{"id":517,"date":"2010-11-09T01:58:49","date_gmt":"2010-11-08T17:58:49","guid":{"rendered":"http:\/\/comzyh.tk\/blog\/?p=517"},"modified":"2015-10-24T16:49:42","modified_gmt":"2015-10-24T08:49:42","slug":"517","status":"publish","type":"post","link":"https:\/\/comzyh.com\/blog\/archives\/517\/","title":{"rendered":"\u5904\u7406SCC(\u5f3a\u8fde\u901a\u5206\u91cf\u95ee\u9898)\u7684Tarjan\u7b97\u6cd5"},"content":{"rendered":"<p>\u5728\u6709\u5411\u56feG\u4e2d,\u5982\u679c\u4e24\u4e2a\u9876\u70b9\u95f4\u81f3\u5c11\u5b58\u5728\u4e00\u6761\u8def\u5f84,\u79f0\u4e24\u4e2a\u9876\u70b9\u5f3a\u8fde\u901a(strongly connected),\u5982\u679c\u6709\u5411\u56feG\u7684\u6bcf\u4e24\u4e2a\u9876\u70b9\u90fd\u5f3a\u8fde\u901a\uff0c\u79f0G\u662f\u4e00\u4e2a\u5f3a\u8fde\u901a\u56fe.<\/p>\n<figure id=\"attachment_516\" aria-describedby=\"caption-attachment-516\" style=\"width: 300px\" class=\"wp-caption alignright\"><a rel=\"attachment wp-att-516\" href=\"http:\/\/www.comzyh.com\/blog\/archives\/517\/scc\/\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"516\" data-permalink=\"https:\/\/comzyh.com\/blog\/archives\/517\/scc\/\" data-orig-file=\"https:\/\/i0.wp.com\/comzyh.com\/upload\/wordpress\/\/2010\/11\/SCC.png?fit=300%2C240&amp;ssl=1\" data-orig-size=\"300,240\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"SCC\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;\u5982\u56fe\u6240\u793a,\u84dd\u8272\u6846\u5708\u8d77\u6765\u7684\u662f\u4e00\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf&lt;\/p&gt;\n\" data-medium-file=\"https:\/\/i0.wp.com\/comzyh.com\/upload\/wordpress\/\/2010\/11\/SCC.png?fit=300%2C240&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/comzyh.com\/upload\/wordpress\/\/2010\/11\/SCC.png?fit=300%2C240&amp;ssl=1\" class=\"size-full wp-image-516\" title=\"SCC\" src=\"https:\/\/i0.wp.com\/comzyh.com\/upload\/wordpress\/\/2010\/11\/SCC.png?resize=300%2C240\" alt=\"\" width=\"300\" height=\"240\" data-recalc-dims=\"1\" \/><\/a><figcaption id=\"caption-attachment-516\" class=\"wp-caption-text\">\u5982\u56fe\u6240\u793a,\u84dd\u8272\u6846\u5708\u8d77\u6765\u7684\u662f\u4e00\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf<\/figcaption><\/figure>\n<p>\u901a\u4fd7\u7684\u8bf4\u6cd5\u662f:\u4ece\u56feG\u5185\u4efb\u610f\u4e00\u4e2a\u70b9\u51fa\u53d1,\u5b58\u5728\u901a\u5411\u56feG\u5185\u4efb\u610f\u4e00\u70b9\u7684\u7684\u4e00\u6761\u8def\u5f84.<\/p>\n<p>\u975e\u5f3a\u8fde\u901a\u56fe\u6709\u5411\u56fe\u7684\u6781\u5927\u5f3a\u8fde\u901a\u5b50\u56fe\uff0c\u79f0\u4e3a\u5f3a\u8fde\u901a\u5206\u91cf(strongly connected components,SCC).<\/p>\n<p>\u6c42\u56fe\u5f3a\u8fde\u901a\u5206\u91cf\u7684\u610f\u4e49\u662f:\u7531\u4e8e\u5f3a\u8fde\u901a\u5206\u91cf\u5185\u90e8\u7684\u8282\u70b9\u6027\u8d28\u76f8\u540c,\u53ef\u4ee5\u5c06\u4e00\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf\u5185\u7684\u8282\u70b9\u7f29\u6210\u4e00\u4e2a\u70b9,\u5373\u6d88\u9664\u4e86\u73af,\u8fd9\u6837,\u539f\u56fe\u5c31\u53d8\u6210\u4e86\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe(directed acyclic graph,DAG).\u663e\u7136\u5bf9\u4e8e\u4e00\u4e2a\u65e0\u5411\u56fe,\u6c42\u5f3a\u8fde\u901a\u5206\u91cf\u6ca1\u6709\u4ec0\u4e48\u610f\u4e49,\u8054\u901a\u5373\u4e3a\u5f3a\u8fde\u901a.<\/p>\n<p>\u6c42\u5f3a\u8fde\u901a\u5206\u91cf\u6bd4\u8f83\u9ad8\u6548\u7684\u7b97\u6cd5\u662fSCC Tarjan\u7b97\u6cd5,BYV\u725b\u6709\u4e00\u4e2a\u5f88\u597d\u7684\u8bf4\u660e,\u63a8\u8350\u5927\u5bb6\u770b\u4e00\u770b:<a href=\"http:\/\/www.byvoid.com\/blog\/scc-tarjan\/\" target=\"_blank\">\u6709\u5411\u56fe\u5f3a\u8fde\u901a\u5206\u91cf\u7684Tarjan\u7b97\u6cd5\u00ab Beyond the Void<\/a>,\u6211\u5728\u8fd9\u91cc\u5c31\u4e0d\u7167\u642c\u4e86.<\/p>\n<p>Tarjan \u7b97\u6cd5\u57fa\u672c\u57fa\u4e8eDFS,\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u662f\u904d\u5386\u56fe\u4e00\u904d,\u4e3a\\(\\Theta (N)\\),Tarjan \u8c8c\u4f3c\u5f88\u559c\u6b22\u6df1\u641c\u7684\u6837\u5b50,LCA\u88ab\u6df1\u641c\u6d3b\u751f\u751f\u7684\u5f04\u6210\u4e86\\(\\Theta (N)\\),SCC \u770b\u6765\u4e00\u6837,Tarjan \u4e00\u51fa\u73b0,\u65f6\u95f4\u590d\u6742\u5ea6\u679c\u7136\u964d\u4e86\u4e00\u4e2a\u6570\u91cf\u7ea7.<\/p>\n<p>\u5148\u770bBYV\u725b\u7684CODE,\u5199\u7684\u771f\u4e0d\u9519,\u867d\u7136\u7b2c\u4e00\u904d\u6211\u6ca1\u770b\u61c2,\u4e0d\u8fc7\u76f8\u4fe1\u52a0\u4e86\u6ce8\u91ca\u540e\u4f1a\u597d\u7406\u89e3\u591a,\u5982\u679c\u6709\u9519\u8bef,\u522b\u6253\u6211.<br \/>\n<!--more--><\/p>\n<pre lang=\"cpp\">\r\nvoid tarjan(int i)\/\/Tarjan \r\n{\r\n\tint j;\r\n\tDFN[i]=LOW[i]=++Dindex;\/\/Index \u65f6\u95f4\u6233 \r\n\tinstack[i]=true;\/\/\u6807\u8bb0\u5165\u6808 \r\n\tStap[++Stop]=i;\/\/\u5165\u6808 \r\n\tfor (edge *e=V[i];e;e=e->next)\/\/\u679a\u4e3e\u6240\u6709\u76f8\u8fde\u8fb9 \r\n\t{\r\n\t\tj=e->t;\/\/\u4e34\u65f6\u53d8\u91cf \r\n\t\tif (!DFN[j])\/\/j\u6ca1\u6709\u88ab\u641c\u7d22\u8fc7 \r\n\t\t{\r\n\t\t\ttarjan(j);\/\/\u9012\u5f52\u641c\u7d22j \r\n\t\t\tif (LOW[j]<LOW[i])\/\/\u56de\u6eaf\u4e2d\u53d1\u73b0j\u627e\u5230\u4e86\u66f4\u8001\u7684\u65f6\u95f4\u6233 \r\n\t\t\t\tLOW[i]=LOW[j];\/\/\u66f4\u65b0\u80fd\u8fbe\u5230\u8001\u65f6\u95f4\u6233 \r\n\t\t}\r\n\t\telse if (instack[j] &#038;&#038; DFN[j]<LOW[i])\/\/\u5982\u679c\u5df2\u7ecf\u5370\u6709\u65f6\u95f4\u6233 \u4e14 \u65f6\u95f4\u6233\u6bd4\u8f83\u5c0f,\u5219\u6709\u73af \r\n\t\t\tLOW[i]=DFN[j];\/\/\u5f53\u524d\u8bb0\u5f55\u53ef\u8ffd\u6eaf\u65f6\u95f4\u6233\u66f4\u65b0 \r\n\t}\r\n\tif (DFN[i]==LOW[i])\/\/\u53ef\u8ffd\u6eaf\u6700\u8001\u662f\u81ea\u5df1,\u8868\u660e\u81ea\u5df1\u662f\u5f53\u524d\u5f3a\u8fde\u901a\u5206\u91cf\u7684\u6808\u5e95 \r\n\t{\r\n\t\tBcnt++;\/\/\u5f3a\u8fde\u901a\u5206\u91cf\u6570\u589e\u52a0 \r\n\t\tdo\r\n\t\t{\r\n\t\t\tj=Stap[Stop--];\/\/\u51fa\u6808\u9876\u5143\u7d20 \r\n\t\t\tinstack[j]=false;\/\/\u6807\u8bb0\u51fa\u6808 \r\n\t\t\tBelong[j]=Bcnt;\/\/\u8bb0\u5f55j\u6240\u5728\u7684\u5f3a\u8fde\u901a\u5206\u91cf\u7f16\u53f7 \r\n\t\t}\r\n\t\twhile (j!=i);\/\/\u5982\u679c\u662f\u5f53\u524d\u5143\u7d20,\u5f39\u6808\u5b8c\u6210 \r\n\t}\r\n}\r\nvoid solve()\r\n{\r\n\tint i;\r\n\tStop=Bcnt=Dindex=0;\r\n\tmemset(DFN,0,sizeof(DFN));\/\/\u6807\u8bb0\u4e3a\u4e3a\u641c\u7d22\u8fc7 \r\n\tfor (i=1;i<=N;i++)\r\n\t\tif (!DFN[i])\r\n\t\t\ttarjan(i);\r\n}\r\n\r\n<\/pre>\n<p>SCC Tarjan\u7b97\u6cd5\u7684\u57fa\u672c\u6846\u67b6:<\/p>\n<ul>\n<li>\u904d\u5386\u4e00\u4e2a\u70b9,\u6307\u5b9a\u4e00\u4e2a\u552f\u4e00\u65f6\u95f4\u6233DFN[i];\u6307\u5b9a\u8be5\u70b9<span style=\"color: #ff0000;\">\u5411\u524d\u8ffd\u6eaf\u53ef\u8ffd\u6eaf\u5230\u7684\u6700\u8001\u65f6\u95f4\u6233<\/span>LOW[i].<\/li>\n<li>\u679a\u4e3e\u5f53\u524d\u70b9\u6240\u6709\u8fb9,\u82e5DFN[j]=0\u8868\u660e\u672a\u88ab\u641c\u7d22\u8fc7,\u9012\u5f52\u641c\u7d22\u4e4b.<\/li>\n<li>\u82e5DFN[j]\u4e0d\u4e3a0,\u5219j\u88ab\u641c\u7d22\u8fc7,\u8fd9\u65f6\u5224\u65adj\u662f\u5426\u5728\u6808\u4e2d,\u4e14j\u7684\u65f6\u95f4\u6233DFN[j]\u5c0f\u4e8e\u5f53\u524d\u65f6\u95f4\u6233DFN[i],\u53ef\u5224\u5b9a\u6210\u73af.\u5c06LOW[i]\u8bbe\u5b9a\u4e3aDFN[j]<\/li>\n<li>\u82e5\u8fd9\u4e2a\u70b9LOW[i]\u548cDFN[i]\u76f8\u7b49,\u8bf4\u660e\u8fd9\u4e2a\u8282\u70b9\u662f<span style=\"color: #ff0000;\">\u6240\u6709\u5f3a\u8fde\u901a\u5206\u91cf\u7684\u5143\u7d20\u4e2d\u5728\u6808\u4e2d\u6700\u65e9\u7684\u8282\u70b9<\/span>.<\/li>\n<li>\u5f39\u6808,\u5c06\u8fd9\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf\u5168\u90e8\u5f39\u51fa,\u7f29\u6210\u70b9.<\/li>\n<\/ul>\n<p>\u8fd9\u91cc\u89e3\u91ca\u4e0b\u6bd4\u8f83\u6666\u6da9\u7684\u4e24\u4e2a\u8bcd:<\/p>\n<p>LOW[i],\u8fd9\u4e2a<span style=\"color: #ff0000;\">\u5411\u524d\u8ffd\u6eaf\u53ef\u8ffd\u6eaf\u5230\u7684\u6700\u8001\u65f6\u95f4\u6233<\/span> \u7684\u610f\u601d\u662f\u6839\u636e\u6709\u5411\u56fe\u7684\u65b9\u5411\u904d\u5386,\u5728\u6709\u73af\u7684\u60c5\u51b5\u4e0b,\u5411\u524d\u8ffd\u6eaf\u53ef\u4ee5\u8fbe\u5230\u8f83\u65e9\u7684\u70b9.\u5728\u6bcf\u6b21\u9012\u5f52\u8c03\u7528Tarjan(j)\u540e\u6211\u4eec\u53ef\u4ee5\u9ad8\u901f\u8f83\u5feb\u7684\u66f4\u65b0LOW[i]<\/p>\n<p>\u81f3\u4e8e<span style=\"color: #ff0000;\">\u6240\u6709\u5f3a\u8fde\u901a\u5206\u91cf\u7684\u5143\u7d20\u4e2d\u5728\u6808\u4e2d\u6700\u65e9\u7684\u8282\u70b9<\/span>.\u662f\u8fd9\u6837\u7684,\u6240\u6709\u81ea\u6210\u5f3a\u8fde\u901a\u5206\u91cf\u7684\u8282\u70b9\u6216\u5b50\u56fe,\u5728\u672c\u6b21\u5f39\u6808\u524d\u90fd\u5df2\u7ecf\u5f39\u51fa\u53bb\u4e86,\u8fd9\u65f6\u6808\u91cc\u6240\u5143\u7d20\u7684LOW\u90fd\u5927\u4e8e\u7b49\u4e8eDFN[\u8be5\u5f3a\u8fde\u901a\u5206\u91cf\u7684\u6700\u65e9\u904d\u5386\u8282\u70b9],\u6808\u9876\u5143\u7d20\u4e00\u5b9a\u6bd4\u4e0b\u9762\u5143\u7d20\u7684\u65f6\u95f4\u6233\u8981\u5927<\/p>\n<p>\u5728\u904d\u5386\u5b8c\u6240\u6709\u76f8\u5173\u8fb9\u4e4b\u540e\u518d\u9a8c\u8bc1(DFN[i]==LOW[i]),\u53ef\u4ee5\u907f\u514d\u6709\u6f0f\u5224\u60c5\u51b5,\u8fd9\u65f6,\u5f53\u524d\u8282\u70b9\u7684\u5b50\u8282\u70b9\u5df2\u7ecf\u5c06LOW\u66f4\u65b0\u7684\u5f88\u4f18\u4e86,\u4e0d\u5b58\u5728\u4e00\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf\u88ab\u5305\u542b\u5728\u4e00\u4e2a\u5f3a\u8fde\u901a\u5206\u91cf\u91cc\u7684\u60c5\u51b5.<\/p>\n<p>\u5b66\u4e60SCC Tarjan\u7b97\u6cd5\u6709\u4e24\u9053\u6d4b\u9a8c\u9898:<\/p>\n<p><a title=\"Popular Cows\" href=\"http:\/\/poj.org\/problem?id=2186\" target=\"_blank\">POJ 2186 Popular Cows<\/a><\/p>\n<p><a title=\"Popular Cows\" href=\"http:\/\/poj.org\/problem?id=1236\" target=\"_blank\">POJ 1236 Network of Schools<\/a><br \/>\n\u53c2\u89c1<a title=\"POJ 2186 &#038; 1236 \u5f3a\u8fde\u901a\u5206\u91cf Tarjan\u7b97\u6cd5\"  href=\"http:\/\/www.comzyh.com\/blog\/archives\/534\/\"  target=\"_blank\">Comzyh\u8fd9\u4e24\u9053\u5f3a\u8fde\u901a\u5206\u91cf\u7684\u9898\u89e3<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6709\u5411\u56feG\u4e2d,\u5982\u679c\u4e24\u4e2a\u9876\u70b9\u95f4\u81f3\u5c11\u5b58\u5728\u4e00\u6761\u8def\u5f84,\u79f0\u4e24\u4e2a\u9876\u70b9\u5f3a\u8fde\u901a(strongly connected),\u5982\u679c\u6709 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[11,9],"tags":[52],"class_list":["post-517","post","type-post","status-publish","format-standard","hentry","category-programing","category-9","tag-52"],"jetpack_publicize_connections":[],"aioseo_notices":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/s6XQWE-517","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts\/517","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/comments?post=517"}],"version-history":[{"count":9,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts\/517\/revisions"}],"predecessor-version":[{"id":895,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts\/517\/revisions\/895"}],"wp:attachment":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/media?parent=517"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/categories?post=517"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/tags?post=517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}