{"id":307,"date":"2022-07-03T22:05:56","date_gmt":"2022-07-03T14:05:56","guid":{"rendered":"https:\/\/www.lazybirds.top\/?p=307"},"modified":"2022-07-06T22:10:43","modified_gmt":"2022-07-06T14:10:43","slug":"%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84-%e6%9c%9f%e6%9c%ab%e5%a4%8d%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/www.lazybirds.top\/?p=307","title":{"rendered":"\u6570\u636e\u7ed3\u6784 &#8211; \u671f\u672b\u590d\u4e60"},"content":{"rendered":"\n<p>\u4e3b\u8981\u6d89\u53ca\u67e5\u627e\u3001\u5916\u90e8\u6392\u5e8f\u3001\u56fe\u7b49\u77e5\u8bc6\u70b9<\/p>\n\n\n\n<!--more-->\n\n\n\n\n      <meta charset=\"utf-8\">\n      <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n      \n      <link rel=\"stylesheet\" href=\"https:\/\/www.lazybirds.top\/katex\/katex.min.css\">\n      \n      <style>\n      \/**\n * prism.js Github theme based on GitHub's theme.\n * @author Sam Clarke\n *\/\ncode[class*=\"language-\"],\npre[class*=\"language-\"] {\n  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href=\"#b%E6%A0%91%E7%9A%84%E6%8F%92%E5%85%A5\">B&#x6811;&#x7684;&#x63D2;&#x5165;<\/a><\/li>\n<li><a href=\"#b%E6%A0%91%E7%9A%84%E5%88%A0%E9%99%A4\">B&#x6811;&#x7684;&#x5220;&#x9664;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#b%E6%A0%91\">B+&#x6811;<\/a><\/li>\n<li><a href=\"#%E9%94%AE%E6%A0%91\">&#x952E;&#x6811;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%93%88%E5%B8%8C%E8%A1%A8\">&#x54C8;&#x5E0C;&#x8868;<\/a>\n<ul>\n<li><a href=\"#%E5%93%88%E5%B8%8C%E5%87%BD%E6%95%B0%E7%9A%84%E6%9E%84%E9%80%A0\">&#x54C8;&#x5E0C;&#x51FD;&#x6570;&#x7684;&#x6784;&#x9020;<\/a>\n<ul>\n<li><a href=\"#%E7%9B%B4%E6%8E%A5%E5%AE%9A%E5%9D%80%E6%B3%95\">&#x76F4;&#x63A5;&#x5B9A;&#x5740;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E6%95%B0%E5%AD%97%E5%88%86%E6%9E%90%E6%B3%95\">&#x6570;&#x5B57;&#x5206;&#x6790;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E5%B9%B3%E6%96%B9%E5%8F%96%E4%B8%AD%E6%B3%95\">&#x5E73;&#x65B9;&#x53D6;&#x4E2D;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E9%99%A4%E7%95%99%E4%BD%99%E6%95%B0%E6%B3%95\">&#x9664;&#x7559;&#x4F59;&#x6570;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E6%8A%98%E5%8F%A0%E6%B3%95%E7%A7%BB%E4%BD%8D%E5%8F%A0%E5%8A%A0-%E9%97%B4%E7%95%8C%E5%8F%A0%E5%8A%A0\">&#x6298;&#x53E0;&#x6CD5;&#xFF1A;&#x79FB;&#x4F4D;&#x53E0;&#x52A0;&#x3001;&#x95F4;&#x754C;&#x53E0;&#x52A0;<\/a><\/li>\n<li><a href=\"#%E4%BF%9D%E7%95%99%E4%BD%99%E6%95%B0%E6%B3%95\">&#x4FDD;&#x7559;&#x4F59;&#x6570;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E9%9A%8F%E6%9C%BA%E6%95%B0%E6%B3%95\">&#x968F;&#x673A;&#x6570;&#x6CD5;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%86%B2%E7%AA%81%E7%9A%84%E5%A4%84%E7%90%86%E6%96%B9%E6%B3%95\">&#x51B2;&#x7A81;&#x7684;&#x5904;&#x7406;&#x65B9;&#x6CD5;<\/a>\n<ul>\n<li><a href=\"#%E5%BC%80%E6%94%BE%E5%AE%9A%E5%9D%80%E6%B3%95\">&#x5F00;&#x653E;&#x5B9A;&#x5740;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E5%86%8D%E5%93%88%E5%B8%8C%E6%B3%95\">&#x518D;&#x54C8;&#x5E0C;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E9%93%BE%E5%9C%B0%E5%9D%80%E6%B3%95\">&#x94FE;&#x5730;&#x5740;&#x6CD5;<\/a><\/li>\n<li><a href=\"#%E5%BB%BA%E7%AB%8B%E5%85%AC%E5%85%B1%E6%BA%A2%E5%87%BA%E5%8C%BA\">&#x5EFA;&#x7ACB;&#x516C;&#x5171;&#x6EA2;&#x51FA;&#x533A;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%93%88%E5%B8%8C%E6%9F%A5%E6%89%BE%E7%9A%84%E6%80%A7%E8%83%BD%E5%88%86%E6%9E%90\">&#x54C8;&#x5E0C;&#x67E5;&#x627E;&#x7684;&#x6027;&#x80FD;&#x5206;&#x6790;<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%A4%96%E9%83%A8%E6%8E%92%E5%BA%8F\">&#x5916;&#x90E8;&#x6392;&#x5E8F;<\/a>\n<ul>\n<li><a href=\"#k%E8%B7%AF%E5%B9%B3%E8%A1%A1%E5%BD%92%E5%B9%B6\">k&#x8DEF;&#x5E73;&#x8861;&#x5F52;&#x5E76;<\/a><\/li>\n<li><a href=\"#%E6%9C%80%E4%BD%B3%E5%BD%92%E5%B9%B6%E6%A0%91\">&#x6700;&#x4F73;&#x5F52;&#x5E76;&#x6811;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%9B%BE\">&#x56FE;<\/a>\n<ul>\n<li><a href=\"#%E5%9B%BE%E7%9A%84%E5%AE%9A%E4%B9%89%E5%92%8C%E6%9C%AF%E8%AF%AD\">&#x56FE;&#x7684;&#x5B9A;&#x4E49;&#x548C;&#x672F;&#x8BED;<\/a><\/li>\n<li><a href=\"#%E5%9B%BE%E7%9A%84%E5%AD%98%E5%82%A8%E7%BB%93%E6%9E%84\">&#x56FE;&#x7684;&#x5B58;&#x50A8;&#x7ED3;&#x6784;<\/a>\n<ul>\n<li><a href=\"#%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5\">&#x90BB;&#x63A5;&#x77E9;&#x9635;<\/a><\/li>\n<li><a href=\"#%E9%82%BB%E6%8E%A5%E8%A1%A8\">&#x90BB;&#x63A5;&#x8868;<\/a><\/li>\n<li><a href=\"#%E5%8D%81%E5%AD%97%E9%93%BE%E8%A1%A8%E6%9C%89%E5%90%91%E5%9B%BE-%E9%82%BB%E6%8E%A5%E5%A4%9A%E9%87%8D%E8%A1%A8%E6%97%A0%E5%90%91%E5%9B%BE\">&#x5341;&#x5B57;&#x94FE;&#x8868;&#xFF08;&#x6709;&#x5411;&#x56FE;&#xFF09;\/ &#x90BB;&#x63A5;&#x591A;&#x91CD;&#x8868;&#xFF08;&#x65E0;&#x5411;&#x56FE;&#xFF09;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%9B%BE%E7%9A%84%E8%BF%9E%E9%80%9A%E6%80%A7%E9%97%AE%E9%A2%98\">&#x56FE;&#x7684;&#x8FDE;&#x901A;&#x6027;&#x95EE;&#x9898;<\/a>\n<ul>\n<li><a href=\"#%E6%9C%89%E5%90%91%E5%9B%BE%E7%9A%84%E5%BC%BA%E8%BF%9E%E9%80%9A%E5%88%86%E9%87%8F\">&#x6709;&#x5411;&#x56FE;&#x7684;&#x5F3A;&#x8FDE;&#x901A;&#x5206;&#x91CF;<\/a><\/li>\n<li><a href=\"#%E6%9C%80%E5%B0%8F%E7%94%9F%E6%88%90%E6%A0%91minimum-cost-spanning-tree\">&#x6700;&#x5C0F;&#x751F;&#x6210;&#x6811;&#xFF08;Minimum Cost Spanning Tree&#xFF09;<\/a>\n<ul>\n<li><a href=\"#prim%E7%AE%97%E6%B3%95\">Prim&#x7B97;&#x6CD5;<\/a><\/li>\n<li><a href=\"#kruskal%E7%AE%97%E6%B3%95\">Kruskal&#x7B97;&#x6CD5;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%85%B3%E8%8A%82%E7%82%B9%E5%92%8C%E9%87%8D%E8%BF%9E%E9%80%9A%E5%88%86%E9%87%8F\">&#x5173;&#x8282;&#x70B9;&#x548C;&#x91CD;&#x8FDE;&#x901A;&#x5206;&#x91CF;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E6%9C%89%E5%90%91%E6%97%A0%E7%8E%AF%E5%9B%BE\">&#x6709;&#x5411;&#x65E0;&#x73AF;&#x56FE;<\/a>\n<ul>\n<li><a href=\"#aov%E7%BD%91%E7%9A%84%E6%8B%93%E6%89%91%E6%8E%92%E5%BA%8F\">AOV&#x7F51;&#x7684;&#x62D3;&#x6251;&#x6392;&#x5E8F;<\/a><\/li>\n<li><a href=\"#aoe%E7%BD%91%E7%9A%84%E5%85%B3%E9%94%AE%E8%B7%AF%E5%BE%84\">AOE&#x7F51;&#x7684;&#x5173;&#x952E;&#x8DEF;&#x5F84;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E6%9C%80%E7%9F%AD%E8%B7%AF%E5%BE%84\">&#x6700;&#x77ED;&#x8DEF;&#x5F84;<\/a>\n<ul>\n<li><a href=\"#dijkstra%E7%AE%97%E6%B3%95\">Dijkstra&#x7B97;&#x6CD5;<\/a><\/li>\n<li><a href=\"#bellman-ford%E7%AE%97%E6%B3%95\">Bellman-Ford&#x7B97;&#x6CD5;<\/a><\/li>\n<li><a href=\"#floyd%E7%AE%97%E6%B3%95\">Floyd&#x7B97;&#x6CD5;<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E5%8A%A8%E6%80%81%E5%AD%98%E5%82%A8%E7%AE%A1%E7%90%86\">&#x52A8;&#x6001;&#x5B58;&#x50A8;&#x7BA1;&#x7406;<\/a>\n<ul>\n<li><a href=\"#%E5%8F%AF%E5%88%A9%E7%94%A8%E7%A9%BA%E9%97%B4%E8%A1%A8\">&#x53EF;&#x5229;&#x7528;&#x7A7A;&#x95F4;&#x8868;<\/a>\n<ul>\n<li><a href=\"#%E9%93%BE%E5%BC%8F%E5%8F%AF%E5%88%A9%E7%94%A8%E7%A9%BA%E9%97%B4%E8%A1%A8%E7%9A%84%E5%88%86%E9%85%8D%E6%96%B9%E5%BC%8F\">&#x94FE;&#x5F0F;&#x53EF;&#x5229;&#x7528;&#x7A7A;&#x95F4;&#x8868;&#x7684;&#x5206;&#x914D;&#x65B9;&#x5F0F;<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#%E8%BE%B9%E7%95%8C%E6%A0%87%E8%AF%86%E6%B3%95boundary-tag-method\">&#x8FB9;&#x754C;&#x6807;&#x8BC6;&#x6CD5;&#xFF08;Boundary Tag Method&#xFF09;<\/a><\/li>\n<li><a href=\"#%E4%BC%99%E4%BC%B4%E7%B3%BB%E7%BB%9Fbuddy-system\">&#x4F19;&#x4F34;&#x7CFB;&#x7EDF;&#xFF08;Buddy System&#xFF09;<\/a><\/li>\n<li><a href=\"#%E6%97%A0%E7%94%A8%E5%8D%95%E5%85%83%E6%94%B6%E9%9B%86garbage-collector-gc\">&#x65E0;&#x7528;&#x5355;&#x5143;&#x6536;&#x96C6;&#xFF08;Garbage Collector, GC&#xFF09;<\/a>\n<ul>\n<li><a href=\"#%E5%BC%95%E7%94%A8%E8%AE%A1%E6%95%B0reference-counting\">&#x5F15;&#x7528;&#x8BA1;&#x6570;(Reference Counting)<\/a><\/li>\n<li><a href=\"#%E6%A0%87%E8%AE%B0%E5%90%8E%E6%B8%85%E9%99%A4mark-and-sweep\">&#x6807;&#x8BB0;&#x540E;&#x6E05;&#x9664;(Mark and Sweep)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1 class=\"mume-header\" id=\"%E6%9F%A5%E6%89%BE\">&#x67E5;&#x627E;<\/h1>\n\n<p>ASL (Average Search Length&#xFF0C; &#x5E73;&#x5747;&#x67E5;&#x627E;&#x957F;&#x5EA6;) &#x5B9A;&#x4E49;&#x4E3A;&#x9700;&#x8981;&#x548C;&#x7ED9;&#x5B9A;&#x503C;&#x8FDB;&#x884C;&#x6BD4;&#x8F83;&#x7684;&#x5173;&#x952E;&#x5B57;&#x7684;&#x4E2A;&#x6570;&#x7684;&#x671F;&#x671B;&#x503C;<\/p>\n<h2 class=\"mume-header\" id=\"%E9%9D%99%E6%80%81%E9%A1%BA%E5%BA%8F%E8%A1%A8%E4%B8%8E%E9%9D%99%E6%80%81%E6%A0%91%E8%A1%A8\">&#x9759;&#x6001;&#x987A;&#x5E8F;&#x8868;&#x4E0E;&#x9759;&#x6001;&#x6811;&#x8868;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E9%A1%BA%E5%BA%8F%E6%9F%A5%E6%89%BE\">&#x987A;&#x5E8F;&#x67E5;&#x627E;<\/h3>\n\n<p>&#x8868;&#x5934;&#x8BBE;&#x7F6E;&#x54E8;&#x5175;&#xFF0C;&#x503C;&#x4E3A;&#x5F85;&#x67E5;&#x627E;&#x503C;&#xFF0C;&#x4ECE;&#x540E;&#x5F80;&#x524D;&#x67E5;&#x627E;<br>\n&#x5FAA;&#x73AF;&#x4E2D;&#x7701;&#x6389;&#x4E86;&#x4E00;&#x6B21;&#x67E5;&#x627E;<br>\n&#x6539;&#x8FDB;&#xFF1A;<\/p>\n<ol>\n<li>&#x6309;&#x5143;&#x7D20;&#x88AB;&#x67E5;&#x627E;&#x7684;&#x9891;&#x7387;&#x5347;&#x5E8F;&#x6392;&#x5E8F;<\/li>\n<li>&#x5C06;&#x521A;&#x67E5;&#x627E;&#x7684;&#x5143;&#x7D20;&#x79FB;&#x81F3;&#x8868;&#x5C3E;&#xFF08;&#x5DF2;&#x53D1;&#x751F;&#x7684;&#x4E8B;&#x4F1A;&#x91CD;&#x590D;&#x53D1;&#x751F;&#xFF09;<\/li>\n<\/ol>\n<h3 class=\"mume-header\" id=\"%E4%BA%8C%E5%88%86%E6%9F%A5%E6%89%BE\">&#x4E8C;&#x5206;&#x67E5;&#x627E;<\/h3>\n\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mi>S<\/mi><msub><mi>L<\/mi><mrow><mi>s<\/mi><mi>u<\/mi><mi>c<\/mi><mi>c<\/mi><\/mrow><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/mfrac><msub><mrow><mi>log<\/mi><mo>&#x2061;<\/mo><\/mrow><mn>2<\/mn><\/msub><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">ASL_{succ}=\\frac{n+1}{n}\\log_2(n+1)-1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">S<\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><span class=\"mord mathnormal mtight\">u<\/span><span class=\"mord mathnormal mtight\">cc<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.1901em;vertical-align:-0.345em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8451em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\"><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.207em;\"><span style=\"top:-2.4559em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2441em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><br>\n&#x9002;&#x7528;&#x4E8E;&#x5927;&#x91CF;&#x7684;&#x9759;&#x6001;&#x6570;&#x636E;<\/p>\n<h3 class=\"mume-header\" id=\"fibonacci%E6%9F%A5%E6%89%BE\">Fibonacci&#x67E5;&#x627E;<\/h3>\n\n<pre data-role=\"codeBlock\" data-info=\"c\" class=\"language-c\"><span class=\"token keyword keyword-int\">int<\/span> <span class=\"token function\">Fib_search<\/span><span class=\"token punctuation\">(<\/span>RecType ST<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token punctuation\">,<\/span> KeyType key <span class=\"token punctuation\">,<\/span> <span class=\"token keyword keyword-int\">int<\/span> n<span class=\"token punctuation\">)<\/span>\n<span class=\"token comment\">\/\/&#x5728;&#x957F;&#x4E3A;n&#x7684;&#x6709;&#x5E8F;&#x8868;ST&#x4E2D;&#x7528;Fibonacci&#x65B9;&#x6CD5;&#x67E5;&#x627E;&#x5173;&#x952E;&#x5B57;&#x4E3A;key&#x7684;&#x8BB0;&#x5F55;&#xFF0C;&#x5176;&#x4E2D;n=fib(j)<\/span>\n<span class=\"token punctuation\">{<\/span> <span class=\"token keyword keyword-int\">int<\/span> Low<span class=\"token operator\">=<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> High<span class=\"token punctuation\">,<\/span> Mid<span class=\"token punctuation\">,<\/span> f1<span class=\"token punctuation\">,<\/span> f2 <span class=\"token punctuation\">;<\/span>\nHigh<span class=\"token operator\">=<\/span>n<span class=\"token punctuation\">;<\/span> f1<span class=\"token operator\">=<\/span><span class=\"token function\">fib<\/span><span class=\"token punctuation\">(<\/span>j<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> f2<span class=\"token operator\">=<\/span><span class=\"token function\">fib<\/span><span class=\"token punctuation\">(<\/span>j<span class=\"token operator\">-<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>\n<span class=\"token keyword keyword-while\">while<\/span> <span class=\"token punctuation\">(<\/span>Low<span class=\"token operator\">&lt;=<\/span>High<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span>\n    Mid<span class=\"token operator\">=<\/span>Low<span class=\"token operator\">+<\/span>f1<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>\n    <span class=\"token keyword keyword-if\">if<\/span> <span class=\"token punctuation\">(<\/span> <span class=\"token function\">EQ<\/span><span class=\"token punctuation\">(<\/span>ST<span class=\"token punctuation\">.<\/span><span class=\"token punctuation\">[<\/span>Mid<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>key<span class=\"token punctuation\">,<\/span> key<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">)<\/span> <span class=\"token keyword keyword-return\">return<\/span><span class=\"token punctuation\">(<\/span>Mid<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">;<\/span>\n    <span class=\"token keyword keyword-else\">else<\/span> <span class=\"token keyword keyword-if\">if<\/span> <span class=\"token punctuation\">(<\/span> <span class=\"token function\">LT<\/span><span class=\"token punctuation\">(<\/span>key<span class=\"token punctuation\">,<\/span> ST<span class=\"token punctuation\">.<\/span><span class=\"token punctuation\">[<\/span>Mid<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>key<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">)<\/span>\n        <span class=\"token punctuation\">{<\/span> High<span class=\"token operator\">=<\/span>Mid<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span> <span class=\"token punctuation\">;<\/span> f2<span class=\"token operator\">=<\/span>f1<span class=\"token operator\">-<\/span>f2 <span class=\"token punctuation\">;<\/span> f1<span class=\"token operator\">=<\/span>f1<span class=\"token operator\">-<\/span>f2 <span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span>\n    <span class=\"token keyword keyword-else\">else<\/span> \n        <span class=\"token punctuation\">{<\/span> Low<span class=\"token operator\">=<\/span>Mid<span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span> <span class=\"token punctuation\">;<\/span>f1<span class=\"token operator\">=<\/span>f1<span class=\"token operator\">-<\/span>f2 <span class=\"token punctuation\">;<\/span> f2<span class=\"token operator\">=<\/span>f2<span class=\"token operator\">-<\/span>f1 <span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span>\n<span class=\"token punctuation\">}<\/span> <span class=\"token keyword keyword-return\">return<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token punctuation\">}<\/span>\n<\/pre><h3 class=\"mume-header\" id=\"%E6%8F%92%E5%80%BC%E6%9F%A5%E6%89%BE\">&#x63D2;&#x503C;&#x67E5;&#x627E;<\/h3>\n\n<p>Key&#x4E0E;ST.elem[i]&#x6BD4;&#x8F83;&#xFF0C;&#x5176;&#x4E2D;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>i<\/mi><mo>=<\/mo><mfrac><mrow><mi>K<\/mi><mi>e<\/mi><mi>y<\/mi><mo>&#x2212;<\/mo><mi>S<\/mi><mi>T<\/mi><mi mathvariant=\"normal\">.<\/mi><mi>e<\/mi><mi>l<\/mi><mi>e<\/mi><mi>m<\/mi><mo stretchy=\"false\">[<\/mo><mi>l<\/mi><mo stretchy=\"false\">]<\/mo><mi mathvariant=\"normal\">.<\/mi><mi>k<\/mi><mi>e<\/mi><mi>y<\/mi><\/mrow><mrow><mi>S<\/mi><mi>T<\/mi><mi mathvariant=\"normal\">.<\/mi><mi>e<\/mi><mi>l<\/mi><mi>e<\/mi><mi>m<\/mi><mo stretchy=\"false\">[<\/mo><mi>h<\/mi><mo stretchy=\"false\">]<\/mo><mi mathvariant=\"normal\">.<\/mi><mi>k<\/mi><mi>e<\/mi><mi>y<\/mi><mo>&#x2212;<\/mo><mi>S<\/mi><mi>T<\/mi><mi mathvariant=\"normal\">.<\/mi><mi>e<\/mi><mi>l<\/mi><mi>e<\/mi><mi>m<\/mi><mo stretchy=\"false\">[<\/mo><mi>l<\/mi><mo stretchy=\"false\">]<\/mo><mi mathvariant=\"normal\">.<\/mi><mi>k<\/mi><mi>e<\/mi><mi>y<\/mi><\/mrow><\/mfrac><mo stretchy=\"false\">(<\/mo><mi>h<\/mi><mo>&#x2212;<\/mo><mi>l<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">i =\\frac{Key&#x2212;ST.elem[l].key}{ST.elem[h].key&#x2212;ST.elem[l].key}(h &#x2212; l + 1)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6595em;\"><\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.363em;vertical-align:-0.936em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">ST<\/span><span class=\"mord\">.<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mclose\">]<\/span><span class=\"mord\">.<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">ey<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">ST<\/span><span class=\"mord\">.<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose\">]<\/span><span class=\"mord\">.<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">ey<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">Key<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">ST<\/span><span class=\"mord\">.<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mclose\">]<\/span><span class=\"mord\">.<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">ey<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">h<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br>\n&#x9002;&#x7528;&#x4E8E;&#x5173;&#x952E;&#x5B57;&#x5747;&#x5300;&#x5206;&#x5E03;<\/p>\n<h3 class=\"mume-header\" id=\"%E6%AC%A1%E4%BC%98%E4%BA%8C%E5%8F%89%E6%A0%91\">&#x6B21;&#x4F18;&#x4E8C;&#x53C9;&#x6811;<\/h3>\n\n<p>&#x6BCF;&#x6B21;&#x53D6;&#x4E0B;&#x503C;&#x6700;&#x5C0F;&#x7684;&#x8282;&#x70B9;&#x4F5C;&#x4E3A;&#x65B0;&#x7684;&#x6839;&#x8282;&#x70B9;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">&#x394;<\/mi><msub><mi>P<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mi mathvariant=\"normal\">&#x2223;<\/mi><munderover><mo>&#x2211;<\/mo><mrow><mi>j<\/mi><mo>=<\/mo><mi>i<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><mi>h<\/mi><\/munderover><msub><mi>w<\/mi><mi>j<\/mi><\/msub><mo>&#x2212;<\/mo><munderover><mo>&#x2211;<\/mo><mrow><mi>j<\/mi><mo>=<\/mo><mi>l<\/mi><\/mrow><mrow><mi>i<\/mi><mo>&#x2212;<\/mo><mn>1<\/mn><\/mrow><\/munderover><msub><mi>w<\/mi><mi>j<\/mi><\/msub><mi mathvariant=\"normal\">&#x2223;<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\Delta P_i=|\\sum_{j=i+1}^h w_j-\\sum_{j=l}^{i-1}w_j|<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\">&#x394;<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.13889em;\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:3.2499em;vertical-align:-1.4138em;\"><\/span><span class=\"mord\">&#x2223;<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.8361em;\"><span style=\"top:-1.8723em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4138em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:3.2499em;vertical-align:-1.4382em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.8117em;\"><span style=\"top:-1.8479em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right:0.01968em;\">l<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mbin mtight\">&#x2212;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4382em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">&#x2223;<\/span><\/span><\/span><\/span><\/span><br>\n&#x9700;&#x8981;&#x9884;&#x5148;&#x6C42;&#x5F97;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>w<\/mi><mi>j<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">w_j<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.7167em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x7684;&#x524D;&#x7F00;&#x548C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>s<\/mi><msub><mi>w<\/mi><mi>j<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">sw_j<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.7167em;vertical-align:-0.2861em;\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.02691em;\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x6570;&#x7EC4;<\/p>\n<h3 class=\"mume-header\" id=\"%E7%B4%A2%E5%BC%95%E9%A1%BA%E5%BA%8F%E6%9F%A5%E6%89%BE%E5%88%86%E5%9D%97%E6%9F%A5%E6%89%BE\">&#x7D22;&#x5F15;&#x987A;&#x5E8F;&#x67E5;&#x627E;\/&#x5206;&#x5757;&#x67E5;&#x627E;<\/h3>\n\n<p>&#x9644;&#x52A0;&#x4E00;&#x4E2A;&#x7D22;&#x5F15;&#x8868;&#xFF0C;&#x5757;&#x95F4;&#x6709;&#x5E8F;&#xFF0C;&#x5757;&#x5185;&#x65E0;&#x5E8F;<br>\n&#x5F53;&#x6BCF;&#x5757;&#x8BB0;&#x5F55;&#x6570;&#x4E3A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>s<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">s<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span>&#x65F6;<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mi>S<\/mi><mi>L<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mfrac><mi>n<\/mi><mi>s<\/mi><\/mfrac><mo>+<\/mo><mi>s<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">ASL=\\frac{1}{2}(\\frac{n}{s}+s)+1<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05764em;\">S<\/span><span class=\"mord mathnormal\">L<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.1901em;vertical-align:-0.345em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8451em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6954em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E5%8A%A8%E6%80%81%E6%9F%A5%E6%89%BE%E8%A1%A8\">&#x52A8;&#x6001;&#x67E5;&#x627E;&#x8868;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E4%BA%8C%E5%8F%89%E6%8E%92%E5%BA%8F%E6%A0%91bst\">&#x4E8C;&#x53C9;&#x6392;&#x5E8F;&#x6811;&#xFF08;BST&#xFF09;<\/h3>\n\n<p>&#x8282;&#x70B9;p&#x5220;&#x9664;&#xFF1A;<br>\n&#x65B9;&#x6CD5;&#x4E00;&#xFF1A;&#x7528;p&#x7684;&#x76F4;&#x63A5;&#x524D;&#x9A71;&#xFF08;&#x6216;&#x76F4;&#x63A5;&#x540E;&#x7EE7;&#xFF09;&#x8282;&#x70B9;s&#x4EE3;&#x66FF;p&#xFF0C;&#x7136;&#x540E;&#x5220;&#x9664;s<br>\n&#x65B9;&#x6CD5;&#x4E8C;&#xFF1A;&#x53D6;s&#x4E3A;p&#x7684;&#x5DE6;&#x5B50;&#x6811;&#x4E2D;&#x6700;&#x53F3;&#x7684;&#x8282;&#x70B9;&#xFF0C;&#x5C06;p&#x7684;&#x53F3;&#x5B50;&#x6811;&#x4F5C;&#x4E3A;s&#x7684;&#x53F3;&#x5B50;&#x6811;<\/p>\n<h3 class=\"mume-header\" id=\"%E5%B9%B3%E8%A1%A1%E4%BA%8C%E5%8F%89%E6%8E%92%E5%BA%8F%E6%A0%91avl\">&#x5E73;&#x8861;&#x4E8C;&#x53C9;&#x6392;&#x5E8F;&#x6811;&#xFF08;AVL&#xFF09;<\/h3>\n\n<p>&#x8282;&#x70B9;&#x7684;&#x5E73;&#x8861;&#x56E0;&#x5B50;bf&#xFF08;Balance Factor&#xFF09;=&#x5DE6;&#x5B50;&#x6811;&#x6DF1;&#x5EA6;-&#x53F3;&#x5B50;&#x6811;&#x6DF1;&#x5EA6;<\/p>\n<h4 class=\"mume-header\" id=\"avl%E6%A0%91%E7%9A%84%E6%8F%92%E5%85%A5\">AVL&#x6811;&#x7684;&#x63D2;&#x5165;<\/h4>\n\n<p>&#x63D2;&#x5165;&#x65B0;&#x7ED3;&#x70B9;&#x65F6;&#xFF0C;&#x4ECE;&#x63D2;&#x5165;&#x4F4D;&#x7F6E;&#x5411;&#x6839;&#x56DE;&#x6EAF;&#xFF0C;&#x68C0;&#x67E5;&#x5404;&#x8282;&#x70B9;&#x5E73;&#x8861;&#x56E0;&#x5B50;<br>\n&#x4ECE;&#x53D1;&#x751F;&#x4E0D;&#x5E73;&#x8861;&#x7684;&#x8282;&#x70B9;&#x8D77;&#xFF0C;&#x6CBF;&#x521A;&#x624D;&#x56DE;&#x6EAF;&#x7684;&#x8DEF;&#x5F84;&#x53D6;&#x76F4;&#x63A5;&#x4E0B;&#x4E24;&#x5C42;&#x7684;&#x8282;&#x70B9;<br>\n&#x82E5;&#x8FD9;&#x4E09;&#x4E2A;&#x8282;&#x70B9;&#x5904;&#x4E8E;&#x4E00;&#x6761;&#x76F4;&#x7EBF;&#x4E0A;&#xFF0C;&#x5219;&#x91C7;&#x7528;&#x5355;&#x65CB;&#x8F6C;&#x8FDB;&#x884C;&#x5E73;&#x8861;&#x5316;<br>\n&#x82E5;&#x8FD9;&#x4E09;&#x4E2A;&#x8282;&#x70B9;&#x5904;&#x4E8E;&#x4E00;&#x6761;&#x6298;&#x7EBF;&#x4E0A;&#xFF0C;&#x5219;&#x91C7;&#x7528;&#x53CC;&#x65CB;&#x8F6C;&#x8FDB;&#x884C;&#x5E73;&#x8861;&#x5316;<\/p>\n<h4 class=\"mume-header\" id=\"avl%E6%A0%91%E7%9A%84%E5%88%A0%E9%99%A4\">AVL&#x6811;&#x7684;&#x5220;&#x9664;<\/h4>\n\n<ol>\n<li>&#x82E5;&#x5220;&#x9664;&#x7684;&#x8282;&#x70B9;&#x4E3A;&#x53F6;&#x5B50;&#x7ED3;&#x70B9;&#xFF0C;&#x5219;&#x76F4;&#x63A5;&#x5220;&#x9664;&#xFF0C;&#x7136;&#x540E;&#x4E00;&#x6B21;&#x5411;&#x4E0A;&#x8C03;&#x6574;&#x4E3A;AVL&#x6811;<\/li>\n<li>&#x82E5;&#x5220;&#x9664;&#x7684;&#x8282;&#x70B9;&#x53EA;&#x6709;&#x5DE6;&#x5B69;&#x5B50;&#x6216;&#x53F3;&#x5B69;&#x5B50;&#xFF0C;&#x5219;&#x7528;&#x5B69;&#x5B50;&#x66FF;&#x6362;<\/li>\n<li>otherwise&#xFF0C;&#x7528;&#x5DE6;&#x5B50;&#x6811;&#x7684;&#x6700;&#x53F3;&#x8282;&#x70B9;&#x66FF;&#x6362;&#x4E3A;&#x5220;&#x9664;&#x8282;&#x70B9;&#xFF0C;&#x7136;&#x540E;&#x5220;&#x9664;&#x5DE6;&#x5B50;&#x6811;&#x7684;&#x6700;&#x53F3;&#x8282;&#x70B9;&#xFF08;&#x8F6C;&#x6362;&#x4E3A;&#x60C5;&#x51B5;1&#xFF09;<\/li>\n<\/ol>\n<h3 class=\"mume-header\" id=\"b%E6%A0%91bt\">B&#x6811;&#xFF08;BT&#xFF09;<\/h3>\n\n<p>&#x76EE;&#x7684;&#xFF1A;&#x964D;&#x4F4E;&#x78C1;&#x76D8;I\/O&#x6B21;&#x6570;<br>\n&#x5E73;&#x8861;&#x7684;&#x591A;&#x8DEF;&#x67E5;&#x627E;&#x6811;<br>\nm&#x9636;B&#x6811;&#x6240;&#x6709;&#x975E;&#x53F6;&#x8282;&#x70B9;&#x5747;&#x81F3;&#x5C11;&#x542B;&#x6709;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">&#x2308;<\/mo><mi>m<\/mi><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><mo stretchy=\"false\">&#x2309;<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\lceil m\/2\\rceil<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mopen\">&#x2308;<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord\">\/2<\/span><span class=\"mclose\">&#x2309;<\/span><\/span><\/span><\/span>&#x68F5;&#x5B50;&#x6811;&#xFF0C;&#x6700;&#x591A;&#x542B;&#x6709;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>m<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">m<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span>&#x68F5;&#x5B50;&#x6811;<br>\n&#x6BCF;&#x4E2A;&#x8282;&#x70B9;&#x5305;&#x542B;m&#x4E2A;&#x5173;&#x952E;&#x5B57;&#xFF0C;m&#x4E2A;&#x8BB0;&#x5F55;&#x6307;&#x9488;&#x5411;&#x91CF;&#xFF0C;m+1&#x4E2A;&#x5B50;&#x6811;&#x6307;&#x9488;&#x5411;&#x91CF;<br>\n<strong>&#x6240;&#x6709;&#x53F6;&#x5B50;&#x7ED3;&#x70B9;&#x90FD;&#x5728;&#x6811;&#x7684;&#x540C;&#x4E00;&#x5C42;&#x4E0A;<\/strong><br>\n&#x53F6;&#x5B50;&#x7ED3;&#x70B9;&#x6570;=&#x603B;&#x5173;&#x952E;&#x5B57;&#x6570;+1<\/p>\n<h4 class=\"mume-header\" id=\"b%E6%A0%91%E7%9A%84%E6%8F%92%E5%85%A5\">B&#x6811;&#x7684;&#x63D2;&#x5165;<\/h4>\n\n<p>&#x9996;&#x5148;&#x68C0;&#x67E5;&#x5728;B&#x6811;&#x4E2D;&#x662F;&#x5426;&#x5B58;&#x5728;&#xFF0C;&#x82E5;&#x4E0D;&#x5B58;&#x5728;&#xFF0C;&#x5373;&#x5728;&#x53F6;&#x5B50;&#x7ED3;&#x70B9;&#x5904;&#x7ED3;&#x675F;&#xFF0C;&#x5219;&#x5728;&#x53F6;&#x5B50;&#x7ED3;&#x70B9;&#x4E2D;&#x63D2;&#x5165;&#x65B0;&#x5143;&#x7D20;&#x3002;&#x6839;&#x636E;&#x8BE5;&#x8282;&#x70B9;&#x5143;&#x7D20;&#x4E2A;&#x6570;&#x5224;&#x65AD;&#x662F;&#x5426;&#x9700;&#x8981;&#x5206;&#x88C2;&#x3002;<\/p>\n<h4 class=\"mume-header\" id=\"b%E6%A0%91%E7%9A%84%E5%88%A0%E9%99%A4\">B&#x6811;&#x7684;&#x5220;&#x9664;<\/h4>\n\n<p>&#x770B;&#x76F8;&#x90BB;&#x5144;&#x5F1F;&#x662F;&#x5426;&#x4E30;&#x6EE1;<br>\n&#x82E5;&#x4E30;&#x6EE1;&#xFF0C;&#x5219;&#x5411;&#x7236;&#x8282;&#x70B9;&#x501F;&#x5143;&#x7D20;&#xFF0C;&#x7236;&#x8282;&#x70B9;&#x5411;&#x76F8;&#x90BB;&#x5144;&#x5F1F;&#x501F;&#x5143;&#x7D20;<br>\n&#x82E5;&#x5747;&#x4E0D;&#x4E30;&#x6EE1;&#xFF0C;&#x5219;&#x4E0E;&#x76F8;&#x90BB;&#x7684;&#x67D0;&#x4E00;&#x5144;&#x5F1F;&#x5408;&#x5E76;&#x6210;&#x4E00;&#x4E2A;&#x8282;&#x70B9;<\/p>\n<h3 class=\"mume-header\" id=\"b%E6%A0%91\">B+&#x6811;<\/h3>\n\n<p>&#x6240;&#x6709;&#x975E;&#x53F6;&#x8282;&#x70B9;&#x4E3A;&#x7D22;&#x5F15;&#xFF0C;&#x53F6;&#x5B50;&#x7ED3;&#x70B9;&#x5305;&#x542B;&#x4E86;&#x6240;&#x6709;&#x5173;&#x952E;&#x5B57;<br>\n&#x975E;&#x53F6;&#x8282;&#x70B9;&#x4EC5;&#x542B;&#x5176;&#x5B50;&#x6811;&#x6839;&#x8282;&#x70B9;&#x4E2D;&#x6700;&#x5927;&#x5173;&#x952E;&#x5B57;<br>\n&#x4F18;&#x70B9;&#xFF1A;<\/p>\n<ol>\n<li>&#x78C1;&#x76D8;&#x8BFB;&#x5199;&#x4EE3;&#x4EF7;&#x4F4E;<\/li>\n<li>&#x67E5;&#x8BE2;&#x6548;&#x7387;&#x7A33;&#x5B9A;<\/li>\n<li>&#x4FBF;&#x4E8E;&#x8303;&#x56F4;&#x67E5;&#x8BE2;<\/li>\n<\/ol>\n<h3 class=\"mume-header\" id=\"%E9%94%AE%E6%A0%91\">&#x952E;&#x6811;<\/h3>\n\n<p>&#x53CC;&#x94FE;&#x6811;<br>\nTrie&#x6811;<\/p>\n<h2 class=\"mume-header\" id=\"%E5%93%88%E5%B8%8C%E8%A1%A8\">&#x54C8;&#x5E0C;&#x8868;<\/h2>\n\n<p>&#x5408;&#x9002;&#x7684;&#x54C8;&#x5E0C;&#x51FD;&#x6570;&#xFF1A;&#x51FD;&#x6570;&#x503C;&#x80FD;&#x5C3D;&#x53EF;&#x80FD;&#x8986;&#x76D6;&#x6574;&#x4E2A;&#x5730;&#x5740;&#x7A7A;&#x95F4;&#x4E14;&#x5747;&#x5300;&#x5730;&#x6620;&#x5C04;&#x5230;&#x5730;&#x5740;&#x7A7A;&#x95F4;&#xFF0C;&#x4F7F;&#x5F97;&#x53D1;&#x751F;&#x51B2;&#x7A81;&#x7684;&#x53EF;&#x80FD;&#x6027;&#x5C3D;&#x53EF;&#x80FD;&#x6700;&#x5C11;<\/p>\n<h3 class=\"mume-header\" id=\"%E5%93%88%E5%B8%8C%E5%87%BD%E6%95%B0%E7%9A%84%E6%9E%84%E9%80%A0\">&#x54C8;&#x5E0C;&#x51FD;&#x6570;&#x7684;&#x6784;&#x9020;<\/h3>\n\n<h4 class=\"mume-header\" id=\"%E7%9B%B4%E6%8E%A5%E5%AE%9A%E5%9D%80%E6%B3%95\">&#x76F4;&#x63A5;&#x5B9A;&#x5740;&#x6CD5;<\/h4>\n\n<h4 class=\"mume-header\" id=\"%E6%95%B0%E5%AD%97%E5%88%86%E6%9E%90%E6%B3%95\">&#x6570;&#x5B57;&#x5206;&#x6790;&#x6CD5;<\/h4>\n\n<p>&#x8BA1;&#x7B97;&#x5404;&#x4F4D;&#x6570;&#x5B57;&#x4E2D;&#x7B26;&#x53F7;&#x5206;&#x5E03;&#x5747;&#x5300;&#x5EA6;<br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>&#x3BB;<\/mi><mi>k<\/mi><\/msub><mo>=<\/mo><munderover><mo>&#x2211;<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>r<\/mi><\/munderover><mo stretchy=\"false\">(<\/mo><msubsup><mi>a<\/mi><mi>i<\/mi><mi>k<\/mi><\/msubsup><mo>&#x2212;<\/mo><mi>n<\/mi><mi mathvariant=\"normal\">\/<\/mi><mi>r<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda_k=\\sum_{i=1}^r(a_i^k-n\/r)^2<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">&#x3BB;<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:2.9291em;vertical-align:-1.2777em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6514em;\"><span style=\"top:-1.8723em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span style=\"top:-3.05em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span><span class=\"mop op-symbol large-op\">&#x2211;<\/span><\/span><\/span><span style=\"top:-4.3em;margin-left:0em;\"><span class=\"pstrut\" style=\"height:3.05em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.02778em;\">r<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.2777em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8991em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1.1141em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">r<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br>\n&#x5176;&#x4E2D;&#xFF0C;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msubsup><mi>a<\/mi><mi>i<\/mi><mi>k<\/mi><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">a_i^k<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.1078em;vertical-align:-0.2587em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8491em;\"><span style=\"top:-2.4413em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2587em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#x8868;&#x793A;&#x7B2C;i&#x4E2A;&#x7B26;&#x53F7;&#x5728;&#x7B2C;k&#x4F4D;&#x4E0A;&#x51FA;&#x73B0;&#x7684;&#x6B21;&#x6570;&#xFF0C;<br>\nn\/r &#x8868;&#x793A;&#x5404;&#x79CD;&#x7B26;&#x53F7;&#x5728; n &#x4E2A;&#x6570;&#x4E2D;&#x5747;&#x5300;&#x51FA;&#x73B0;&#x7684;&#x671F;&#x671B;&#x503C;<br>\n&#x8BA1;&#x7B97;&#x51FA;&#x7684;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>&#x3BB;<\/mi><mi>k<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\lambda_k<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" 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class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><\/span><\/span><\/span><br>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>&#x3B1;<\/mi><mo>=<\/mo><mfrac><mtext>&#x8868;&#x4E2D;&#x586B;&#x5165;&#x7684;&#x8BB0;&#x5F55;&#x6570;<\/mtext><mtext>&#x54C8;&#x5E0C;&#x8868;&#x957F;&#x5EA6;<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha=\\frac{&#x8868;&#x4E2D;&#x586B;&#x5165;&#x7684;&#x8BB0;&#x5F55;&#x6570;}{&#x54C8;&#x5E0C;&#x8868;&#x957F;&#x5EA6;}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">&#x3B1;<\/span><span class=\"mspace\" 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id=\"%E6%9C%89%E5%90%91%E5%9B%BE%E7%9A%84%E5%BC%BA%E8%BF%9E%E9%80%9A%E5%88%86%E9%87%8F\">&#x6709;&#x5411;&#x56FE;&#x7684;&#x5F3A;&#x8FDE;&#x901A;&#x5206;&#x91CF;<\/h3>\n\n<ol>\n<li>&#x5BF9;&#x539F;&#x56FE;&#x53D6;&#x53CD;&#xFF0C;&#x4ECE;&#x4EFB;&#x610F;&#x4E00;&#x4E2A;&#x9876;&#x70B9;&#x5F00;&#x59CB;&#x5BF9;&#x53CD;&#x5411;&#x56FE;&#x8FDB;&#x884C;&#x9006;&#x540E;&#x7EED;DFS&#x904D;&#x5386;<\/li>\n<li>&#x6309;&#x7167;&#x9006;&#x540E;&#x7EED;&#x904D;&#x5386;&#x4E2D;&#x6808;&#x4E2D;&#x7684;&#x9876;&#x70B9;&#x51FA;&#x6808;&#x987A;&#x5E8F;&#xFF0C;&#x5BF9;&#x539F;&#x56FE;&#x8FDB;&#x884C;DFS&#x904D;&#x5386;&#xFF0C;&#x4E00;&#x6B21;DFS&#x904D;&#x5386;&#x4E2D;&#x8BBF;&#x95EE;&#x7684;&#x6240;&#x6709;&#x9876;&#x70B9;&#x90FD;&#x5C5E;&#x4E8E;&#x540C;&#x4E00;&#x5F3A;&#x8FDE;&#x901A;&#x5206;&#x91CF;<\/li>\n<\/ol>\n<p>&#x4E0D;&#x8BBA;&#x4ECE;&#x54EA;&#x4E2A;&#x9876;&#x70B9;&#x5F00;&#x59CB;&#xFF0C;&#x56FE;&#x4E2D;&#x6709;&#x591A;&#x5C11;&#x4E2A;&#x5F3A;&#x8FDE;&#x901A;&#x5206;&#x91CF;&#xFF0C;&#x9006;&#x540E;&#x7EED;&#x904D;&#x5386;&#x7684;&#x6808;&#x4E2D;&#x9876;&#x70B9;&#x7684;&#x987A;&#x5E8F;&#x4E00;&#x5B9A;&#x4F1A;&#x4FDD;&#x8BC1;&#xFF1A;<strong>&#x88AB;&#x6307;&#x5411;&#x7684;&#x5F3A;&#x8FDE;&#x901A;&#x5206;&#x91CF;&#x7684;&#x81F3;&#x5C11;&#x4E00;&#x4E2A;&#x9876;&#x70B9;&#x6392;&#x5728;&#x6307;&#x5411;&#x8FD9;&#x4E2A;&#x8FDE;&#x901A;&#x5206;&#x91CF;&#x7684;&#x6240;&#x6709;&#x9876;&#x70B9;&#x524D;&#x9762;&#x3002;<\/strong><\/p>\n<h3 class=\"mume-header\" id=\"%E6%9C%80%E5%B0%8F%E7%94%9F%E6%88%90%E6%A0%91minimum-cost-spanning-tree\">&#x6700;&#x5C0F;&#x751F;&#x6210;&#x6811;&#xFF08;Minimum Cost Spanning Tree&#xFF09;<\/h3>\n\n<h4 class=\"mume-header\" id=\"prim%E7%AE%97%E6%B3%95\">Prim&#x7B97;&#x6CD5;<\/h4>\n\n<p><strong>&#x9010;&#x6B65;&#x6DFB;&#x52A0;&#x7ED3;&#x70B9;<\/strong>w&#xFF0C;w&#x8981;&#x6EE1;&#x8DB3;&#xFF1A;&#x65B0;&#x6DFB;&#x52A0;&#x7684;w&#x548C;&#x5DF2;&#x7ECF;&#x5728;&#x751F;&#x6210;&#x6811;&#x4E0A;&#x7684;&#x9876;&#x70B9;v&#x4E4B;&#x95F4;&#x5B58;&#x5728;&#x4E00;&#x6761;&#x8FB9;&#xFF0C;&#x8BE5;&#x8FB9;&#x7684;&#x6743;&#x503C;&#x5728;&#x6240;&#x6709;&#x8FDE;&#x901A;&#x9876;&#x70B9;w&#x548C;v&#x4E4B;&#x95F4;&#x7684;&#x8FB9;&#x4E2D;&#x53D6;&#x503C;&#x6700;&#x5C0F;<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n^2)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.0641em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#xFF0C;&#x9002;&#x7528;&#x4E8E;&#x7A20;&#x5BC6;&#x56FE;<\/p>\n<h4 class=\"mume-header\" id=\"kruskal%E7%AE%97%E6%B3%95\">Kruskal&#x7B97;&#x6CD5;<\/h4>\n\n<p>&#x5148;&#x6784;&#x9020;&#x4E00;&#x4E2A;&#x53EA;&#x542B; n &#x4E2A;&#x9876;&#x70B9;&#x7684;&#x5B50;&#x56FE; SG&#xFF0C;&#x7136;&#x540E;&#x4ECE;&#x6743;&#x503C;&#x6700;&#x5C0F;&#x7684;&#x8FB9;&#x5F00;&#x59CB;&#xFF0C;&#x82E5;&#x6DFB;&#x52A0;&#x5B83;&#x4E0D;&#x4F1A;&#x4F7F;&#x5F97;SG &#x4E2D;&#x4EA7;&#x751F;&#x56DE;&#x8DEF;&#xFF0C;&#x5219;&#x5728; SG &#x4E0A;<strong>&#x52A0;&#x4E0A;&#x8FD9;&#x6761;&#x8FB9;<\/strong>&#xFF0C;&#x5982;&#x6B64;&#x91CD;&#x590D;&#xFF0C;&#x76F4;&#x81F3;&#x52A0;&#x4E0A; n-1 &#x6761;&#x8FB9;&#x4E3A;&#x6B62;<\/p>\n<p>&#x8003;&#x8651;&#x5230;&#x9700;&#x8981;&#x5BF9;&#x8FB9;&#x8FDB;&#x884C;&#x6392;&#x5E8F;&#xFF0C;&#x53EF;&#x4EE5;&#x7528;&#x5806;&#x5B58;&#x653E;&#x8FB9;&#xFF0C;&#x4F7F;&#x5F97;&#x6BCF;&#x6B21;&#x9009;&#x53D6;&#x6700;&#x5C0F;&#x6743;&#x503C;&#x7684;&#x8FB9;&#x4EC5;&#x9700;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>l<\/mi><mi>o<\/mi><mi>g<\/mi><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(loge)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">g<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<p>&#x5173;&#x952E;&#xFF1A;&#x5224;&#x65AD;&#x56DE;&#x8DEF;&#xFF08;&#x5C06;&#x751F;&#x6210;&#x6811;T&#x7684;&#x8FDE;&#x901A;&#x5206;&#x91CF;&#x770B;&#x6210;&#x7B49;&#x4EF7;&#x7C7B;&#xFF0C;&#x5E76;&#x67E5;&#x96C6;&#xFF09;<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>e<\/mi><mi>log<\/mi><mo>&#x2061;<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(e\\log{e})<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mop\">lo<span style=\"margin-right:0.01389em;\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#xFF0C;&#x9002;&#x7528;&#x4E8E;&#x7A00;&#x758F;&#x56FE;<\/p>\n<h3 class=\"mume-header\" id=\"%E5%85%B3%E8%8A%82%E7%82%B9%E5%92%8C%E9%87%8D%E8%BF%9E%E9%80%9A%E5%88%86%E9%87%8F\">&#x5173;&#x8282;&#x70B9;&#x548C;&#x91CD;&#x8FDE;&#x901A;&#x5206;&#x91CF;<\/h3>\n\n<p>&#x91CD;&#x8FDE;&#x901A;&#x56FE;&#xFF1A;&#x6CA1;&#x6709;&#x5173;&#x8282;&#x70B9;&#x7684;&#x8FDE;&#x901A;&#x56FE;<\/p>\n<p>&#x8FDE;&#x901A;&#x5EA6;k&#xFF1A;&#x8FDE;&#x901A;&#x56FE;&#x4E0A;&#x81F3;&#x5C11;&#x5220;&#x53BB;k&#x4E2A;&#x9876;&#x70B9;&#x624D;&#x80FD;&#x7834;&#x574F;&#x56FE;&#x7684;&#x8FDE;&#x901A;&#x6027;<br>\n&#x4E00;&#x4E2A;&#x8868;&#x793A;&#x901A;&#x4FE1;&#x7F51;&#x7EDC;&#x7684;&#x56FE;&#x7684;&#x8FDE;&#x901A;&#x5EA6;&#x8D8A;&#x9AD8;&#xFF0C;&#x5176;&#x7CFB;&#x7EDF;&#x8D8A;&#x53EF;&#x9AD8;<\/p>\n<ol>\n<li>\n<p>&#x82E5;&#x751F;&#x6210;&#x6811;&#x7684;&#x6839;&#x7ED3;&#x70B9;&#x6709;&#x4E24;&#x4E2A;&#x6216;&#x4E24;&#x4E2A;&#x4EE5;&#x4E0A;&#x7684;&#x5206;&#x652F;&#xFF0C;&#x5219;&#x6B64;&#x9876;&#x70B9;(&#x751F;&#x6210;&#x6811;&#x7684;&#x6839;)&#x5FC5;&#x4E3A;&#x5173;&#x8282;&#x70B9;<\/p>\n<\/li>\n<li>\n<p>&#x5BF9;&#x751F;&#x6210;&#x6811;&#x4E0A;&#x7684;&#x4EFB;&#x610F;&#x4E00;&#x4E2A;&#x5185;&#x90E8;&#x7ED3;&#x70B9;v(&#x975E;&#x53F6;&#x5B50;&#x7ED3;&#x70B9;)&#xFF0C;&#x82E5;&#x5176;&#x67D0;&#x68F5;&#x5B50;&#x6811;&#x7684;&#x6839;&#x6216;&#x5B50;&#x6811;&#x4E2D;&#x7684;&#x5176;&#x5B83;&#x7ED3;&#x70B9;&#x6CA1;&#x6709;&#x548C;v&#x7956;&#x5148;&#x76F8;&#x901A;&#x7684;&#x56DE;&#x8FB9;&#xFF0C;&#x5219;&#x8BE5;&#x7ED3;&#x70B9;v&#x5FC5;&#x4E3A;&#x5173;&#x8282;&#x70B9;<\/p>\n<\/li>\n<\/ol>\n<p>&#x5B9A;&#x4E49;&#xFF1A;<\/p>\n<ul>\n<li>low(v) = Min{visited[v], low[w], visited[k] }<\/li>\n<li>&#x5176;&#x4E2D;\n<ul>\n<li>&#x9876;&#x70B9;w &#x662F;&#x751F;&#x6210;&#x6811;&#x4E0A;&#x9876;&#x70B9;v&#x7684;&#x5B69;&#x5B50;<\/li>\n<li>&#x9876;&#x70B9;k &#x662F;&#x751F;&#x6210;&#x6811;&#x4E0A;&#x548C;&#x9876;&#x70B9;v&#x7531;&#x56DE;&#x8FB9;&#x76F8;&#x8054;&#x63A5;&#x7684;&#x7956;&#x5148;<\/li>\n<li>visited&#x8BB0;&#x5F55;&#x6DF1;&#x5EA6;&#x4F18;&#x5148;&#x751F;&#x6210;&#x6811;&#x7684;&#x524D;&#x5E8F;&#x5E8F;&#x5217;&#x4E2D;&#x7684;&#x5E8F;&#x53F7;<\/li>\n<li>low&#x7531;&#x540E;&#x7EED;&#x904D;&#x5386;&#x6DF1;&#x5EA6;&#x4F18;&#x5148;&#x751F;&#x6210;&#x6811;&#x6C42;&#x5F97;<\/li>\n<\/ul>\n<\/li>\n<li>&#x82E5;&#x5BF9;&#x9876;&#x70B9;v&#xFF0C;&#x5728;&#x751F;&#x6210;&#x6811;&#x4E0A;&#x5B58;&#x5728;&#x4E00;&#x4E2A;&#x5B50;&#x6811;&#x6839;w&#xFF0C; &#x4E14;low[w] &#x2265; visited[v]&#xFF0C;&#x5219;&#x9876;&#x70B9;v&#x4E3A;&#x5173;&#x8282;&#x70B9;<\/li>\n<\/ul>\n<h2 class=\"mume-header\" id=\"%E6%9C%89%E5%90%91%E6%97%A0%E7%8E%AF%E5%9B%BE\">&#x6709;&#x5411;&#x65E0;&#x73AF;&#x56FE;<\/h2>\n\n<h3 class=\"mume-header\" id=\"aov%E7%BD%91%E7%9A%84%E6%8B%93%E6%89%91%E6%8E%92%E5%BA%8F\">AOV&#x7F51;&#x7684;&#x62D3;&#x6251;&#x6392;&#x5E8F;<\/h3>\n\n<p>&#x6709;&#x5411;&#x65E0;&#x73AF;&#x56FE;&#xFF08;directed acycline graph, DAG&#xFF09;<br>\nAOV&#x7F51;&#xFF08;Activity on Vertex Network&#xFF09;<\/p>\n<p>&#x7B97;&#x6CD5;&#xFF1A;<\/p>\n<ol>\n<li>&#x5728;AOV&#x7F51;&#x4E2D;&#x9009;&#x62E9;&#x4E00;&#x4E2A;&#x6CA1;&#x6709;&#x524D;&#x9A71;&#x7684;&#x9876;&#x70B9;&#x5E76;&#x8F93;&#x51FA;<\/li>\n<li>&#x5728;AOV&#x7F51;&#x4E2D;&#x5220;&#x9664;&#x8BE5;&#x9876;&#x70B9;&#x4EE5;&#x53CA;&#x4ECE;&#x8BE5;&#x9876;&#x70B9;&#x51FA;&#x53D1;&#x7684;(&#x4EE5;&#x8BE5;&#x9876;&#x70B9;&#x4E3A;&#x5C3E;&#x7684;&#x5F27;)&#x6240;&#x6709;&#x6709;&#x5411;&#x5F27;(&#x8FB9;)<\/li>\n<li>&#x91CD;&#x590D;&#x6267;&#x884C;&#x524D;&#x4E24;&#x6B65;&#xFF0C;&#x76F4;&#x5230;&#x56FE;&#x4E2D;&#x5168;&#x90E8;&#x9876;&#x70B9;&#x90FD;&#x5DF2;&#x8F93;&#x51FA;(&#x56FE;&#x4E2D;&#x65E0;&#x73AF;)&#x6216;&#x56FE;&#x4E2D;&#x4E0D;&#x5B58;&#x5728;&#x65E0;&#x524D;&#x9A71;&#x7684;&#x9876;&#x70B9;(&#x56FE;&#x4E2D;&#x5FC5;&#x6709;&#x73AF;)<\/li>\n<\/ol>\n<p>&#x8BBE;&#x7ACB;&#x6808;&#xFF0C;&#x7528;&#x6765;&#x6682;&#x5B58;&#x5165;&#x5EA6;&#x4E3A;0&#x7684;&#x9876;&#x70B9;<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n+e)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>&#xFF1A;<\/p>\n<ul>\n<li>&#x7EDF;&#x8BA1;&#x5404;&#x9876;&#x70B9;&#x7684;&#x5165;&#x5EA6;&#xFF1A;&#x65F6;&#x95F4;&#x590D;&#x6742;&#x5EA6;&#x662F;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n+e)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#xFF1B;<\/li>\n<li>&#x5165;&#x5EA6;&#x4E3A;0&#x7684;&#x9876;&#x70B9;&#x5165;&#x6808;&#xFF1A;&#x65F6;&#x95F4;&#x590D;&#x6742;&#x5EA6;&#x662F;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> &#xFF1B;<\/li>\n<li>&#x6392;&#x5E8F;&#x8FC7;&#x7A0B;&#xFF1A;&#x9876;&#x70B9;&#x5165;&#x6808;&#x548C;&#x51FA;&#x6808;&#x64CD;&#x4F5C;&#x6267;&#x884C;n&#x6B21;&#xFF0C;&#x5165;&#x5EA6;&#x51CF;1&#x7684;&#x64CD;&#x4F5C;&#x5171;&#x6267;&#x884C;e&#x6B21;&#xFF0C;&#x65F6;&#x95F4;&#x590D;&#x6742;&#x5EA6;&#x662F;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n+e)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p>&#x6709;&#x5411;&#x56FE;&#x65E0;&#x73AF;&#x65F6;&#xFF0C;&#x4E5F;&#x53EF;&#x5229;&#x7528;&#x6DF1;&#x5EA6;&#x4F18;&#x5148;&#x904D;&#x5386;&#x8FDB;&#x884C;&#x62D3;&#x6251;&#x6392;&#x5E8F;<\/p>\n<h3 class=\"mume-header\" id=\"aoe%E7%BD%91%E7%9A%84%E5%85%B3%E9%94%AE%E8%B7%AF%E5%BE%84\">AOE&#x7F51;&#x7684;&#x5173;&#x952E;&#x8DEF;&#x5F84;<\/h3>\n\n<p>AOE&#x7F51;&#xFF08;Activity On Edge Network&#xFF09;<\/p>\n<p>&#x5B9A;&#x4E49;&#xFF1A;<\/p>\n<ul>\n<li>e(i)&#x8868;&#x793A;&#x6D3B;&#x52A8;ai&#x7684;&#x6700;&#x65E9;&#x5F00;&#x59CB;&#x65F6;&#x95F4;<\/li>\n<li>l(i)&#x8868;&#x793A;&#x5728;&#x4E0D;&#x5F71;&#x54CD;&#x8FDB;&#x5EA6;&#x7684;&#x524D;&#x63D0;&#x4E0B;&#xFF0C;&#x6D3B;&#x52A8;ai&#x7684;&#x6700;&#x665A;&#x5F00;&#x59CB;&#x65F6;&#x95F4;<\/li>\n<\/ul>\n<p>&#x5219;&#xFF1A;l(i)-e(i)&#x8868;&#x793A;&#x6D3B;&#x52A8;ai&#x7684;&#x65F6;&#x95F4;&#x4F59;&#x91CF;&#xFF0C;&#x82E5;l(i)-e(i)=0&#x8868;&#x793A;&#x6D3B;&#x52A8;ai&#x662F;&#x5173;&#x952E;&#x6D3B;&#x52A8;<\/p>\n<p>&#x5B9A;&#x4E49;&#xFF1A;<\/p>\n<ul>\n<li>ve(i)&#x8868;&#x793A;&#x4E8B;&#x4EF6;&#xFF08;&#x9876;&#x70B9;&#xFF09;vi&#x7684;&#x6700;&#x65E9;&#x53D1;&#x751F;&#x65F6;&#x95F4;&#xFF0C;&#x5373;&#x4ECE;&#x8D77;&#x70B9;&#x5230;&#x9876;&#x70B9;vi&#x7684;&#x6700;&#x957F;&#x8DEF;&#x5F84;&#x957F;&#x5EA6;<\/li>\n<li>vl(i)&#x8868;&#x793A;&#x4E8B;&#x4EF6;&#xFF08;&#x9876;&#x70B9;&#xFF09;vi&#x7684;&#x6700;&#x665A;&#x53D1;&#x751F;&#x65F6;&#x95F4;&#xFF0C;&#x5373;&#x4ECE;&#x9876;&#x70B9;vi&#x5230;&#x6C47;&#x70B9;&#x7684;&#x6700;&#x77ED;&#x8DEF;&#x5F84;&#x957F;&#x5EA6;<\/li>\n<\/ul>\n<p>&#x5219;&#xFF1A;<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">{<\/mo><mtable rowspacing=\"0.25em\" columnalign=\"right left\" columnspacing=\"0em\"><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>e<\/mi><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>v<\/mi><mi>e<\/mi><mo stretchy=\"false\">(<\/mo><mi>j<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><mtr><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><\/mrow><\/mstyle><\/mtd><mtd><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><mrow><\/mrow><mi>l<\/mi><mo stretchy=\"false\">(<\/mo><mi>i<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>v<\/mi><mi>l<\/mi><mo stretchy=\"false\">(<\/mo><mi>k<\/mi><mo stretchy=\"false\">)<\/mo><mo>&#x2212;<\/mo><mi>d<\/mi><mi>u<\/mi><mi>t<\/mi><mo stretchy=\"false\">(<\/mo><mo>&lt;<\/mo><mi>j<\/mi><mo separator=\"true\">,<\/mo><mi>k<\/mi><mo>&gt;<\/mo><mo stretchy=\"false\">)<\/mo><\/mrow><\/mstyle><\/mtd><\/mtr><\/mtable><\/mrow><annotation encoding=\"application\/x-tex\">\\left\\{\\begin{aligned}\n    &amp;e(i)=ve(j)\\\\\n    &amp;l(i)=vl(k)-dut(&lt;j,k&gt;)\n\\end{aligned}\\right.<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:3em;vertical-align:-1.25em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.75em;\"><span style=\"top:-3.75em;\"><span class=\"pstrut\" style=\"height:2.84em;\"><\/span><span class=\"mord\"><\/span><\/span><span style=\"top:-2.25em;\"><span class=\"pstrut\" style=\"height:2.84em;\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.25em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.75em;\"><span style=\"top:-3.91em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-2.41em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">v<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">&#x2212;<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mopen\">(<\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">&#x200B;<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.25em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#x7B97;&#x6CD5;&#xFF1A;<\/p>\n<ol>\n<li>&#x4ECE;&#x62D3;&#x6251;&#x6392;&#x5E8F;&#x7684;&#x5E8F;&#x5217;&#x7684;&#x7B2C;&#x4E00;&#x4E2A;&#x9876;&#x70B9;(&#x6E90;&#x70B9;)&#x5F00;&#x59CB;&#xFF0C;&#x6309;&#x62D3;&#x6251;&#x987A;&#x5E8F;&#x4F9D;&#x6B21;&#x8BA1;&#x7B97;&#x6BCF;&#x4E2A;&#x4E8B;&#x4EF6;&#x7684;&#x6700;&#x65E9;&#x53D1;&#x751F;&#x65F6;&#x95F4;ve(i)<\/li>\n<li>&#x4ECE;&#x62D3;&#x6251;&#x6392;&#x5E8F;&#x7684;&#x5E8F;&#x5217;&#x7684;&#x6700;&#x540E;&#x4E00;&#x4E2A;&#x9876;&#x70B9;(&#x6C47;&#x70B9;)&#x5F00;&#x59CB;&#xFF0C;&#x6309;&#x9006;&#x62D3;&#x6251;&#x987A;&#x5E8F;&#x4F9D;&#x6B21;&#x8BA1;&#x7B97;&#x6BCF;&#x4E2A;&#x4E8B;&#x4EF6;&#x7684;&#x6700;&#x665A;&#x53D1;&#x751F; &#x65F6;&#x95F4;vl(i)<\/li>\n<li>&#x8BA1;&#x7B97;e(i),l(i)&#xFF0C;&#x627E;&#x5230;l(i)-e(i)=0&#x7684;&#x6D3B;&#x52A8;<\/li>\n<\/ol>\n<p>&#x4E3A;&#x4E86;2&#xFF0C;&#x589E;&#x8BBE;&#x4E00;&#x4E2A;&#x6808;&#x4EE5;&#x8BB0;&#x5F55;&#x62D3;&#x6251;&#x6709;&#x5E8F;&#x5E8F;&#x5217;&#xFF0C;&#x5219;&#x5728;&#x8BA1;&#x7B97;&#x6C42;&#x5F97;&#x5404;&#x9876;&#x70B9;&#x7684;ve&#x503C;&#x4E4B;&#x540E;&#xFF0C;&#x4ECE;&#x6808;&#x9876;&#x81F3;&#x6808;&#x5E95;&#x4FBF;&#x4E3A;&#x9006;&#x62D3;&#x6251;&#x6709;&#x5E8F;&#x5E8F;&#x5217;&#xFF1B;&#x4EA6;&#x53EF;&#x5229;&#x7528;DFS&#x51FD;&#x6570;&#xFF0C;&#x5728;&#x9000;&#x51FA;DFS&#x51FD;&#x6570;&#x4E4B;&#x524D;&#x8BA1;&#x7B97;&#x9876;&#x70B9;v&#x7684;vl&#x503C;&#x3002;<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>+<\/mo><mi>e<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n+e)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<h2 class=\"mume-header\" id=\"%E6%9C%80%E7%9F%AD%E8%B7%AF%E5%BE%84\">&#x6700;&#x77ED;&#x8DEF;&#x5F84;<\/h2>\n\n<h3 class=\"mume-header\" id=\"dijkstra%E7%AE%97%E6%B3%95\">Dijkstra&#x7B97;&#x6CD5;<\/h3>\n\n<p>&#x8FB9;&#x4E0A;&#x6743;&#x503C;&#x975E;&#x8D1F;&#x60C5;&#x5F62;&#x7684;&#x5355;&#x6E90;&#x6700;&#x77ED;&#x8DEF;&#x5F84;&#x95EE;&#x9898;<\/p>\n<p>&#x7C7B;&#x4F3C;Prim&#x7B97;&#x6CD5;<\/p>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n^2)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.0641em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<h3 class=\"mume-header\" id=\"bellman-ford%E7%AE%97%E6%B3%95\">Bellman-Ford&#x7B97;&#x6CD5;<\/h3>\n\n<p>&#x8FB9;&#x4E0A;&#x6743;&#x503C;&#x4E3A;&#x4EFB;&#x610F;&#x503C;&#x7684;&#x5355;&#x6E90;&#x6700;&#x77ED;&#x8DEF;&#x5F84;&#x95EE;&#x9898;<\/p>\n<h3 class=\"mume-header\" id=\"floyd%E7%AE%97%E6%B3%95\">Floyd&#x7B97;&#x6CD5;<\/h3>\n\n<p>&#x6240;&#x6709;&#x9876;&#x70B9;&#x4E4B;&#x95F4;&#x7684;&#x6700;&#x77ED;&#x8DEF;&#x5F84;<\/p>\n<p>&#x7B97;&#x6CD5;&#xFF1A;<\/p>\n<ol>\n<li>&#x8BBE;&#x9876;&#x70B9;&#x96C6;S(&#x521D;&#x503C;&#x4E3A;&#x7A7A;)&#xFF0C;&#x7528;&#x6570;&#x7EC4;D&#x7684;&#x6BCF;&#x4E2A;&#x5143;&#x7D20;D[i][j]&#x4FDD;&#x5B58;&#x4ECE;Vi&#x53EA;&#x7ECF;&#x8FC7;S&#x4E2D;&#x7684;&#x9876;&#x70B9;&#x5230;&#x8FBE;Vj&#x7684;&#x6700;&#x77ED;&#x8DEF;&#x5F84;&#x957F;&#x5EA6;<\/li>\n<li>&#x5C06;&#x56FE;&#x4E2D;&#x4E00;&#x4E2A;&#x9876;&#x70B9;Vk&#x52A0;&#x5165;&#x5230;S&#x4E2D;&#xFF0C;&#x4FEE;&#x6539;D[i][j]&#x7684;&#x503C;<br>\n<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>D<\/mi><mo stretchy=\"false\">[<\/mo><mi>i<\/mi><mo stretchy=\"false\">]<\/mo><mo stretchy=\"false\">[<\/mo><mi>j<\/mi><mo stretchy=\"false\">]<\/mo><mo>=<\/mo><mi>M<\/mi><mi>i<\/mi><mi>n<\/mi><mo stretchy=\"false\">{<\/mo><mi>D<\/mi><mo stretchy=\"false\">[<\/mo><mi>i<\/mi><mo stretchy=\"false\">]<\/mo><mo stretchy=\"false\">[<\/mo><mi>j<\/mi><mo stretchy=\"false\">]<\/mo><mo separator=\"true\">,<\/mo><mo stretchy=\"false\">(<\/mo><mi>D<\/mi><mo stretchy=\"false\">[<\/mo><mi>i<\/mi><mo stretchy=\"false\">]<\/mo><mo stretchy=\"false\">[<\/mo><mi>k<\/mi><mo stretchy=\"false\">]<\/mo><mo>+<\/mo><mi>D<\/mi><mo stretchy=\"false\">[<\/mo><mi>k<\/mi><mo stretchy=\"false\">]<\/mo><mo stretchy=\"false\">[<\/mo><mi>j<\/mi><mo stretchy=\"false\">]<\/mo><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">}<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">D[i][j]=Min \\{D[i][j] , (D[i][k]+D[k][j]) \\}<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.10903em;\">M<\/span><span class=\"mord mathnormal\">in<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">D<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.03148em;\">k<\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.05724em;\">j<\/span><span class=\"mclose\">])}<\/span><\/span><\/span><\/span><\/li>\n<li>&#x91CD;&#x590D;&#x4E0A;&#x4E00;&#x6B65;&#xFF0C;&#x76F4;&#x5230;G&#x7684;&#x6240;&#x6709;&#x9876;&#x70B9;&#x90FD;&#x52A0;&#x5165;&#x5230;S&#x4E2D;&#x4E3A;&#x6B62;<\/li>\n<\/ol>\n<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>n<\/mi><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">O(n^3)<\/annotation><\/semantics><\/math><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1.0641em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.02778em;\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<h1 class=\"mume-header\" id=\"%E5%8A%A8%E6%80%81%E5%AD%98%E5%82%A8%E7%AE%A1%E7%90%86\">&#x52A8;&#x6001;&#x5B58;&#x50A8;&#x7BA1;&#x7406;<\/h1>\n\n<h2 class=\"mume-header\" id=\"%E5%8F%AF%E5%88%A9%E7%94%A8%E7%A9%BA%E9%97%B4%E8%A1%A8\">&#x53EF;&#x5229;&#x7528;&#x7A7A;&#x95F4;&#x8868;<\/h2>\n\n<h3 class=\"mume-header\" id=\"%E9%93%BE%E5%BC%8F%E5%8F%AF%E5%88%A9%E7%94%A8%E7%A9%BA%E9%97%B4%E8%A1%A8%E7%9A%84%E5%88%86%E9%85%8D%E6%96%B9%E5%BC%8F\">&#x94FE;&#x5F0F;&#x53EF;&#x5229;&#x7528;&#x7A7A;&#x95F4;&#x8868;&#x7684;&#x5206;&#x914D;&#x65B9;&#x5F0F;<\/h3>\n\n<ul>\n<li>&#x9996;&#x6B21;&#x62DF;&#x5408;&#x6CD5;<\/li>\n<li>&#x6700;&#x4F73;&#x62DF;&#x5408;&#x6CD5;<\/li>\n<li>&#x6700;&#x5DEE;&#x62DF;&#x5408;&#x6CD5;<\/li>\n<\/ul>\n<h2 class=\"mume-header\" id=\"%E8%BE%B9%E7%95%8C%E6%A0%87%E8%AF%86%E6%B3%95boundary-tag-method\">&#x8FB9;&#x754C;&#x6807;&#x8BC6;&#x6CD5;&#xFF08;Boundary Tag Method&#xFF09;<\/h2>\n\n<h2 class=\"mume-header\" id=\"%E4%BC%99%E4%BC%B4%E7%B3%BB%E7%BB%9Fbuddy-system\">&#x4F19;&#x4F34;&#x7CFB;&#x7EDF;&#xFF08;Buddy System&#xFF09;<\/h2>\n\n<h2 class=\"mume-header\" id=\"%E6%97%A0%E7%94%A8%E5%8D%95%E5%85%83%E6%94%B6%E9%9B%86garbage-collector-gc\">&#x65E0;&#x7528;&#x5355;&#x5143;&#x6536;&#x96C6;&#xFF08;Garbage Collector, GC&#xFF09;<\/h2>\n\n<p>&#x8981;&#x53CA;&#x65F6;&#x91CA;&#x653E;&#x5171;&#x4EAB;&#x7ED3;&#x70B9;&#x6240;&#x5360;&#x7684;&#x7A7A;&#x95F4;&#xFF0C;&#x5FC5;&#x987B;&#x7ED9;&#x6BCF;&#x4E2A;&#x7ED3;&#x70B9;&#x589E;&#x8BBE;&#x4E00;&#x4E2A;&#x5171;&#x4EAB;&#x8BA1;&#x6570;&#x5668;&#xFF0C;&#x8BB0;&#x5F55;&#x672C;&#x7ED3;&#x70B9;&#x88AB;&#x51E0;&#x4E2A;&#x94FE;&#x5171;&#x4EAB;&#xFF0C;&#x5F53;&#x7ED3;&#x70B9;&#x4ECE;&#x67D0;&#x4E00;&#x94FE;&#x4E2D;&#x88AB;&#x5220;&#x9664;&#x65F6;&#xFF0C;&#x5C31;&#x5C06;&#x6B64;&#x8BA1;&#x6570;&#x5668;&#x51CF;1&#xFF0C;&#x53CD;&#x4E4B;&#x5728;&#x63D2;&#x5165;&#x65F6;&#x8BA1;&#x6570;&#x5668;&#x52A0;1&#xFF0C;&#x4E00;&#x65E6;&#x8BE5;&#x8BA1;&#x6570;&#x5668;&#x88AB;&#x51CF;&#x5230;0&#x65F6;&#xFF0C;&#x8BF4;&#x660E;&#x8BE5;&#x7ED3;&#x70B9;&#x5728;&#x7ED3;&#x6784;&#x4E2D;&#x4E0D;&#x518D;&#x6709;&#x7528;&#xFF0C;&#x4FBF;&#x53EF;&#x4EE5;&#x56DE;&#x6536;&#x3002;<\/p>\n<h3 class=\"mume-header\" id=\"%E5%BC%95%E7%94%A8%E8%AE%A1%E6%95%B0reference-counting\">&#x5F15;&#x7528;&#x8BA1;&#x6570;(Reference Counting)<\/h3>\n\n<ul>\n<li>&#x5728;&#x6240;&#x4F7F;&#x7528;&#x7684;&#x6570;&#x636E;&#x7ED3;&#x6784;\/&#x5BF9;&#x8C61;&#x4E2D;&#x589E;&#x52A0;&#x4E00;&#x4E2A;&#x8BA1;&#x6570;&#x57DF;&#xFF0C;&#x5B83;&#x7684;&#x503C;&#x4E3A;&#x6307;&#x5411;&#x8BE5;&#x6570;&#x636E;&#x7ED3;&#x6784;\/&#x5BF9;&#x8C61;&#x7684;&#x6307;&#x9488;&#x6570;&#x76EE;<\/li>\n<li>&#x5F53;&#x8BE5;&#x8BA1;&#x6570;&#x5668;&#x503C;&#x4E3A;0&#x65F6;&#xFF0C;&#x8BE5;&#x6570;&#x636E;&#x7ED3;&#x6784;&#x624D;&#x88AB;&#x91CA;&#x653E;<\/li>\n<li>&#x4E0D;&#x8DB3;&#xFF1A;&#x4E0D;&#x80FD;&#x5E94;&#x5BF9;&#x5FAA;&#x73AF;&#x5F15;&#x7528;<\/li>\n<\/ul>\n<h3 class=\"mume-header\" id=\"%E6%A0%87%E8%AE%B0%E5%90%8E%E6%B8%85%E9%99%A4mark-and-sweep\">&#x6807;&#x8BB0;&#x540E;&#x6E05;&#x9664;(Mark and Sweep)<\/h3>\n\n<ul>\n<li>&#x5F53;&#x53EF;&#x7528;&#x7A7A;&#x95F4;&#x8868;&#x4E3A;&#x7A7A;&#x65F6;&#xFF0C;(Mark)&#x6682;&#x505C;&#x6267;&#x884C;&#x7A0B;&#x5E8F;&#xFF0C;&#x4ECE;&#x6839;&#x96C6;&#x5408;(root set)&#x5F00;&#x59CB;&#xFF0C;&#x5C06;&#x5185;&#x5B58;&#x6574;&#x4E2A;&#x904D;&#x5386;&#x4E00;&#x6B21;&#xFF0C;&#x6807;&#x8BB0;&#x88AB;&#x6839;&#x96C6;&#x5408;&#x76F4;&#x63A5;&#x6216;&#x95F4;&#x63A5;&#x5F15;&#x7528;&#x7684;&#x5BF9;&#x8C61;&#xFF1B;(Sweep)&#x904D;&#x5386;&#x6574;&#x4E2A;&#x5185;&#x5B58;&#xFF0C;&#x5C06;&#x672A;&#x6807;&#x8BB0;&#x7684;&#x5BF9;&#x8C61;&#x90FD;&#x5F53;&#x4F5C;&#x5783;&#x573E;&#xFF0C;&#x628A;&#x8FD9;&#x4E9B;&#x7A7A;&#x95F4;&#x94FE;&#x63A5;&#x5728;&#x4E00;&#x8D77;&#xFF0C;&#x5F62;&#x6210;&#x4E00;&#x4E2A;&#x65B0;&#x7684;&#x53EF;&#x7528;&#x7A7A;&#x95F4;&#x8868;&#xFF0C;&#x7136;&#x540E;&#xFF0C;&#x518D;&#x7EE7;&#x7EED;&#x7A0B;&#x5E8F;&#x6267;&#x884C;<\/li>\n<li>Mark&#x9636;&#x6BB5;&#xFF1A;&#x7528;&#x9012;&#x5F52;&#x6216;&#x975E;&#x9012;&#x5F52;&#x8FDB;&#x884C;&#x904D;&#x5386;<\/li>\n<li>&#x4E0D;&#x8DB3;&#xFF1A;&#x9700;&#x8981;&#x4E2D;&#x65AD;&#x7A0B;&#x5E8F;&#x6267;&#x884C;<\/li>\n<\/ul>\n\n      <\/div>\n      \n      \n    \n    \n    \n    \n    \n    \n    \n    \n 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