4292\" y=\"0\"><\/use><use xlink:href=\"#E100-MJMAIN-2E\" x=\"4737\" y=\"0\"><\/use><use xlink:href=\"#E100-MJMAIN-2E\" x=\"5182\" y=\"0\"><\/use><use xlink:href=\"#E100-MJMAIN-2E\" x=\"5626\" y=\"0\"><\/use><use xlink:href=\"#E100-MJMAIN-2C\" x=\"6071\" y=\"0\"><\/use><g transform=\"translate(6516,0)\"><use xlink:href=\"#E100-MJMATHI-4C\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E100-MJMATHI-6E\" x=\"963\" y=\"-213\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">L_1,L_2,L_4,...,L_n<\/script><span>)\u603b\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.353ex\" height=\"2.811ex\" viewBox=\"0 -906.7 4457.6 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E101-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E101-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 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xlink:href=\"#E101-MJMATHI-6E\" x=\"3468\" y=\"0\"><\/use><use xlink:href=\"#E101-MJMAIN-29\" x=\"4068\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n^3logn)<\/script><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"25.477ex\" height=\"3.745ex\" viewBox=\"0 -1107.7 10969.4 1612.3\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.172ex;\"><defs><path stroke-width=\"0\" id=\"E102-MJMATHI-3B4\" d=\"M195 609Q195 656 227 686T302 717Q319 716 351 709T407 697T433 690Q451 682 451 662Q451 644 438 628T403 612Q382 612 348 641T288 671T249 657T235 628Q235 584 334 463Q401 379 401 292Q401 169 340 80T205 -10H198Q127 -10 83 36T36 153Q36 286 151 382Q191 413 252 434Q252 435 245 449T230 481T214 521T201 566T195 609ZM112 130Q112 83 136 55T204 27Q233 27 256 51T291 111T309 178T316 232Q316 267 309 298T295 344T269 400L259 396Q215 381 183 342T137 256T118 179T112 130Z\"><\/path><path stroke-width=\"0\" id=\"E102-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E102-MJMATHI-69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E102-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 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182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z\"><\/path><path stroke-width=\"0\" id=\"E151-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E151-MJMATHI-4D\" d=\"M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 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364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E151-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E151-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><path stroke-width=\"0\" id=\"E151-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E151-MJMATHI-50\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E151-MJMAIN-28\" x=\"751\" y=\"0\"><\/use><use xlink:href=\"#E151-MJMATHI-4D\" x=\"1140\" y=\"0\"><\/use><use xlink:href=\"#E151-MJMAIN-29\" x=\"2191\" y=\"0\"><\/use><use xlink:href=\"#E151-MJMAIN-3D\" x=\"2857\" y=\"0\"><\/use><g transform=\"translate(3913,0)\"><use xlink:href=\"#E151-MJMATHI-4D\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E151-MJMATHI-65\" x=\"1520\" y=\"513\"><\/use><\/g><use xlink:href=\"#E151-MJMATHI-6D\" x=\"5418\" y=\"0\"><\/use><use xlink:href=\"#E151-MJMATHI-6F\" x=\"6296\" y=\"0\"><\/use><use xlink:href=\"#E151-MJMATHI-64\" x=\"6781\" y=\"0\"><\/use><use xlink:href=\"#E151-MJMATHI-6E\" x=\"7304\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">P(M)=M^e mod n<\/script><\/p><p><span>\u89e3\u5bc6\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"16.829ex\" height=\"2.811ex\" viewBox=\"0 -906.7 7245.9 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E152-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 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193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E152-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E152-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 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xlink:href=\"#E152-MJMATHI-6D\" x=\"4759\" y=\"0\"><\/use><use xlink:href=\"#E152-MJMATHI-6F\" x=\"5637\" y=\"0\"><\/use><use xlink:href=\"#E152-MJMATHI-64\" x=\"6122\" y=\"0\"><\/use><use xlink:href=\"#E152-MJMATHI-6E\" x=\"6645\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">S(C) = C^d mod n<\/script><\/p><p><span>\u77e5\u9053<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"2.297ex\" height=\"1.994ex\" viewBox=\"0 -755.9 989 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E153-MJMATHI-65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 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xlink:href=\"#E153-MJMATHI-64\" x=\"466\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">ed<\/script><span>\u4e4b\u540e\u7834\u89e3<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 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y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E162-MJMATHI-6C\" x=\"1100\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E162-MJMATHI-6E\" x=\"1398\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E162-MJMATHI-6E\" x=\"1998\" y=\"0\"><\/use><\/g><\/g><\/g><use xlink:href=\"#E162-MJMAIN-3D\" x=\"6327\" y=\"0\"><\/use><use xlink:href=\"#E162-MJMAIN-31\" x=\"7383\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">lim _{n->\\infty} \\frac{\\pi(n)}{n\/lnn} = 1<\/script><\/p><p><span>\u2460\u3001\u7b80\u5355\u7d20\u6570\u6d4b\u8bd5\u65b9\u6cd5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"6.942ex\" height=\"2.811ex\" viewBox=\"0 -856.4 2989 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E163-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E163-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E163-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E163-MJMAIN-221A\" d=\"M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z\"><\/path><path stroke-width=\"0\" id=\"E163-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E163-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E163-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><g transform=\"translate(1167,0)\"><use xlink:href=\"#E163-MJMAIN-221A\" x=\"0\" y=\"-62\"><\/use><rect stroke=\"none\" width=\"600\" height=\"60\" x=\"833\" y=\"678\"><\/rect><use xlink:href=\"#E163-MJMATHI-6E\" x=\"833\" y=\"0\"><\/use><\/g><use xlink:href=\"#E163-MJMAIN-29\" x=\"2600\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(\\sqrt{n})<\/script><\/p><p><span>\u82e5<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E217-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">n<\/script><span>\u88ab<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"13.91ex\" height=\"2.811ex\" viewBox=\"0 -856.4 5989 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E165-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E165-MJMAIN-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><path stroke-width=\"0\" id=\"E165-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 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id=\"E165-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E165-MJMAIN-221A\" d=\"M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 178Z\"><\/path><path stroke-width=\"0\" id=\"E165-MJMAIN-230B\" d=\"M229 734Q229 735 230 737T232 740T235 744T239 747T244 749T251 750Q262 748 269 735V-235Q266 -240 256 -249L147 -250H77Q43 -250 32 -247T21 -230T32 -213T72 -209Q79 -209 99 -209T133 -210H229V734Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E165-MJMAIN-32\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-2C\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-33\" x=\"944\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-2C\" x=\"1444\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-2E\" x=\"1889\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-2E\" x=\"2333\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-2E\" x=\"2778\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-2C\" x=\"3223\" y=\"0\"><\/use><use xlink:href=\"#E165-MJMAIN-230A\" x=\"3667\" y=\"0\"><\/use><g transform=\"translate(4111,0)\"><use xlink:href=\"#E165-MJMAIN-221A\" x=\"0\" y=\"-62\"><\/use><rect stroke=\"none\" width=\"600\" height=\"60\" x=\"833\" y=\"678\"><\/rect><use xlink:href=\"#E165-MJMATHI-6E\" x=\"833\" y=\"0\"><\/use><\/g><use xlink:href=\"#E165-MJMAIN-230B\" x=\"5544\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">2,3,...,\\lfloor \\sqrt{n} \\rfloor<\/script><span>\u4e2d\u7684\u67d0\u4e2a\u6570\u6574\u9664\uff0c\u5219<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E217-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">n<\/script><span>\u4e0d\u662f\u7d20\u6570<\/span><\/p><p><span>\u2461\u3001\u968f\u673a\u7b97\u6cd5\uff1a\u5728n\u9644\u8fd1\u83b7\u53d6\u4e00\u4e2a\u7d20\u6570\uff0c\u5927\u6982\u8981\u68c0\u67e5<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"3.479ex\" height=\"1.994ex\" viewBox=\"0 -755.9 1498 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E167-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E167-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E167-MJMATHI-6C\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E167-MJMATHI-6E\" x=\"298\" y=\"0\"><\/use><use xlink:href=\"#E167-MJMATHI-6E\" x=\"898\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">lnn<\/script><span>\u4e2a\u6570<\/span><\/p><p><span>\u7d20\u6570<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E217-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">n<\/script><span>\u5747\u6ee1\u8db3<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"16.385ex\" height=\"2.811ex\" viewBox=\"0 -906.7 7054.5 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path 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405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E169-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E169-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 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y=\"0\"><\/use><use xlink:href=\"#E169-MJMAIN-31\" x=\"3290\" y=\"0\"><\/use><use xlink:href=\"#E169-MJMAIN-28\" x=\"3790\" y=\"0\"><\/use><use xlink:href=\"#E169-MJMATHI-6D\" x=\"4179\" y=\"0\"><\/use><use xlink:href=\"#E169-MJMATHI-6F\" x=\"5057\" y=\"0\"><\/use><use xlink:href=\"#E169-MJMATHI-64\" x=\"5542\" y=\"0\"><\/use><use xlink:href=\"#E169-MJMATHI-6E\" x=\"6065\" y=\"0\"><\/use><use xlink:href=\"#E169-MJMAIN-29\" x=\"6665\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">a^{n-1} = 1(modn)<\/script><\/p><p><span>\u2462\u3001\u4f2a\u7d20\u6570\u6d4b\u8bd5\u7b97\u6cd5\uff1a\u6d4b\u8bd5\u4e00\u4e2a\u6570\u662f\u5426\u6ee1\u8db3\u4e0a\u5f0f\uff0c\u4e0d\u6ee1\u8db3\u5219\u4e00\u5b9a\u662f\u5408\u6570\uff0c\u6ee1\u8db3\u4e0d\u4e00\u5b9a\u662f\u7d20\u6570\uff0c\u53ef\u80fd\u662f\u4f2a\u7d20\u6570<\/span><\/p><p><span>\u2463\u3001Miller-Rabin\u968f\u673a\u6027\u7d20\u6570\u6d4b\u8bd5\u7b97\u6cd5\uff1a<\/span><\/p><p><span>\u5bf9\u4f2a\u7d20\u6570\u6d4b\u8bd5\u7b97\u6cd5\u7684\u6539\u8fdb\uff1a\u91c7\u7528\u591a\u4e2a(<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.089ex\" height=\"1.41ex\" viewBox=\"0 -504.6 469 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E170-MJMATHI-73\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E170-MJMATHI-73\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">s<\/script><span>\u4e2a)\u57fa<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.229ex\" height=\"1.41ex\" viewBox=\"0 -504.6 529 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E171-MJMATHI-61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E171-MJMATHI-61\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">a<\/script><span>\uff0c\u5728\u8ba1\u7b97<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.319ex\" height=\"2.344ex\" viewBox=\"0 -906.7 4442.9 1009.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E172-MJMATHI-61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><path stroke-width=\"0\" id=\"E172-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E172-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E172-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E172-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 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289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E172-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E172-MJMATHI-61\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(529,362)\"><use transform=\"scale(0.707)\" xlink:href=\"#E172-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E172-MJMAIN-2212\" x=\"600\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E172-MJMAIN-31\" x=\"1378\" y=\"0\"><\/use><\/g><use xlink:href=\"#E172-MJMATHI-6D\" x=\"1956\" y=\"0\"><\/use><use xlink:href=\"#E172-MJMATHI-6F\" x=\"2834\" y=\"0\"><\/use><use xlink:href=\"#E172-MJMATHI-64\" x=\"3319\" y=\"0\"><\/use><use xlink:href=\"#E172-MJMATHI-6E\" x=\"3842\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">a^{n-1} modn <\/script><span>\u7684\u8fc7\u7a0b\u4e2d\u662f\u5426\u5b58\u5728\u6a21<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E217-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">n<\/script><span>\u4f591\u7684\u975e\u5e73\u51e1\u5e73\u65b9\u6839<\/span><\/p><p><span>\u82e5<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E217-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">n<\/script><span>\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.331ex\" height=\"2.461ex\" viewBox=\"0 -806.1 573 1059.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.588ex;\"><defs><path stroke-width=\"0\" id=\"E175-MJMATHI-3B2\" d=\"M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E175-MJMATHI-3B2\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\beta<\/script><span>\u4f4d\u6570\uff0c\u7b97\u6cd5\u8fdb\u884c<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.999ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2583 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E176-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E176-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E176-MJMATHI-73\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"><\/path><path stroke-width=\"0\" id=\"E176-MJMATHI-3B2\" d=\"M29 -194Q23 -188 23 -186Q23 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stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E176-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E176-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E176-MJMATHI-73\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E176-MJMATHI-3B2\" x=\"1621\" y=\"0\"><\/use><use xlink:href=\"#E176-MJMAIN-29\" x=\"2194\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(s \\beta)<\/script><span>\u6b21\u7b97\u672f\u8fd0\u7b97\u548c<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.058ex\" height=\"2.811ex\" viewBox=\"0 -906.7 3038.7 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E177-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E177-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E177-MJMATHI-73\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"><\/path><path stroke-width=\"0\" id=\"E177-MJMATHI-3B2\" d=\"M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z\"><\/path><path stroke-width=\"0\" id=\"E177-MJMAIN-33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"><\/path><path stroke-width=\"0\" id=\"E177-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E177-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E177-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E177-MJMATHI-73\" x=\"1152\" y=\"0\"><\/use><g transform=\"translate(1621,0)\"><use xlink:href=\"#E177-MJMATHI-3B2\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E177-MJMAIN-33\" x=\"813\" y=\"513\"><\/use><\/g><use xlink:href=\"#E177-MJMAIN-29\" x=\"2649\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(s\\beta ^3)<\/script><span>\u6b21\u4f4d\u8fd0\u7b97<\/span><\/p><p><span>\u7b97\u6cd5\u8bef\u5224\u7387\u4e0d\u8d85\u8fc7<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"3.442ex\" height=\"2.227ex\" viewBox=\"0 -906.7 1481.8 958.9\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.121ex;\"><defs><path stroke-width=\"0\" id=\"E178-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E178-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E178-MJMATHI-73\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E178-MJMAIN-32\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(500,392)\"><use transform=\"scale(0.707)\" xlink:href=\"#E178-MJMAIN-2212\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E178-MJMATHI-73\" x=\"778\" y=\"0\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">2^{-s}<\/script><\/p><h4><a name=\"\u5341\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5\" class=\"md-header-anchor\"><\/a><span>\u5341\u3001\u5b57\u7b26\u4e32\u5339\u914d\u7b97\u6cd5<\/span><\/h4><p><strong><span>1\u3001\u6734\u7d20\u7b97\u6cd5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"17.698ex\" height=\"2.577ex\" viewBox=\"0 -806.1 7619.9 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E179-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E179-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E179-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E179-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E179-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E179-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E179-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E179-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 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y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O ((n-m+1)m)<\/script><\/strong><\/p><p><span>\u6700\u574f\u60c5\u51b5\u5728\u6a21\u5f0f\u4e32\u548c\u5f85\u6d4b\u4e32\u90fd\u662f\u540c\u4e00\u4e2a\u5143\u7d20\u7ec4\u6210\u7684\u65f6\u5019\u4ea7\u751f(\u6bcf\u4e00\u6b21\u5339\u914d\u90fd\u6210\u529f)<\/span><\/p><p><strong><span>2\u3001Rabin-Karp\u7b97\u6cd5<\/span><\/strong><\/p><p><span>\u5c06\u6a21\u5f0f\u4e32\u770b\u6210\u4e00\u4e2a\u6574\u6570\uff0c\u5f85\u6d4b\u4e32\u4e2d\u76f8\u540c\u4f4d\u6570\u7684\u4e32\u770b\u6210\u6574\u6570\uff0c\u6bd4\u8f83\u4e24\u4e2a\u6574\u6570\u7684\u6a21n\u7684\u503c<\/span><\/p><p><span>\u6574\u6570\u7684\u8ba1\u7b97\uff1a<\/span><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"47.083ex\" height=\"2.577ex\" viewBox=\"0 -806.1 20271.7 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path 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415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E180-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 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y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-5D\" x=\"9519\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-68\" x=\"9797\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-29\" x=\"10373\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-2B\" x=\"10984\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-54\" x=\"11984\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-5B\" x=\"12688\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-73\" x=\"12966\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-2B\" x=\"13658\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-6D\" x=\"14658\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-2B\" x=\"15758\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-31\" x=\"16758\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-5D\" x=\"17258\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMAIN-29\" x=\"17536\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-6D\" x=\"17925\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-6F\" x=\"18803\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-64\" x=\"19288\" y=\"0\"><\/use><use xlink:href=\"#E180-MJMATHI-71\" x=\"19811\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\"> t_{s+1} = (d(t_s - T[s+1]h) + T[s+m+1])modq<\/script><\/p><p><span>\u9884\u5904\u7406\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.653ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2434 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E181-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E181-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E181-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E181-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E181-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E181-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E181-MJMATHI-6D\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E181-MJMAIN-29\" x=\"2045\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta (m)<\/script><\/p><p><span>\u6700\u574f\u60c5\u51b5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"17.698ex\" height=\"2.577ex\" viewBox=\"0 -806.1 7619.9 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E182-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E182-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E182-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E182-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E182-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E182-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E182-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E182-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E182-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMAIN-28\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMATHI-6E\" x=\"1541\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMAIN-2212\" x=\"2363\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMATHI-6D\" x=\"3363\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMAIN-2B\" x=\"4463\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMAIN-31\" x=\"5463\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMAIN-29\" x=\"5963\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMATHI-6D\" x=\"6352\" y=\"0\"><\/use><use xlink:href=\"#E182-MJMAIN-29\" x=\"7230\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O((n-m+1)m)<\/script><\/p><p><span>\u5e73\u5747\u60c5\u51b5\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.851ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4241.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E183-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E183-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E183-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E183-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E183-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E183-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E183-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E183-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E183-MJMATHI-6D\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E183-MJMAIN-2B\" x=\"2252\" y=\"0\"><\/use><use xlink:href=\"#E183-MJMATHI-6E\" x=\"3252\" y=\"0\"><\/use><use xlink:href=\"#E183-MJMAIN-29\" x=\"3852\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(m+n)<\/script><\/p><p><strong><span>3\u3001\u6709\u9650\u81ea\u52a8\u673a<\/span><\/strong><\/p><p><span>\u9884\u5904\u7406\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"10.137ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4364.3 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E184-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E184-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E184-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E184-MJMAIN-7C\" d=\"M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z\"><\/path><path stroke-width=\"0\" id=\"E184-MJSZ1-2211\" d=\"M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z\"><\/path><path stroke-width=\"0\" id=\"E184-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E184-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E184-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E184-MJMATHI-6D\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E184-MJMAIN-7C\" x=\"2030\" y=\"0\"><\/use><use xlink:href=\"#E184-MJSZ1-2211\" x=\"2474\" y=\"0\"><\/use><use xlink:href=\"#E184-MJMAIN-7C\" x=\"3697\" y=\"0\"><\/use><use xlink:href=\"#E184-MJMAIN-29\" x=\"3975\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(m |\\sum|)<\/script><span> <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.518ex\" height=\"2.577ex\" viewBox=\"0 -806.1 1945.3 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E185-MJMAIN-7C\" d=\"M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z\"><\/path><path stroke-width=\"0\" id=\"E185-MJSZ1-2211\" d=\"M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E185-MJMAIN-7C\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E185-MJSZ1-2211\" x=\"444\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMAIN-7C\" x=\"1667\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">|\\sum|<\/script><span>\u4e3a\u4e00\u4e2a\u5143\u7d20\u53ef\u9009\u7684\u8f93\u5165\u603b\u6570<\/span><\/p><p><span>\u8fd0\u884c\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E186-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E186-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E186-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E186-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E186-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E186-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E186-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E186-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta( n)<\/script><\/p><p><strong><span>4\u3001KMP\u7b97\u6cd5<\/span><\/strong><\/p><p><span>\u9884\u5904\u7406\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.618ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2419 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E187-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E187-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E187-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E187-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E187-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E187-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E187-MJMATHI-6D\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E187-MJMAIN-29\" x=\"2030\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(m)<\/script><\/p><p><span>\u8fd0\u884c\u65f6\u95f4\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"5.008ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2156 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E188-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E188-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E188-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMATHI-6E\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E188-MJMAIN-29\" x=\"1767\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(n)<\/script><\/p><p><span>\u524d\u7f00\u51fd\u6570\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"3.691ex\" height=\"2.577ex\" viewBox=\"0 -806.1 1589 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E189-MJMATHI-3C0\" d=\"M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z\"><\/path><path stroke-width=\"0\" id=\"E189-MJMAIN-5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"><\/path><path stroke-width=\"0\" id=\"E189-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><path stroke-width=\"0\" id=\"E189-MJMAIN-5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E189-MJMATHI-3C0\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E189-MJMAIN-5B\" x=\"573\" y=\"0\"><\/use><use xlink:href=\"#E189-MJMATHI-71\" x=\"851\" y=\"0\"><\/use><use xlink:href=\"#E189-MJMAIN-5D\" x=\"1311\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\pi[q]<\/script><span>\u662f\u80fd\u6784\u6210<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"2.479ex\" height=\"2.577ex\" viewBox=\"0 -755.9 1067.3 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E190-MJMATHI-50\" d=\"M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z\"><\/path><path stroke-width=\"0\" id=\"E190-MJMATHI-71\" d=\"M33 157Q33 258 109 349T280 441Q340 441 372 389Q373 390 377 395T388 406T404 418Q438 442 450 442Q454 442 457 439T460 434Q460 425 391 149Q320 -135 320 -139Q320 -147 365 -148H390Q396 -156 396 -157T393 -175Q389 -188 383 -194H370Q339 -192 262 -192Q234 -192 211 -192T174 -192T157 -193Q143 -193 143 -185Q143 -182 145 -170Q149 -154 152 -151T172 -148Q220 -148 230 -141Q238 -136 258 -53T279 32Q279 33 272 29Q224 -10 172 -10Q117 -10 75 30T33 157ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E190-MJMATHI-50\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E190-MJMATHI-71\" x=\"907\" y=\"-213\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">P_q<\/script><span>\u771f\u540e\u7f00\u7684\u6700\u957f\u524d\u7f00\u957f\u5ea6<\/span><\/p><h4><a name=\"\u5341\u4e00\u4e3b\u5b9a\u7406\" class=\"md-header-anchor\"><\/a><span>\u5341\u4e00\u3001\u4e3b\u5b9a\u7406<\/span><\/h4><p><span>\u5bf9\u9012\u5f52\u5f0f<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"21.742ex\" height=\"3.044ex\" viewBox=\"0 -806.1 9361.3 1310.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.172ex;\"><defs><path stroke-width=\"0\" id=\"E191-MJMATHI-54\" d=\"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z\"><\/path><path stroke-width=\"0\" id=\"E191-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E191-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 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y=\"-340\"><\/use><\/g><use transform=\"scale(0.707)\" xlink:href=\"#E196-MJMATHI-61\" x=\"1663\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E196-MJMAIN-2B\" x=\"2192\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E196-MJMATHI-3F5\" x=\"2970\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E196-MJMAIN-29\" x=\"7459\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">f(n) = \\Omega(n^{log_ba + \\epsilon})<\/script><span> \u4e14<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"14.716ex\" height=\"3.044ex\" viewBox=\"0 -806.1 6335.8 1310.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.172ex;\"><defs><path stroke-width=\"0\" id=\"E197-MJMATHI-61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><path stroke-width=\"0\" id=\"E197-MJMATHI-66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 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transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"544\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E197-MJMATHI-6E\" x=\"84\" y=\"582\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E197-MJMATHI-62\" x=\"170\" y=\"-559\"><\/use><\/g><\/g><use xlink:href=\"#E197-MJMAIN-29\" x=\"2252\" y=\"0\"><\/use><use xlink:href=\"#E197-MJMAIN-2264\" x=\"2919\" y=\"0\"><\/use><use xlink:href=\"#E197-MJMATHI-63\" x=\"3974\" y=\"0\"><\/use><use xlink:href=\"#E197-MJMATHI-66\" x=\"4407\" y=\"0\"><\/use><use xlink:href=\"#E197-MJMAIN-28\" x=\"4957\" y=\"0\"><\/use><use xlink:href=\"#E197-MJMATHI-6E\" x=\"5346\" y=\"0\"><\/use><use xlink:href=\"#E197-MJMAIN-29\" x=\"5946\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">af(\\frac{n}{b}) \\leq cf(n)<\/script><span>(c < 1, n\u8db3\u591f\u5927)\uff0c\u5219<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"15.895ex\" height=\"2.577ex\" viewBox=\"0 -806.1 6843.6 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E198-MJMATHI-54\" d=\"M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z\"><\/path><path stroke-width=\"0\" id=\"E198-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 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y=\"0\"><\/use><use xlink:href=\"#E198-MJMAIN-3A9\" x=\"3415\" y=\"0\"><\/use><use xlink:href=\"#E198-MJMAIN-28\" x=\"4137\" y=\"0\"><\/use><use xlink:href=\"#E198-MJMATHI-66\" x=\"4526\" y=\"0\"><\/use><use xlink:href=\"#E198-MJMAIN-28\" x=\"5076\" y=\"0\"><\/use><use xlink:href=\"#E198-MJMATHI-6E\" x=\"5465\" y=\"0\"><\/use><use xlink:href=\"#E198-MJMAIN-29\" x=\"6065\" y=\"0\"><\/use><use xlink:href=\"#E198-MJMAIN-29\" x=\"6454\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">T(n) = \\Omega(f(n))<\/script><\/p><h3><a name=\"\u6570\u636e\u7ed3\u6784\" class=\"md-header-anchor\"><\/a><span>\u6570\u636e\u7ed3\u6784<\/span><\/h3><p><strong><span>1\u3001\u7ea2\u9ed1\u6811<\/span><\/strong><\/p><p><span>\u6027\u8d28\uff1a\u4e00\u68f5\u6709n\u4e2a\u5185\u90e8\u8282\u70b9\u7684\u7ea2\u9ed1\u6811\u7684\u9ad8\u5ea6\u81f3\u591a\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"11.296ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4863.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E199-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E199-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E199-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E199-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 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749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E199-MJMAIN-32\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMATHI-6C\" x=\"500\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMATHI-6F\" x=\"798\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMATHI-67\" x=\"1283\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMAIN-28\" x=\"1763\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMATHI-6E\" x=\"2152\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMAIN-2B\" x=\"2974\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMAIN-31\" x=\"3974\" y=\"0\"><\/use><use xlink:href=\"#E199-MJMAIN-29\" x=\"4474\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">2log(n+1)<\/script><\/p><p><span>LEFT-ROTATE\u3001RIGHT-ROTATE\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.74ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2041 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E200-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E200-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E200-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E200-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E200-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E200-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E200-MJMAIN-31\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E200-MJMAIN-29\" x=\"1652\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(1)<\/script><\/p><p><span>RB-INSERT\u3001RB-DELETE\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E201-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E201-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 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stroke-width=\"0\" id=\"E201-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E201-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E201-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(logn)<\/script><\/p><p><span>RB-INSERT\u7684\u4e09\u79cd\u8c03\u6574\u60c5\u51b5\uff1a<\/span><\/p><p><span>\u5f53z\u7684\u7236\u6bcd\u4e3a\u7ea2\u8272\u65f6\uff1a<\/span><\/p><p><span>\u2460\u3001z\u7684\u53d4\u8282\u70b9\u662f\u7ea2\u8272\u7684<\/span><\/p><p><span>z\u989c\u8272\u4e0d\u53d8\uff0cz\u7684\u7236\u6bcd\u548c\u53d4\u8282\u70b9\u5168\u90e8\u6539\u4e3a\u9ed1\u8272\uff0cz\u7684\u7236\u6bcd\u7684\u7236\u6bcd\u6539\u4e3a\u7ea2\u8272<\/span><\/p><p><span>z\u7f6e\u4e3az\u7684\u7236\u6bcd\u7684\u7236\u6bcd<\/span><\/p><p><span>\u2461\u3001z\u7684\u53d4\u8282\u70b9\u662f\u9ed1\u8272\u7684\u4e14z\u662f\u53f3\u5b69\u5b50<\/span><\/p><p><span>z\u53d8\u4e3az\u7684\u7236\u6bcd\uff0c\u5de6\u65cb\uff0c\u4f7fz\u53d8\u4e3a\u5de6\u5b69\u5b50\uff0c\u8f6c\u2462<\/span><\/p><p><span>\u2462\u3001z\u7684\u53d4\u8282\u70b9\u662f\u9ed1\u8272\u7684\u4e14z\u662f\u5de6\u5b69\u5b50<\/span><\/p><p><span>z\u7684\u7236\u6bcd\u7684\u7236\u6bcd\u53f3\u65cb\uff0c\u4e14\u989c\u8272\u6539\u4e3a\u7ea2\u8272\uff0cz\u7684\u7236\u6bcd\u6539\u4e3a\u9ed1\u8272<\/span><\/p><p><strong><span>\u4e00\u6b21\u5faa\u73af\u81f3\u591a2\u6b21\u65cb\u8f6c\uff0c\u2461->\u2462<\/span><\/strong><\/p><p><span>RB-DELETE:<\/span><\/p><p><span>\u5220\u9664z\u65f6\uff0c\u82e5z\u7684\u5b50\u8282\u70b9\u5c11\u4e8e2\u4e2a\uff0c\u5219\u5c06z\u5220\u9664\uff0cz\u7684\u5b50\u8282\u70b9\u8865\u4f4d\uff0c\u8865\u4f4d\u8282\u70b9\u989c\u8272\u4e0d\u6539\u53d8\uff0c\u82e5z\u539f\u6765\u662f\u9ed1\u8272\u7684\uff0c\u5219\u4ee5\u8865\u4f4d\u8282\u70b9\u4e3a\u53c2\u6570\u8fdb\u5165\u8c03\u6574<\/span><\/p><p><span>\u82e5z\u7684\u5b50\u8282\u70b9\u4e3a2\u4e2a\uff0c\u5219\u627e\u5230z\u7684\u53f3\u5b50\u6811\u4e2d\u7684\u6700\u5de6\u8282\u70b9\uff0c\u53d6\u51fa\u5b83\uff0c\u5904\u7406\u5b83\u7684\u5b50\u6811\u540e\u7528\u5b83\u8865\u4f4d\uff0c\u8865\u4f4d\u8282\u70b9\u989c\u8272\u4e0e\u539f\u8282\u70b9\u4e00\u81f4\uff0c\u82e5\u8865\u4f4d\u8282\u70b9\u539f\u6765\u662f\u9ed1\u8272\u7684\uff0c\u5219\u4ee5\u8865\u4f4d\u8282\u70b9\u539f\u53f3\u5b50\u6811\u7684\u6839\u4e3a\u53c2\u6570\u8fdb\u5165\u8c03\u6574<\/span><\/p><p><span>\u56db\u79cd\u8c03\u6574\u60c5\u51b5\uff1a<\/span><\/p><p><span>\u5f53x\u662f\u9ed1\u8272\u65f6\uff1a<\/span><\/p><p><span>\u2460\u3001x\u7684\u5144\u5f1f\u8282\u70b9\u662f\u7ea2\u8272\u7684<\/span><\/p><p><span>x\u7684\u5144\u5f1f\u8282\u70b9\u6539\u4e3a\u9ed1\u8272\uff0cx\u7684\u7236\u6bcd\u6539\u4e3a\u7ea2\u8272\u5e76\u5de6\u65cb<\/span><\/p><p><span>x\u4e0d\u52a8\uff0cx\u7684\u5144\u5f1f\u8282\u70b9\u53d1\u751f\u53d8\u5316\uff0c\u91cd\u65b0\u6c42x\u7684\u5144\u5f1f\u8282\u70b9\uff0c\u8f6c\u2461\u6216\u2462\u6216\u2463<\/span><\/p><p><span>\u2461\u3001x\u7684\u5144\u5f1f\u8282\u70b9\u662f\u9ed1\u8272\u7684\uff0c\u800c\u4e14x\u7684\u5144\u5f1f\u8282\u70b9\u7684\u5b50\u8282\u70b9\u90fd\u662f\u9ed1\u8272<\/span><\/p><p><span>\u5c06x\u7684\u5144\u5f1f\u8282\u70b9\u6539\u4e3a\u7ea2\u8272<\/span><\/p><p><span>x\u53d8\u4e3ax\u7684\u7236\u6bcd<\/span><\/p><p><span>\u2462\u3001x\u7684\u5144\u5f1f\u8282\u70b9\u662f\u9ed1\u8272\u7684\uff0c\u800c\u4e14x\u7684\u5144\u5f1f\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u662f\u7ea2\u8272\uff0c\u53f3\u5b69\u5b50\u662f\u9ed1\u8272<\/span><\/p><p><span>x\u7684\u5144\u5f1f\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u6539\u4e3a\u9ed1\u8272\uff0cx\u7684\u5144\u5f1f\u8282\u70b9\u6539\u4e3a\u7ea2\u8272\u5e76\u53f3\u65cb\uff0c\u8f6c\u2463<\/span><\/p><p><span>\u2463\u3001x\u7684\u5144\u5f1f\u8282\u70b9\u4e3a\u9ed1\u8272\uff0c\u800c\u4e14x\u7684\u5144\u5f1f\u8282\u70b9\u7684\u53f3\u5b69\u5b50\u4e3a\u7ea2\u8272<\/span><\/p><p><span>x\u7684\u7236\u6bcd\u6539\u4e3a\u9ed1\u8272\uff0cx\u7684\u5144\u5f1f\u8282\u70b9\u6539\u4e3a\u7ea2\u8272\uff0cx\u7684\u5144\u5f1f\u8282\u70b9\u7684\u53f3\u5b69\u5b50\u6539\u4e3a\u9ed1\u8272\uff0cx\u7684\u7236\u6bcd\u5de6\u65cb<\/span><\/p><p><span>x\u53d8\u4e3a\u6839<\/span><\/p><p><strong><span>x\u7684\u989c\u8272\u4e3a\u7ea2\u8272\u6216x\u4e3a\u6839\u8282\u70b9\u65f6\u9000\u51fa\u5faa\u73af\uff0cx\u7684\u989c\u8272\u8981\u6539\u4e3a\u9ed1\u8272<\/span><\/strong><\/p><p><strong><span>\u4e00\u6b21\u5faa\u73af\u81f3\u591a3\u6b21\u65cb\u8f6c\uff0c\u2460->\u2462->\u2463<\/span><\/strong><\/p><p><strong><span>2\u3001\u52a8\u6001\u987a\u5e8f\u7edf\u8ba1\u6811<\/span><\/strong><\/p><p><span>OS-SELECT\u3001OS-RANK\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E202-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E202-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E202-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E202-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E202-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E202-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E202-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E202-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(logn) <\/script><\/p><p><span>INSERT\u3001DELETE\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E204-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E204-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(logn )<\/script><\/p><p><strong><span>3\u3001\u533a\u95f4\u6811<\/span><\/strong><\/p><p><span>INTERVAL-SEARCH\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E204-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E204-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E204-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E204-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(logn )<\/script><\/p><p><strong><span>4\u3001\u4e8c\u9879\u6811<\/span><\/strong><\/p><p><span>\u4e8c\u9879\u6811<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"2.851ex\" height=\"2.344ex\" viewBox=\"0 -755.9 1227.4 1009.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.588ex;\"><defs><path stroke-width=\"0\" id=\"E205-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"><\/path><path stroke-width=\"0\" id=\"E205-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E205-MJMATHI-42\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E205-MJMATHI-6B\" x=\"1073\" y=\"-213\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">B_k<\/script><span>\u7531\u4e24\u68f5\u4e8c\u9879\u6811<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.95ex\" height=\"2.461ex\" viewBox=\"0 -755.9 2131.1 1059.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E206-MJMATHI-42\" d=\"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z\"><\/path><path stroke-width=\"0\" id=\"E206-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path stroke-width=\"0\" id=\"E206-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E206-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E206-MJMATHI-42\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(759,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E206-MJMATHI-6B\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E206-MJMAIN-2212\" x=\"521\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E206-MJMAIN-31\" x=\"1299\" y=\"0\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">B_{k-1}<\/script><span>\u6784\u6210\uff0c\u4e00\u68f5\u6811\u7684\u6839\u662f\u53e6\u4e00\u68f5\u6811\u7684\u6839\u7684\u6700\u5de6\u5b69\u5b50<\/span><\/p><p><span>\u6027\u8d28\uff1a<\/span><\/p><p><span>\u2460\u3001\u5171\u6709<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"2.249ex\" height=\"2.344ex\" viewBox=\"0 -956.9 968.4 1009.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.121ex;\"><defs><path stroke-width=\"0\" id=\"E207-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E207-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E207-MJMAIN-32\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E207-MJMATHI-6B\" x=\"707\" y=\"555\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">2^k<\/script><span>\u4e2a\u7ed3\u70b9<\/span><\/p><p><span>\u2461\u3001\u9ad8\u5ea6\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.21ex\" height=\"1.994ex\" viewBox=\"0 -755.9 521 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E216-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E216-MJMATHI-6B\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">k<\/script><\/p><p><span>\u2462\u3001\u5728\u6df1\u5ea6<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"0.801ex\" height=\"1.994ex\" viewBox=\"0 -755.9 345 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E209-MJMATHI-69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E209-MJMATHI-69\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">i<\/script><span>\u5904\u6070\u597d\u6709<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"2.749ex\" height=\"3.044ex\" viewBox=\"0 -906.7 1183.4 1310.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.938ex;\"><defs><path stroke-width=\"0\" id=\"E210-MJMATHI-43\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 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291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E210-MJMATHI-43\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E210-MJMATHI-69\" x=\"1093\" y=\"498\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E210-MJMATHI-6B\" x=\"1011\" y=\"-462\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">C ^i _k<\/script><span>\u4e2a\u7ed3\u70b9<\/span><\/p><p><span>\u2463\u3001\u6839\u7684\u5ea6\u6570\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.21ex\" height=\"1.994ex\" viewBox=\"0 -755.9 521 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E216-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E216-MJMATHI-6B\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">k<\/script><span>\uff0c\u5927\u4e8e\u5176\u4ed6\u4efb\u4f55\u7ed3\u70b9\u7684\u5ea6\u6570\uff0c\u6839\u7684\u5b69\u5b50\u4ece\u5de6\u5230\u53f3\u4f9d\u6b21\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"18.912ex\" height=\"2.461ex\" viewBox=\"0 -755.9 8142.7 1059.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E212-MJMATHI-42\" d=\"M231 637Q204 637 199 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402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path stroke-width=\"0\" id=\"E212-MJMAIN-2212\" d=\"M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z\"><\/path><path stroke-width=\"0\" id=\"E212-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E212-MJMAIN-2C\" d=\"M78 35T78 60T94 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x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E212-MJMAIN-2212\" x=\"521\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E212-MJMAIN-32\" x=\"1299\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E212-MJMAIN-2C\" x=\"4706\" y=\"0\"><\/use><use xlink:href=\"#E212-MJMAIN-2E\" x=\"5151\" y=\"0\"><\/use><use xlink:href=\"#E212-MJMAIN-2E\" x=\"5596\" y=\"0\"><\/use><use xlink:href=\"#E212-MJMAIN-2E\" x=\"6040\" y=\"0\"><\/use><use xlink:href=\"#E212-MJMAIN-2C\" x=\"6485\" y=\"0\"><\/use><g transform=\"translate(6930,0)\"><use xlink:href=\"#E212-MJMATHI-42\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E212-MJMAIN-30\" x=\"1073\" y=\"-213\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">B_{k-1},B_{k-2},...,B_0<\/script><span>\u7684\u6839<\/span><\/p><p><span>\u2464\u3001\u5728\u4e00\u68f5\u5305\u542b<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E217-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">n<\/script><span>\u4e2a\u7ed3\u70b9\u7684\u4e8c\u9879\u6811\u4e2d\uff0c\u4efb\u610f\u7ed3\u70b9\u7684\u6700\u5927\u5ea6\u6570\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.327ex\" height=\"2.461ex\" viewBox=\"0 -755.9 1863 1059.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E214-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 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y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">logn<\/script><\/p><p><strong><span>5\u3001\u4e8c\u9879\u5806<\/span><\/strong><\/p><p><span>\u4e8c\u9879\u5806\u7531\u6ee1\u8db3\u4e0b\u5217\u4e24\u6761\u6027\u8d28\u7684\u4e00\u7ec4\u4e8c\u9879\u6811\u6784\u6210\uff1a<\/span><\/p><p><span>\u2460\u3001\u6bcf\u4e2a\u4e8c\u9879\u6811\u6ee1\u8db3\u6700\u5c0f\u5806\u6027\u8d28\uff0c\u7ed3\u70b9\u7684\u5173\u952e\u5b57\u5927\u4e8e\u7b49\u4e8e\u7236\u6bcd\u7ed3\u70b9\u7684\u5173\u952e\u5b57<\/span><\/p><p><span>\u2461\u3001\u5bf9\u4e8e\u4efb\u610f\u975e\u8d1f\u6574\u6570<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.21ex\" height=\"1.994ex\" viewBox=\"0 -755.9 521 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E216-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E216-MJMATHI-6B\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">k<\/script><span>\uff0c\u5728\u4e8c\u9879\u5806\u4e2d\u6700\u591a\u6709\u4e00\u9897\u4e8c\u9879\u6811\u7684\u6839\u7ed3\u70b9\u7684\u5ea6\u6570\u4e3a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.21ex\" height=\"1.994ex\" viewBox=\"0 -755.9 521 858.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E216-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E216-MJMATHI-6B\" x=\"0\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">k<\/script><span>\uff0c\u6545\u5728\u4e00\u4e2a\u6709<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.394ex\" height=\"1.41ex\" viewBox=\"0 -504.6 600 607.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E217-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 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stroke-width=\"0\" id=\"E218-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E218-MJMAIN-230A\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMATHI-6C\" x=\"444\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMATHI-6F\" x=\"742\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMATHI-67\" x=\"1227\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMATHI-6E\" x=\"1707\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMAIN-230B\" x=\"2307\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMAIN-2B\" x=\"2973\" y=\"0\"><\/use><use xlink:href=\"#E218-MJMAIN-31\" x=\"3973\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\lfloor logn \\rfloor +1<\/script><span>\u68f5\u4e8c\u9879\u6811<\/span><\/p><p><span>INSERT\u3001MINIMUM\u3001UNION\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.811ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3363 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E219-MJMAIN-3A9\" d=\"M55 454Q55 503 75 546T127 617T197 665T272 695T337 704H352Q396 704 404 703Q527 687 596 615T666 454Q666 392 635 330T559 200T499 83V80H543Q589 81 600 83T617 93Q622 102 629 135T636 172L637 177H677V175L660 89Q645 3 644 2V0H552H488Q461 0 456 3T451 20Q451 89 499 235T548 455Q548 512 530 555T483 622T424 656T361 668Q332 668 303 658T243 626T193 560T174 456Q174 380 222 233T270 20Q270 7 263 0H77V2Q76 3 61 89L44 175V177H84L85 172Q85 171 88 155T96 119T104 93Q109 86 120 84T178 80H222V83Q206 132 162 199T87 329T55 454Z\"><\/path><path stroke-width=\"0\" 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179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E219-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E219-MJMAIN-3A9\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMAIN-28\" x=\"722\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMATHI-6C\" x=\"1111\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMATHI-6F\" x=\"1409\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMATHI-67\" x=\"1894\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMATHI-6E\" x=\"2374\" y=\"0\"><\/use><use xlink:href=\"#E219-MJMAIN-29\" x=\"2974\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Omega(logn)<\/script><\/p><p><span>EXTRACT-MIN\u3001DECREASE-KEY\u3001DELETE\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.941ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3419 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E220-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><path stroke-width=\"0\" id=\"E220-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E220-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" 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transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E220-MJMAIN-398\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMAIN-28\" x=\"778\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMATHI-6C\" x=\"1167\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMATHI-6F\" x=\"1465\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMATHI-67\" x=\"1950\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMATHI-6E\" x=\"2430\" y=\"0\"><\/use><use xlink:href=\"#E220-MJMAIN-29\" x=\"3030\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(logn)<\/script><\/p><p><span>\u4e0e\u4e8c\u53c9\u5806\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u540c\u7684\u64cd\u4f5c\u662fMINIMUM(\u4e8c\u53c9\u5806\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.74ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2041 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E221-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E221-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E221-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E221-MJMAIN-29\" d=\"M60 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-0.705ex;\"><defs><path stroke-width=\"0\" id=\"E224-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 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-250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E224-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(log n)<\/script><span>)\u3001UNION(\u4e8c\u53c9\u5806\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.973ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2141 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E223-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E223-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E223-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E223-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E223-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMATHI-6E\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E223-MJMAIN-29\" x=\"1752\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O( n )<\/script><span>\u4e8c\u9879\u5806\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"7.906ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3404 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E224-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E224-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E224-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-6C\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-6F\" x=\"1450\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-67\" x=\"1935\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMATHI-6E\" x=\"2415\" y=\"0\"><\/use><use xlink:href=\"#E224-MJMAIN-29\" x=\"3015\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(log n)<\/script><span>)<\/span><\/p><p><span>UNION\u64cd\u4f5c\u7684\u60c5\u51b5\uff1a<\/span><\/p><p><span>\u2460\u3001x\u548cnext-x\u6307\u5411\u7684\u4e24\u68f5\u4e8c\u9879\u6811\u5ea6\u6570\u4e0d\u4e00\u6837<\/span><\/p><p><span>\u4e0d\u9700\u8981\u8fde\u63a5\uff0c\u76f4\u63a5\u8df3\u8fc7<\/span><\/p><p><span>\u2461\u3001x\u548cnext-x\u6307\u5411\u7684\u4e24\u68f5\u4e8c\u9879\u6811\u5ea6\u6570\u4e00\u6837\uff0c\u4f46\u662fnext-x\u7684\u540e\u4e00\u68f5\u4e8c\u9879\u6811\u7684\u5ea6\u6570\u4e5f\u4e00\u6837<\/span><\/p><p><span>\u4e0d\u9700\u8981\u8fde\u63a5\u524d\u4e24\u68f5\u6811\uff0c\u8df3\u8fc7\u4e00\u4e2a\uff0c\u8fde\u63a5\u540e\u4e24\u68f5\u6811<\/span><\/p><p><span>\u2462\u3001x\u548cnext-x\u6307\u5411\u7684\u4e24\u68f5\u4e8c\u9879\u6811\u5ea6\u6570\u4e00\u6837<\/span><\/p><p><span>\u6839\u636ex\u7684\u6839\u548cnext-x\u7684\u6839\u7684\u5927\u5c0f\u60c5\u51b5\uff0c\u786e\u5b9a\u600e\u6837\u5f62\u6210\u4e00\u68f5\u65b0\u6811\uff0c\u6ce8\u610f\u5f53x\u4e3a\u8868\u5934\u65f6\u8981\u66f4\u6539<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"8.217ex\" height=\"2.577ex\" viewBox=\"0 -806.1 3538 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E225-MJMATHI-68\" d=\"M137 683Q138 683 209 688T282 694Q294 694 294 685Q294 674 258 534Q220 386 220 383Q220 381 227 388Q288 442 357 442Q411 442 444 415T478 336Q478 285 440 178T402 50Q403 36 407 31T422 26Q450 26 474 56T513 138Q516 149 519 151T535 153Q555 153 555 145Q555 144 551 130Q535 71 500 33Q466 -10 419 -10H414Q367 -10 346 17T325 74Q325 90 361 192T398 345Q398 404 354 404H349Q266 404 205 306L198 293L164 158Q132 28 127 16Q114 -11 83 -11Q69 -11 59 -2T48 16Q48 30 121 320L195 616Q195 629 188 632T149 637H128Q122 643 122 645T124 664Q129 683 137 683Z\"><\/path><path stroke-width=\"0\" id=\"E225-MJMATHI-65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><path stroke-width=\"0\" id=\"E225-MJMATHI-61\" d=\"M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><path stroke-width=\"0\" id=\"E225-MJMATHI-64\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><path stroke-width=\"0\" id=\"E225-MJMAIN-5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"><\/path><path stroke-width=\"0\" id=\"E225-MJMATHI-48\" d=\"M228 637Q194 637 192 641Q191 643 191 649Q191 673 202 682Q204 683 219 683Q260 681 355 681Q389 681 418 681T463 682T483 682Q499 682 499 672Q499 670 497 658Q492 641 487 638H485Q483 638 480 638T473 638T464 637T455 637Q416 636 405 634T387 623Q384 619 355 500Q348 474 340 442T328 395L324 380Q324 378 469 378H614L615 381Q615 384 646 504Q674 619 674 627T617 637Q594 637 587 639T580 648Q580 650 582 660Q586 677 588 679T604 682Q609 682 646 681T740 680Q802 680 835 681T871 682Q888 682 888 672Q888 645 876 638H874Q872 638 869 638T862 638T853 637T844 637Q805 636 794 634T776 623Q773 618 704 340T634 58Q634 51 638 51Q646 48 692 46H723Q729 38 729 37T726 19Q722 6 716 0H701Q664 2 567 2Q533 2 504 2T458 2T437 1Q420 1 420 10Q420 15 423 24Q428 43 433 45Q437 46 448 46H454Q481 46 514 49Q520 50 522 50T528 55T534 64T540 82T547 110T558 153Q565 181 569 198Q602 330 602 331T457 332H312L279 197Q245 63 245 58Q245 51 253 49T303 46H334Q340 38 340 37T337 19Q333 6 327 0H312Q275 2 178 2Q144 2 115 2T69 2T48 1Q31 1 31 10Q31 12 34 24Q39 43 44 45Q48 46 59 46H65Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Q285 635 228 637Z\"><\/path><path stroke-width=\"0\" id=\"E225-MJMAIN-5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E225-MJMATHI-68\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E225-MJMATHI-65\" x=\"576\" y=\"0\"><\/use><use xlink:href=\"#E225-MJMATHI-61\" x=\"1042\" y=\"0\"><\/use><use xlink:href=\"#E225-MJMATHI-64\" x=\"1571\" y=\"0\"><\/use><use xlink:href=\"#E225-MJMAIN-5B\" x=\"2094\" y=\"0\"><\/use><use xlink:href=\"#E225-MJMATHI-48\" x=\"2372\" y=\"0\"><\/use><use xlink:href=\"#E225-MJMAIN-5D\" x=\"3260\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">head[H]<\/script><\/p><p><span>INSERT\uff1a<\/span><\/p><p><span>\u5c06\u63d2\u5165\u7684\u65b0\u8282\u70b9\u5f53\u6210\u4e00\u4e2a\u65b0\u5806\uff0c\u5408\u5e76\u4e24\u4e2a\u65b0\u5806<\/span><\/p><p><span>EXTRACT-MIN\uff1a<\/span><\/p><p><span>\u5c06\u5305\u542b\u6700\u5c0f\u5173\u952e\u5b57\u7684\u4e8c\u9879\u6811\u4ece\u539f\u6765\u7684\u5806\u4e0a\u5220\u9664\uff0c\u5c06\u53d6\u51fa\u7684\u4e8c\u9879\u6811\u7684\u6839\u8282\u70b9\u5220\u6389\uff0c\u5269\u4e0b\u7684\u53d8\u4e3a\u4e00\u4e2a\u4e8c\u9879\u5806\uff0c\u5408\u5e76\u4e24\u4e2a\u4e8c\u9879\u5806<\/span><\/p><p><span>DECREASE-KEY\uff1a<\/span><\/p><p><span>\u4fee\u6539\u4e00\u4e2a\u8282\u70b9\u7684\u5173\u952e\u5b57\u4e4b\u540e\u8ba9\u5176\u5192\u6ce1\u4e0a\u5347<\/span><\/p><p><span>DELETE\uff1a<\/span><\/p><p><span>\u5c06\u8981\u5220\u9664\u7684\u5173\u952e\u5b57\u51cf\u5c0f\u5230\u6b63\u65e0\u7a77<\/span><\/p><p><span>\u8c03\u7528EXTRACT-MIN<\/span><\/p><p><strong><span>6\u3001\u4e0d\u76f8\u4ea4\u96c6\u5408<\/span><\/strong><\/p><p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"11.523ex\" height=\"2.811ex\" viewBox=\"0 -856.4 4961.2 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E226-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"><\/path><path stroke-width=\"0\" id=\"E226-MJMATHI-69\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E226-MJSZ1-22C0\" d=\"M119 -249T97 -249T65 -235T55 -207Q55 -201 56 -198Q58 -190 218 268T380 729Q392 750 416 750Q438 750 451 732Q453 728 534 498T695 36L775 -194Q777 -204 777 -208Q777 -222 767 -235T735 -249Q713 -249 700 -231Q696 -225 557 177L416 579L276 177Q136 -226 132 -231Q119 -249 97 -249Z\"><\/path><path stroke-width=\"0\" id=\"E226-MJMATHI-6A\" d=\"M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z\"><\/path><path stroke-width=\"0\" id=\"E226-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path stroke-width=\"0\" id=\"E226-MJMAIN-2205\" d=\"M331 696Q335 708 339 722T345 744T350 759T357 769T367 772Q374 772 381 767T388 754Q388 746 377 712L366 673L378 661Q460 575 460 344Q460 281 456 234T432 126T373 27Q319 -22 250 -22Q214 -22 180 -7Q168 -3 168 -4L159 -33Q148 -71 142 -75Q138 -78 132 -78Q124 -78 118 -72T111 -60Q111 -52 122 -18L133 21L125 29Q39 111 39 344Q39 596 137 675Q187 716 251 716Q265 716 278 714T296 710T315 703T331 696ZM276 676Q264 679 246 679Q196 679 159 631Q134 597 128 536T121 356Q121 234 127 174T151 80L234 366Q253 430 275 506T308 618L318 654Q318 656 294 669L276 676ZM181 42Q207 16 250 16Q291 16 324 47Q354 78 366 136T378 356Q378 470 372 528T349 616L348 613Q348 611 264 326L181 42Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E226-MJMATHI-53\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E226-MJMATHI-69\" x=\"866\" y=\"-213\"><\/use><use xlink:href=\"#E226-MJSZ1-22C0\" x=\"1123\" y=\"-1\"><\/use><g transform=\"translate(2123,0)\"><use xlink:href=\"#E226-MJMATHI-53\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E226-MJMATHI-6A\" x=\"866\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E226-MJMAIN-3D\" x=\"3405\" y=\"0\"><\/use><use xlink:href=\"#E226-MJMAIN-2205\" x=\"4461\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">S_i \\bigwedge S_j = \\emptyset<\/script><\/p><p><span>\u53ef\u7528\u4e8e\u6c42\u5f3a\u8fde\u901a\u5206\u91cf<\/span><\/p><p><strong><span>\u4f7f\u7528\u94fe\u8868\u8868\u793a\uff1a<\/span><\/strong><\/p><p><span>MAKE-SET\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.74ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2041 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E227-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E227-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E227-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E227-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E227-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E227-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E227-MJMAIN-31\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E227-MJMAIN-29\" x=\"1652\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O( 1 )<\/script><\/p><p><span>\u5177\u6709n\u4e2aMAKE-SET\u64cd\u4f5c\u7684m\u4e2a\u5305\u542bMAKE-SET\u3001UNION\u3001FIND-SET\u64cd\u4f5c\u7684\u5e8f\u5217\u96c6\u5408\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\uff1a<\/span><\/p><p><span>\u672a\u7ecf\u8fc7\u4efb\u4f55\u4f18\u5316\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"6.026ex\" height=\"2.811ex\" viewBox=\"0 -906.7 2594.6 1210.2\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E228-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMAIN-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path stroke-width=\"0\" id=\"E228-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E228-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E228-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><g transform=\"translate(1152,0)\"><use xlink:href=\"#E228-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E228-MJMAIN-32\" x=\"848\" y=\"513\"><\/use><\/g><use xlink:href=\"#E228-MJMAIN-29\" x=\"2205\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(n^2)<\/script><\/p><p><span>\u91c7\u7528\u52a0\u6743\u5408\u5e76\u5f0f\u7684\u542f\u53d1\u7b56\u7565(\u603b\u662f\u5c06\u8868\u957f\u8f83\u5c0f\u7684\u96c6\u5408\u5408\u5e76\u5230\u8868\u957f\u8f83\u5927\u7684\u96c6\u5408\u4e2d)\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"14.178ex\" height=\"2.577ex\" viewBox=\"0 -806.1 6104.4 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E229-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E229-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E229-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E229-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E229-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E229-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E229-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E229-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 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y=\"0\"><\/use><use xlink:href=\"#E229-MJMATHI-67\" x=\"4635\" y=\"0\"><\/use><use xlink:href=\"#E229-MJMATHI-6E\" x=\"5115\" y=\"0\"><\/use><use xlink:href=\"#E229-MJMAIN-29\" x=\"5715\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(m+nlogn)<\/script><\/p><p><strong><span>\u4f7f\u7528\u68ee\u6797\u8868\u793a\uff1a<\/span><\/strong><\/p><p><span>\u6309\u79e9\u5408\u5e76\u3001\u8def\u5f84\u538b\u7f29<\/span><\/p><p><span>\u5177\u6709n\u4e2aMAKE-SET\u64cd\u4f5c\u7684m\u4e2a\u5305\u542bMAKE-SET\u3001UNION\u3001FIND-SET\u64cd\u4f5c\u7684\u5e8f\u5217\u96c6\u5408\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\uff1a<\/span><\/p><p><span>\u5355\u72ec\u4f7f\u7528\u6309\u79e9\u5408\u5e76\uff1a<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"9.945ex\" height=\"2.577ex\" viewBox=\"0 -806.1 4282 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E230-MJMATHI-4F\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path stroke-width=\"0\" id=\"E230-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E230-MJMATHI-6D\" d=\"M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 181Q151 335 151 342Q154 357 154 369Q154 405 129 405Q107 405 92 377T69 316T57 280Q55 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E230-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E230-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E230-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 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transform=\"translate(7156,0)\"><use xlink:href=\"#E231-MJMATHI-67\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(477,-442)\"><use transform=\"scale(0.707)\" xlink:href=\"#E231-MJMAIN-32\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E231-MJMAIN-2B\" x=\"500\" y=\"0\"><\/use><g transform=\"translate(903,0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"420\" height=\"60\" x=\"0\" y=\"146\"><\/rect><use transform=\"scale(0.5)\" xlink:href=\"#E231-MJMATHI-66\" x=\"144\" y=\"867\"><\/use><use transform=\"scale(0.5)\" xlink:href=\"#E231-MJMATHI-6E\" x=\"119\" y=\"-488\"><\/use><\/g><\/g><\/g><\/g><use xlink:href=\"#E231-MJMATHI-6E\" x=\"9297\" y=\"0\"><\/use><use xlink:href=\"#E231-MJMAIN-29\" x=\"9897\" y=\"0\"><\/use><use xlink:href=\"#E231-MJMAIN-29\" x=\"10286\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\Theta(n + f \\cdot (1 + log _{2+\\frac{f}{n}} n))<\/script><span> <\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"1.277ex\" height=\"2.577ex\" viewBox=\"0 -806.1 550 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E232-MJMATHI-66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"><\/path><\/defs><g stroke=\"currentColor\" 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0 -1 0 0)\"><use xlink:href=\"#E233-MJMATHI-4F\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMAIN-28\" x=\"763\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMATHI-6D\" x=\"1152\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMAIN-22C5\" x=\"2252\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMATHI-3B1\" x=\"2752\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMAIN-28\" x=\"3392\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMATHI-6E\" x=\"3781\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMAIN-29\" x=\"4381\" y=\"0\"><\/use><use xlink:href=\"#E233-MJMAIN-29\" x=\"4770\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">O(m \\cdot \\alpha(n))<\/script><\/p><p> <\/p><h3><a name=\"\u7279\u6b8a\u516c\u5f0f\" class=\"md-header-anchor\"><\/a><span>\u7279\u6b8a\u516c\u5f0f<\/span><\/h3><p><span>1.<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"21.926ex\" height=\"2.928ex\" viewBox=\"0 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stroke-width=\"0\" id=\"E235-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMAIN-2192\" d=\"M56 237T56 250T70 270H835Q719 357 692 493Q692 494 692 496T691 499Q691 511 708 511H711Q720 511 723 510T729 506T732 497T735 481T743 456Q765 389 816 336T935 261Q944 258 944 250Q944 244 939 241T915 231T877 212Q836 186 806 152T761 85T740 35T732 4Q730 -6 727 -8T711 -11Q691 -11 691 0Q691 7 696 25Q728 151 835 230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMAIN-221E\" d=\"M55 217Q55 305 111 373T254 442Q342 442 419 381Q457 350 493 303L507 284L514 294Q618 442 747 442Q833 442 888 374T944 214Q944 128 889 59T743 -11Q657 -11 580 50Q542 81 506 128L492 147L485 137Q381 -11 252 -11Q166 -11 111 57T55 217ZM907 217Q907 285 869 341T761 397Q740 397 720 392T682 378T648 359T619 335T594 310T574 285T559 263T548 246L543 238L574 198Q605 158 622 138T664 94T714 61T765 51Q827 51 867 100T907 217ZM92 214Q92 145 131 89T239 33Q357 33 456 193L425 233Q364 312 334 337Q285 380 233 380Q171 380 132 331T92 214Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMATHI-78\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path stroke-width=\"0\" id=\"E235-MJMATHI-65\" d=\"M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E235-MJMAIN-6C\"><\/use><use xlink:href=\"#E235-MJMAIN-69\" x=\"278\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-6D\" x=\"556\" y=\"0\"><\/use><g transform=\"translate(1389,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E235-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E235-MJMAIN-2192\" x=\"600\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E235-MJMAIN-221E\" x=\"1600\" y=\"0\"><\/use><\/g><use xlink:href=\"#E235-MJMAIN-28\" x=\"3327\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-31\" x=\"3716\" y=\"0\"><\/use><use xlink:href=\"#E235-MJMAIN-2B\" x=\"4438\" y=\"0\"><\/use><g transform=\"translate(5216,0)\"><g transform=\"translate(342,0)\"><rect stroke=\"none\" width=\"544\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E235-MJMATHI-78\" x=\"98\" y=\"582\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E235-MJMATHI-6E\" x=\"84\" y=\"-488\"><\/use><\/g><\/g><g transform=\"translate(6223,0)\"><use xlink:href=\"#E235-MJMAIN-29\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E235-MJMATHI-6E\" x=\"550\" y=\"513\"><\/use><\/g><use xlink:href=\"#E235-MJMAIN-3D\" x=\"7414\" y=\"0\"><\/use><g transform=\"translate(8470,0)\"><use xlink:href=\"#E235-MJMATHI-65\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E235-MJMATHI-78\" x=\"659\" y=\"513\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">\\lim_{n\\to\\infty}(1+\\frac{x}{n})^n = e^x<\/script><\/p><p><span>2.<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"20.619ex\" height=\"3.044ex\" viewBox=\"0 -806.1 8877.7 1310.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.172ex;\"><defs><path stroke-width=\"0\" id=\"E236-MJMATHI-78\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z\"><\/path><path stroke-width=\"0\" id=\"E236-MJMAIN-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path stroke-width=\"0\" id=\"E236-MJMAIN-2B\" d=\"M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z\"><\/path><path stroke-width=\"0\" id=\"E236-MJMAIN-2264\" d=\"M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"><\/path><path stroke-width=\"0\" id=\"E236-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E236-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E236-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E236-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g transform=\"translate(120,0)\"><rect stroke=\"none\" width=\"1428\" height=\"60\" x=\"0\" y=\"220\"><\/rect><use transform=\"scale(0.707)\" xlink:href=\"#E236-MJMATHI-78\" x=\"723\" y=\"582\"><\/use><g transform=\"translate(60,-376)\"><use transform=\"scale(0.707)\" xlink:href=\"#E236-MJMAIN-31\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E236-MJMAIN-2B\" x=\"500\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E236-MJMATHI-78\" x=\"1278\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E236-MJMAIN-2264\" x=\"1945\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMATHI-6C\" x=\"3001\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMATHI-6E\" x=\"3299\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMAIN-28\" x=\"3899\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMAIN-31\" x=\"4288\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMAIN-2B\" x=\"5010\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMATHI-78\" x=\"6011\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMAIN-29\" x=\"6583\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMAIN-2264\" x=\"7249\" y=\"0\"><\/use><use xlink:href=\"#E236-MJMATHI-78\" x=\"8305\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">\\frac{x}{1+x}\\leq ln(1+x) \\leq x<\/script><\/p><p><span>3.<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"19.211ex\" height=\"2.577ex\" viewBox=\"0 -806.1 8271.6 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E237-MJMATHI-6C\" d=\"M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMATHI-6F\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMATHI-67\" d=\"M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMAIN-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMAIN-21\" d=\"M78 661Q78 682 96 699T138 716T180 700T199 661Q199 654 179 432T158 206Q156 198 139 198Q121 198 119 206Q118 209 98 431T78 661ZM79 61Q79 89 97 105T141 121Q164 119 181 104T198 61Q198 31 181 16T139 1Q114 1 97 16T79 61Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMAIN-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMAIN-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path stroke-width=\"0\" id=\"E237-MJMAIN-398\" d=\"M56 340Q56 423 86 494T164 610T270 680T388 705Q521 705 621 601T722 341Q722 260 693 191T617 75T510 4T388 -22T267 3T160 74T85 189T56 340ZM610 339Q610 428 590 495T535 598T463 651T384 668Q332 668 289 638T221 566Q168 485 168 339Q168 274 176 235Q189 158 228 105T324 28Q356 16 388 16Q415 16 442 24T501 54T555 111T594 205T610 339ZM223 263V422H263V388H514V422H554V263H514V297H263V263H223Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E237-MJMATHI-6C\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-6F\" x=\"298\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-67\" x=\"783\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMAIN-28\" x=\"1263\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-6E\" x=\"1652\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMAIN-21\" x=\"2252\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMAIN-29\" x=\"2530\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMAIN-3D\" x=\"3196\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMAIN-398\" x=\"4252\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMAIN-28\" x=\"5030\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-6E\" x=\"5419\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-6C\" x=\"6019\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-6F\" x=\"6317\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-67\" x=\"6802\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMATHI-6E\" x=\"7282\" y=\"0\"><\/use><use xlink:href=\"#E237-MJMAIN-29\" x=\"7882\" y=\"0\"><\/use><\/g><\/svg><\/span><script type=\"math\/tex\">log(n!) = \\Theta (nlogn)<\/script><\/p><p><span>4.<\/span><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"22.754ex\" height=\"3.861ex\" viewBox=\"0 -1208.2 9796.8 1662.6\" role=\"img\" focusable=\"false\" style=\"vertical-align: -1.055ex;\"><defs><path stroke-width=\"0\" id=\"E238-MJSZ1-2211\" d=\"M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z\"><\/path><path stroke-width=\"0\" id=\"E238-MJMATHI-6E\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path stroke-width=\"0\" id=\"E238-MJMATHI-6B\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 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transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-32\" x=\"736\" y=\"513\"><\/use><\/g><use xlink:href=\"#E238-MJMAIN-3D\" x=\"3847\" y=\"0\"><\/use><g transform=\"translate(4625,0)\"><g transform=\"translate(397,0)\"><rect stroke=\"none\" width=\"4653\" height=\"60\" x=\"0\" y=\"220\"><\/rect><g transform=\"translate(60,581)\"><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMATHI-6E\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-28\" x=\"600\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMATHI-6E\" x=\"989\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-2B\" x=\"1589\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-31\" x=\"2367\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-29\" x=\"2867\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-28\" x=\"3256\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-32\" x=\"3645\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMATHI-6E\" x=\"4145\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-2B\" x=\"4745\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-31\" x=\"5523\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-29\" x=\"6023\" y=\"0\"><\/use><\/g><use transform=\"scale(0.707)\" xlink:href=\"#E238-MJMAIN-36\" x=\"3040\" y=\"-531\"><\/use><\/g><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">\\sum ^n _{k=0} k^2= \\frac{n(n+1)(2n+1)}{6}<\/script><\/p><p> <\/p><\/div>\n<\/body>\n<\/html>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u7b97\u6cd5\u57fa\u7840\u671f\u672b\u603b\u7ed3 \u7b97\u6cd5\u57fa\u7840\u671f\u672b\u603b\u7ed3 \u7b97\u6cd5\u5206\u6790 \u4e00\u3001\u6392\u5e8f\u7b97\u6cd5 1\u3001\u63d2\u5165\u6392\u5e8f\uff1a \u6700\u574f\u60c5\u51b5\uff1a \u5f53\u6570\u7ec4\u9006\u5e8f\u65f6\u53d1\u751f \u6700\u597d\u60c5\u51b5\uff1a \u5f53\u6570\u7ec4\u987a\u5e8f\u65f6\u53d1\u751f \u7b97\u6cd5\u65f6\u95f4\u590d\u6742\u5ea6\u4e3b\u8981\u6765\u81ea\u5bf9\u6570\u7ec4\u7684\u904d\u5386\u4ee5\u53ca\u5143\u7d20\u7684\u79fb\u52a8\uff0c\u4fee\u6539\u641c\u7d22\u7b97\u6cd5\u5e76\u4e0d\u80fd\u6539\u8fdb\u65f6\u95f4\u590d\u6742\u5ea6 \u7a33\u5b9a 2\u3001\u5f52\u5e76\u6392\u5e8f\uff1a \u9012\u5f52\u5f0f\uff1a \u7a33\u5b9a 3\u3001\u5806\u6392\u5e8f\uff1a \u4e0e\u5806\u6392\u5e8f\u76f8\u5173\u7684\u8fc7\u7a0b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff1a MAX-HEAPIFY: BUILD-MAX-HEAP: MAX-HEAP-INSERT, HEAP-EXTRACT-MAX,… <\/p>\n<div class=\"art-el-more\"><a href=\"https:\/\/yunpeng.site\/index.php\/2021\/04\/16\/algsum\/\" class=\"art-link art-color-link art-w-chevron\">Read more<\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[3],"tags":[6,5],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/posts\/104"}],"collection":[{"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/comments?post=104"}],"version-history":[{"count":5,"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/posts\/104\/revisions"}],"predecessor-version":[{"id":411,"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/posts\/104\/revisions\/411"}],"wp:attachment":[{"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/media?parent=104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/categories?post=104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/yunpeng.site\/index.php\/wp-json\/wp\/v2\/tags?post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}