{"id":109458,"date":"2026-09-24T07:24:54","date_gmt":"2026-09-23T23:24:54","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/109458.html"},"modified":"2026-09-24T07:24:54","modified_gmt":"2026-09-23T23:24:54","slug":"uva-11896-inglorious-gangs","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/109458.html","title":{"rendered":"UVa 11896 Inglorious Gangs"},"content":{"rendered":"<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<p>\u5728\u7f6a\u6076\u90fd\u5e02\u4e2d&#xff0c;\u5e2e\u6d3e\u4ee5\u8f66\u961f\u5f62\u5f0f\u5728\u8857\u9053\u4e0a\u884c\u9a76\u3002\u8b66\u5bdf\u6570\u91cf\u4e0d\u8db3&#xff0c;\u53ea\u80fd\u7531\u4e00\u540d\u8b66\u5bdf\u8ffd\u6355\u4e00\u4e2a\u5e2e\u6d3e\u8f66\u961f\u3002\u5f53\u8f66\u961f\u5230\u8fbe\u67d0\u4e2a\u4ea4\u53c9\u8def\u53e3\u65f6&#xff0c;\u6bcf\u8f86\u5e2e\u6d3e\u8f66\u8f86\u4f1a\u5206\u522b\u9a76\u5411\u4e0d\u540c\u7684\u65b9\u5411&#xff0c;\u4f7f\u843d\u5355\u7684\u8b66\u5bdf\u56f0\u60d1&#xff0c;\u5e2e\u6d3e\u4ece\u800c\u9003\u8131\u3002\u8b66\u65b9\u77e5\u9053&#xff0c;\u5e2e\u6d3e\u8f66\u961f\u53ea\u6709\u5728\u80fd\u591f\u4e8e\u57ce\u5e02\u4e2d\u67d0\u5904\u91cd\u65b0\u96c6\u7ed3\u7684\u60c5\u51b5\u4e0b\u624d\u4f1a\u5206\u5f00\u3002\u4ed6\u4eec\u8ba1\u5212\u5c01\u9501\u90e8\u5206\u9053\u8def&#xff0c;\u9632\u6b62\u8f66\u961f\u5206\u5f00&#xff0c;\u4ece\u800c\u8ba9\u8b66\u5bdf\u80fd\u4e00\u76f4\u8ffd\u6355\u76f4\u5230\u6293\u4f4f\u4ed6\u4eec\u3002<\/p>\n<p>\u57ce\u5e02\u5730\u56fe\u662f\u6709\u5411\u56fe&#xff0c;\u8282\u70b9\u8868\u793a\u4ea4\u53c9\u8def\u53e3&#xff0c;\u6709\u5411\u8fb9\u8868\u793a\u9053\u8def\u3002\u4f60\u9700\u8981\u5224\u65ad\u5728\u7ed9\u5b9a\u7684\u672a\u5c01\u9501\u9053\u8def\u4e0b&#xff0c;\u662f\u5426\u5df2\u7ecf\u80fd\u591f\u56f0\u4f4f\u5e2e\u6d3e\u3002\u5982\u679c\u80fd\u56f0\u4f4f&#xff0c;\u8f93\u51fa Trapped&#xff0c;\u5426\u5219\u8f93\u51fa Not Trapped\u3002<\/p>\n<p>\u5f62\u5f0f\u5316\u5730\u8bf4&#xff1a;\u5224\u65ad\u6709\u5411\u56fe\u4e2d\u662f\u5426\u5b58\u5728\u4e24\u4e2a\u4e0d\u540c\u7684\u9876\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">vv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f7f\u5f97\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">vv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u5b58\u5728\u4e24\u6761\u8fb9\u4e0d\u76f8\u4ea4\u7684\u8def\u5f84&#xff08;\u5373\u8def\u5f84\u95f4\u6ca1\u6709\u5171\u4eab\u7684\u6709\u5411\u8fb9&#xff0c;\u4f46\u53ef\u4ee5\u5171\u4eab\u9876\u70b9&#xff09;\u3002\u82e5\u5b58\u5728&#xff0c;\u5e2e\u6d3e\u53ef\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5904\u5206\u53c9&#xff0c;\u5e76\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">vv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u5904\u91cd\u65b0\u96c6\u7ed3&#xff0c;\u4ece\u800c\u9003\u8131\u3002<\/p>\n<h3>\u8f93\u5165\u683c\u5f0f<\/h3>\n<p>\u7b2c\u4e00\u884c\u4e00\u4e2a\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TT<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span>&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">T\u2264100T \\\\le 100<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">100<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u8868\u793a\u6d4b\u8bd5\u7528\u4f8b\u6570\u91cf\u3002<\/p>\n<p>\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u4ee5\u4e24\u4e2a\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">NN<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">MM<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u5f00\u5934&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\u2264N\u226450001 \\\\le N \\\\le 5000<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7804em;vertical-align: -0.136em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5000<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">M\u2264105M \\\\le 10^5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" 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\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u5206\u522b\u8868\u793a\u4ea4\u53c9\u8def\u53e3\u7684\u6570\u91cf\u548c\u672a\u5c01\u9501\u9053\u8def\u7684\u6570\u91cf\u3002<\/p>\n<p>\u63a5\u4e0b\u6765 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">MM<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><\/span><\/span><\/span><\/span> \u884c&#xff0c;\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">vv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span>&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\u2264u,v\u2264N1 \\\\le u, v \\\\le N<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7804em;vertical-align: -0.136em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8304em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">u\u2260vu \\\\neq v<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u8868\u793a\u5b58\u5728\u4e00\u6761\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">vv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u7684\u6709\u5411\u9053\u8def\u3002<\/p>\n<p>\u4fdd\u8bc1\u6ca1\u6709\u81ea\u73af&#xff0c;\u4f46\u53ef\u80fd\u5b58\u5728\u5e73\u884c\u8fb9\u3002<\/p>\n<h3>\u8f93\u51fa\u683c\u5f0f<\/h3>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b&#xff0c;\u8f93\u51fa\u4e00\u884c&#xff1a;\u82e5\u80fd\u591f\u56f0\u4f4f\u5e2e\u6d3e&#xff0c;\u6253\u5370 Trapped&#xff1b;\u5426\u5219\u6253\u5370 Not Trapped\u3002<\/p>\n<h3>\u6837\u4f8b<\/h3>\n<p>\u8f93\u5165<\/p>\n<p>2<br \/>\n3 3<br \/>\n1 2<br \/>\n2 3<br \/>\n1 3<br \/>\n4 4<br \/>\n1 2<br \/>\n2 3<br \/>\n3 4<br \/>\n4 2<\/p>\n<p>\u8f93\u51fa<\/p>\n<p>Not Trapped<br \/>\nTrapped<\/p>\n<p>\u89e3\u91ca&#xff1a;<\/p>\n<ul>\n<li>\u7b2c\u4e00\u7ec4&#xff1a;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u6709\u4e24\u6761\u8fb9\u5206\u522b\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">22<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">33<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">22<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u53c8\u80fd\u5230\u8fbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">33<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e2e\u6d3e\u53ef\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5206\u53c9&#xff0c;\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">33<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u6c47\u5408&#xff0c;\u5b58\u5728\u8fb9\u4e0d\u76f8\u4ea4\u8def\u5f84\u3002<\/li>\n<li>\u7b2c\u4e8c\u7ec4&#xff1a;\u552f\u4e00\u7684\u73af\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2\u21923\u21924\u219222 \\\\to 3 \\\\to 4 \\\\to 2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">4<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u51fa\u53d1\u53ea\u6709\u4e00\u6761\u8def\u5f84\u8fdb\u5165\u8be5\u73af&#xff0c;\u65e0\u6cd5\u5206\u53c9\u540e\u91cd\u805a&#xff0c;\u56e0\u6b64\u56f0\u4f4f\u3002<\/li>\n<\/ul>\n<h3>\u9898\u76ee\u5206\u6790<\/h3>\n<p>\u672c\u9898\u7684\u672c\u8d28\u662f\u5224\u65ad\u6709\u5411\u56fe\u4e2d\u662f\u5426\u5b58\u5728\u4e24\u6761\u8fb9\u4e0d\u76f8\u4ea4\u7684\u8def\u5f84\u3002\u6839\u636e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Menger\\\\texttt{Menger}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Menger<\/span><\/span><\/span><\/span><\/span><\/span> \u5b9a\u7406&#xff08;\u8fb9\u8fde\u901a\u5ea6\u7248\u672c&#xff09;&#xff0c;\u4e24\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">vv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u5b58\u5728\u4e24\u6761\u8fb9\u4e0d\u76f8\u4ea4\u8def\u5f84\u7b49\u4ef7\u4e8e\u5b83\u4eec\u4e4b\u95f4\u7684\u8fb9\u8fde\u901a\u5ea6\u81f3\u5c11\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">22<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5728\u7f51\u7edc\u6d41\u4e2d\u8868\u73b0\u4e3a\u6700\u5927\u6d41\u4e0d\u5c0f\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">22<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff08;\u6bcf\u6761\u8fb9\u5bb9\u91cf\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u4f46\u76f4\u63a5\u5bf9\u6bcf\u4e00\u5bf9\u51fa\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u22652\\\\ge 2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7719em;vertical-align: -0.136em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u7684\u8282\u70b9\u8dd1\u6700\u5927\u6d41&#xff0c;\u590d\u6742\u5ea6\u9ad8\u8fbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N\u22c5M\u22c5N)O(N \\\\cdot M \\\\cdot \\\\sqrt{N})<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1767em;vertical-align: -0.25em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9267em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8867em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1133em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u65e0\u6cd5\u627f\u53d7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">N\u22645000N \\\\le 5000<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5000<\/span><\/span><\/span><\/span><\/span> \u7684\u89c4\u6a21\u3002<\/p>\n<p>\u6211\u4eec\u9700\u8981\u66f4\u9ad8\u6548\u7684\u65b9\u6cd5\u3002\u89c2\u5bdf\u56fe\u7684\u7ed3\u6784&#xff1a;<\/p>\n<ul>\n<li>\u5f3a\u8fde\u901a\u5206\u91cf&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u5185\u90e8&#xff1a;\u82e5\u4e00\u4e2a\u5927\u5c0f\u81f3\u5c11\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">22<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u4e2d\u67d0\u4e2a\u9876\u70b9\u6709\u4e24\u6761\u8fb9\u6307\u5411\u540c\u4e00 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u7684\u5176\u4ed6\u9876\u70b9&#xff0c;\u5219\u7531\u4e8e\u5f3a\u8fde\u901a\u6027&#xff0c;\u8fd9\u4e24\u6761\u8fb9\u51fa\u53d1\u7684\u8def\u5f84\u5fc5\u7136\u80fd\u5728\u8be5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u67d0\u5904\u6c47\u5408&#xff0c;\u4ece\u800c\u5f62\u6210\u8fb9\u4e0d\u76f8\u4ea4\u8def\u5f84\u3002<\/li>\n<li>\u8de8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u7f29\u70b9\u540e\u5f97\u5230\u6709\u5411\u65e0\u73af\u56fe&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u4e2d&#xff0c;\u82e5\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u51fa\u5ea6\u81f3\u5c11\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">22<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e14\u5b58\u5728\u4e24\u6761\u4e0d\u540c\u7684\u51fa\u8fb9\u6307\u5411\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5b83\u4eec\u7684\u201c\u53ef\u8fbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u96c6\u5408\u201d\u6709\u4ea4\u96c6&#xff0c;\u5219\u6700\u65e9\u7684\u4ea4\u6c47 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5904\u4e00\u5b9a\u5b58\u5728\u8fb9\u4e0d\u76f8\u4ea4\u7684\u8def\u5f84&#xff08;\u56e0\u4e3a\u4e0d\u540c\u5206\u652f\u9996\u6b21\u6c47\u5408\u65f6&#xff0c;\u8fdb\u5165\u8be5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u8fb9\u5fc5\u7136\u4e0d\u540c&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u5173\u952e\u8f6c\u5316&#xff1a;\u6211\u4eec\u4e0d\u9700\u8981\u7cbe\u786e\u627e\u5230\u6c47\u5408\u9876\u70b9&#xff0c;\u53ea\u9700\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u4e2d\u68c0\u67e5\u53ef\u8fbe\u96c6\u7684\u4ea4\u96c6\u5373\u53ef\u3002<\/p>\n<h3>\u89e3\u9898\u601d\u8def<\/h3>\n<h4>\u7b2c\u4e00\u6b65&#xff1a;\u5f3a\u8fde\u901a\u5206\u91cf\u7f29\u70b9<\/h4>\n<p>\u4f7f\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Tarjan\\\\texttt{Tarjan}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Tarjan<\/span><\/span><\/span><\/span><\/span><\/span> \u7b97\u6cd5\u6c42\u51fa\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u8bb0\u5f55\u6bcf\u4e2a\u9876\u70b9\u6240\u5c5e\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7f16\u53f7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cuc_u<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" 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\">u<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ee5\u53ca\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5927\u5c0f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">sz[c]sz[c]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">sz<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u7edf\u8ba1\u6bcf\u4e2a\u9876\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5728\u539f\u56fe\u4e2d&#xff0c;\u8fde\u5411\u540c\u4e00 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u51fa\u8fb9\u6570\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">innerOut[u]\\\\textit{innerOut}[u]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord textit\">innerOut<\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h4>\u7b2c\u4e8c\u6b65&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u90e8\u5feb\u901f\u5224\u5b9a<\/h4>\n<p>\u904d\u5386\u6bcf\u4e2a\u5927\u5c0f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u22652\\\\ge 2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7719em;vertical-align: -0.136em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u82e5\u5176\u4e2d\u5b58\u5728\u67d0\u4e2a\u9876\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">innerOut[u]\u22652\\\\textit{innerOut}[u] \\\\ge 2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord text\"><span class=\"mord textit\">innerOut<\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5219\u76f4\u63a5\u5224\u5b9a\u5b58\u5728\u8fb9\u4e0d\u76f8\u4ea4\u8def\u5f84&#xff08;\u5e2e\u6d3e\u53ef\u9003\u8131&#xff09;\u3002\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u6709\u4e24\u6761\u8fb9\u7559\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u90e8&#xff0c;\u5f3a\u8fde\u901a\u6027\u4fdd\u8bc1\u8fd9\u4e24\u6761\u8def\u5f84\u53ef\u4ee5\u6c47\u5408\u3002<\/p>\n<h4>\u7b2c\u4e09\u6b65&#xff1a;\u6784\u5efa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u5e76\u8ba1\u7b97\u53ef\u8fbe\u96c6<\/h4>\n<p>\u5ffd\u7565 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u90e8\u7684\u8fb9&#xff0c;\u5c06\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u89c6\u4e3a\u4e00\u4e2a\u8d85\u7ea7\u8282\u70b9&#xff0c;\u5efa\u7acb <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u540c\u65f6\u7edf\u8ba1\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u51fa\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">dout[c]d_{\\\\text{out}}[c]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" 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 text mtight\"><span class=\"mord mtight\">out<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u62d3\u6251\u6392\u5e8f&#xff0c;\u6309\u62d3\u6251\u9006\u5e8f\u8ba1\u7b97\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u53ef\u8fbe\u96c6\u5408 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R[c]R[c]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7528\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">bitset\\\\texttt{bitset}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">bitset<\/span><\/span><\/span><\/span><\/span><\/span> \u5b58\u50a8&#xff08;\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">N\u22645000N \\\\le 5000<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5000<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">bitset\\\\texttt{bitset}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">bitset<\/span><\/span><\/span><\/span><\/span><\/span> \u4ec5\u9700\u7ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">625625<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">625<\/span><\/span><\/span><\/span><\/span> \u5b57\u8282&#xff0c;\u5feb\u901f\u4e14\u7a7a\u95f4\u5145\u8db3&#xff09;\u3002<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">R[c]&#061;{c}\u222a\u22c3v\u2208dag[c]R[v]R[c] &#061; \\\\{c\\\\} \\\\cup \\\\bigcup_{v \\\\in \\\\text{dag}[c]} R[v]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/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=\"mopen\">{<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">}<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u222a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.566em;vertical-align: -1.516em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.809em;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: 0.0359em\">v<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord text mtight\"><span class=\"mord mtight\">dag<\/span><\/span><span class=\"mopen mtight\">[<\/span><span class=\"mord mathnormal mtight\">c<\/span><span class=\"mclose mtight\">]<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u22c3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.516em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>\u7b2c\u56db\u6b65&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u4e2d\u5224\u5b9a<\/h4>\n<p>\u5bf9\u4e8e\u6bcf\u4e2a\u51fa\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u22652\\\\ge 2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7719em;vertical-align: -0.136em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cc<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f9d\u6b21\u68c0\u67e5\u5b83\u7684\u6240\u6709\u51fa\u8fb9\u90bb\u5c45\u5bf9\u5e94\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span>&#xff1a;<\/p>\n<ul>\n<li>\u7ef4\u62a4\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">bitset\\\\texttt{bitset}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">bitset<\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">seen\\\\textit{seen}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord text\"><span class=\"mord textit\">seen<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8868\u793a\u5df2\u904d\u5386\u8fc7\u7684\u90bb\u5c45\u7684\u53ef\u8fbe\u96c6\u4e4b\u5e76\u3002<\/li>\n<li>\u82e5\u5f53\u524d\u90bb\u5c45\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">seen\\\\textit{seen}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord text\"><span class=\"mord textit\">seen<\/span><\/span><\/span><\/span><\/span><\/span> \u6709\u4ea4\u96c6&#xff0c;\u5219\u8bf4\u660e\u5b58\u5728\u4e24\u6761\u4e0d\u540c\u7684\u51fa\u8fb9&#xff0c;\u5b83\u4eec\u7684\u53ef\u8fbe\u96c6\u6709\u91cd\u53e0&#xff0c;\u4ece\u800c\u5b58\u5728\u8fb9\u4e0d\u76f8\u4ea4\u8def\u5f84\u3002<\/li>\n<li>\u82e5\u6709\u4ea4\u96c6&#xff0c;\u76f4\u63a5\u5224\u5b9a\u53ef\u9003\u8131\u3002<\/li>\n<\/ul>\n<p>\u82e5\u6240\u6709\u68c0\u67e5\u5747\u672a\u53d1\u73b0&#xff0c;\u5219\u8f93\u51fa Trapped\u3002<\/p>\n<h4>\u6b63\u786e\u6027\u8bc1\u660e<\/h4>\n<ul>\n<li>\u5185\u90e8\u5224\u5b9a&#xff1a;\u82e5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u90e8\u6709\u81f3\u5c11\u4e24\u6761\u51fa\u8fb9&#xff0c;\u8bbe\u6307\u5411 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">yy<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span>\u3002\u7531\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5f3a\u8fde\u901a&#xff0c;\u5b58\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x\u21ddyx \\\\rightsquigarrow y<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u21dd<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">y\u21dduy \\\\rightsquigarrow u<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u21dd<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u7b49\u8def\u5f84&#xff0c;\u7ed3\u5408 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u7684\u51fa\u8fb9&#xff0c;\u603b\u80fd\u6784\u9020\u51fa\u4e24\u6761\u8fb9\u4e0d\u76f8\u4ea4\u7684\u8def\u5f84\u5230\u8fbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u67d0\u9876\u70b9&#xff08;\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u81ea\u8eab\u6216\u7ecf\u7531\u73af\u56de\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uu<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u7b49&#xff09;\u3002<\/li>\n<li>\u8de8 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5224\u5b9a&#xff1a;\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cc<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span> \u6709\u4e24\u6761\u51fa\u8fb9\u5206\u522b\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R[p]\u2229R[q]\u2260\u2205R[p] \\\\cap R[q] \\\\neq \\\\emptyset<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2229<\/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: 0.0077em\">R<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">\u2205<\/span><\/span><\/span><\/span><\/span>\u3002\u53d6\u4ea4\u96c6\u4e2d\u7684\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5219\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u548c\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u7684\u8def\u5f84\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u4e2d\u4e0d\u4f1a\u5171\u4eab\u8fb9&#xff08;\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">p\u2260qp \\\\neq q<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u4e14\u4e24\u6761\u8def\u5f84\u8fdb\u5165 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u7684\u8fb9\u5fc5\u4e0d\u540c&#xff08;\u5426\u5219\u5b83\u4eec\u4f1a\u5728\u66f4\u65e9\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5c31\u6c47\u5408&#xff0c;\u4e0e\u201c\u6700\u65e9\u4ea4\u96c6\u201d\u77db\u76fe&#xff09;\u3002\u56e0\u6b64&#xff0c;\u539f\u56fe\u4e2d\u5b58\u5728\u4ece\u67d0\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">u\u2208cu \\\\in c<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span> \u51fa\u53d1&#xff0c;\u7ecf\u8fc7\u4e0d\u540c\u8fb9\u5230\u8fbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ww<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><\/span><\/span><\/span> \u4e2d\u67d0\u9876\u70b9\u7684\u4e24\u6761\u8fb9\u4e0d\u76f8\u4ea4\u8def\u5f84\u3002<\/li>\n<\/ul>\n<h4>\u590d\u6742\u5ea6\u5206\u6790<\/h4>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Tarjan\\\\texttt{Tarjan}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Tarjan<\/span><\/span><\/span><\/span><\/span><\/span> \u7f29\u70b9&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N&#043;M)O(N &#043; M)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/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: 0.109em\">M<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u6784\u5efa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u4e0e\u62d3\u6251\u6392\u5e8f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N&#043;M)O(N &#043; M)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/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: 0.109em\">M<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u8ba1\u7b97\u53ef\u8fbe\u96c6&#xff1a;\u5171 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N)O(N)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">bitset\\\\texttt{bitset}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">bitset<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u4e2a\u5927\u5c0f\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">N\/64N\/64<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mord\">\/64<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5408\u5e76\u5728\u62d3\u6251\u5e8f\u4e0b\u603b\u65f6\u95f4\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N\u22c5(N\/64))\u22484\u00d7105O(N \\\\cdot (N\/64)) \\\\approx 4 \\\\times 10^5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mord\">\/64<\/span><span class=\"mclose\">))<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">4<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" 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\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6b21\u4f4d\u8fd0\u7b97&#xff0c;\u975e\u5e38\u5feb\u3002<\/li>\n<li>\u4ea4\u96c6\u5224\u5b9a&#xff1a;\u6bcf\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u6700\u591a\u904d\u5386\u5176\u51fa\u8fb9&#xff0c;\u603b\u4f4d\u8fd0\u7b97\u6b21\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(M\u22c5(N\/64))O(M \\\\cdot (N\/64))<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mord\">\/64<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span> \u4e5f\u5728\u5408\u7406\u8303\u56f4\u5185\u3002<\/li>\n<li>\u603b\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N2\/64&#043;M)O(N^2\/64 &#043; M)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" 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=\"mord\">\/64<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/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: 0.109em\">M<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N2\/64&#043;M)O(N^2\/64 &#043; M)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" 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=\"mord\">\/64<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/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: 0.109em\">M<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5747\u53ef\u901a\u8fc7\u3002<\/li>\n<\/ul>\n<h3>\u4ee3\u7801\u5b9e\u73b0<\/h3>\n<p><span class=\"token comment\">\/\/ Inglorious Gangs<\/span><br \/>\n<span class=\"token comment\">\/\/ UVa ID: 11896<\/span><br \/>\n<span class=\"token comment\">\/\/ Verdict: Accepted<\/span><br \/>\n<span class=\"token comment\">\/\/ Submission Date: 2026-06-22<\/span><br \/>\n<span class=\"token comment\">\/\/ UVa Run Time: 0.370s<\/span><br \/>\n<span class=\"token comment\">\/\/<\/span><br \/>\n<span class=\"token comment\">\/\/ \u7248\u6743\u6240\u6709&#xff08;C&#xff09;2026&#xff0c;\u90b1\u79cb\u3002metaphysis # yeah dot net<\/span><\/p>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span> <span class=\"token string\">&lt;bits\/stdc&#043;&#043;.h&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">solve<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    ios<span class=\"token double-colon punctuation\">::<\/span><span class=\"token function\">sync_with_stdio<\/span><span class=\"token punctuation\">(<\/span><span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> cin<span class=\"token punctuation\">.<\/span><span class=\"token function\">tie<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">nullptr<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> T<span class=\"token punctuation\">;<\/span> cin <span class=\"token operator\">&gt;&gt;<\/span> T<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>T<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> N<span class=\"token punctuation\">,<\/span> M<span class=\"token punctuation\">;<\/span> cin <span class=\"token operator\">&gt;&gt;<\/span> N <span class=\"token operator\">&gt;&gt;<\/span> M<span class=\"token punctuation\">;<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span>vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span> <span class=\"token function\">g<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">od<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token function\">id<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">bool<\/span> parallel <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        unordered_set<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span><span class=\"token operator\">&gt;<\/span> E<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> M<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">;<\/span> cin <span class=\"token operator\">&gt;&gt;<\/span> u <span class=\"token operator\">&gt;&gt;<\/span> v<span class=\"token punctuation\">;<\/span><br \/>\n            g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            od<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span> id<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span> key <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1LL<\/span> <span class=\"token operator\">*<\/span> u <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#043;<\/span> v<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>E<span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span>key<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>second<span class=\"token punctuation\">)<\/span> parallel <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>parallel<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;Not Trapped\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ Tarjan\u7b97\u6cd5\u7f29\u70b9<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">dfn<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token function\">low<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token function\">comp<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">bool<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">inSt<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        stack<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> st<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> tm <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> sc <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        function<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">void<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">&gt;<\/span> dfs <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token operator\">&amp;<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            dfn<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> low<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>tm<span class=\"token punctuation\">;<\/span><br \/>\n            st<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> inSt<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>dfn<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    <span class=\"token function\">dfs<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    low<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>low<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> low<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>inSt<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> low<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>low<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> dfn<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>low<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> dfn<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token operator\">&#043;&#043;<\/span>sc<span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> v<span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">do<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    v <span class=\"token operator\">&#061;<\/span> st<span class=\"token punctuation\">.<\/span><span class=\"token function\">top<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> st<span class=\"token punctuation\">.<\/span><span class=\"token function\">pop<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    inSt<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    comp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> sc<span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>v <span class=\"token operator\">!&#061;<\/span> u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> N<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>dfn<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token function\">dfs<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ SCC \u5185\u90e8\u51fa\u5ea6\u4e0e\u5927\u5c0f<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">innerOut<\/span><span class=\"token punctuation\">(<\/span>N <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token function\">sz<\/span><span class=\"token punctuation\">(<\/span>sc <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> N<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span> sz<span class=\"token punctuation\">[<\/span>comp<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> u <span class=\"token operator\">&lt;&#061;<\/span> N<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>u<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>comp<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> comp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> innerOut<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token keyword\">bool<\/span> escaped <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> c <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> c <span class=\"token operator\">&lt;&#061;<\/span> sc <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token operator\">!<\/span>escaped<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>c<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>sz<span class=\"token punctuation\">[<\/span>c<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> u <span class=\"token operator\">&lt;&#061;<\/span> N<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>u<span class=\"token punctuation\">)<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>comp<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> c <span class=\"token operator\">&amp;&amp;<\/span> innerOut<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> escaped <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>escaped<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;Not Trapped\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u68c0\u67e5\u539f\u56fe\u4e2d\u8282\u70b9\u51fa\u5ea6&gt;&#061;2\u4e14\u4e24\u6761\u8fb9\u8fdb\u5165\u540c\u4e00\u4e2a\u5927\u5c0f&gt;&#061;2\u7684SCC<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> u <span class=\"token operator\">&lt;&#061;<\/span> N <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token operator\">!<\/span>escaped<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>u<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>od<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            unordered_set<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> seenSCC<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> c <span class=\"token operator\">&#061;<\/span> comp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>sz<span class=\"token punctuation\">[<\/span>c<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;&#061;<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token operator\">!<\/span>seenSCC<span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span>c<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>second<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> escaped <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>escaped<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;Not Trapped\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u7f29\u70b9 DAG<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span>vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span> <span class=\"token function\">dag<\/span><span class=\"token punctuation\">(<\/span>sc <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">dout<\/span><span class=\"token punctuation\">(<\/span>sc <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token function\">din<\/span><span class=\"token punctuation\">(<\/span>sc <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span>unordered_set<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span> <span class=\"token function\">tmp<\/span><span class=\"token punctuation\">(<\/span>sc <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> u <span class=\"token operator\">&lt;&#061;<\/span> N<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>u<span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>comp<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">!&#061;<\/span> comp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>tmp<span class=\"token punctuation\">[<\/span>comp<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span>comp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span>second<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                        dag<span class=\"token punctuation\">[<\/span>comp<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>comp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                        dout<span class=\"token punctuation\">[<\/span>comp<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                        din<span class=\"token punctuation\">[<\/span>comp<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u62d3\u6251\u6392\u5e8f<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> tp<span class=\"token punctuation\">;<\/span><br \/>\n        queue<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> q<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> sc<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>din<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>q<span class=\"token punctuation\">.<\/span><span class=\"token function\">empty<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">front<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">pop<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            tp<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v <span class=\"token operator\">:<\/span> dag<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">&#8212;<\/span>din<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u6bcf\u4e2aSCC\u7684\u53ef\u8fbe\u96c6<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span>bitset<span class=\"token operator\">&lt;<\/span><span class=\"token number\">5005<\/span><span class=\"token operator\">&gt;&gt;<\/span> <span class=\"token function\">R<\/span><span class=\"token punctuation\">(<\/span>sc <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">auto<\/span> it <span class=\"token operator\">&#061;<\/span> tp<span class=\"token punctuation\">.<\/span><span class=\"token function\">rbegin<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> it <span class=\"token operator\">!&#061;<\/span> tp<span class=\"token punctuation\">.<\/span><span class=\"token function\">rend<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>it<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> <span class=\"token operator\">*<\/span>it<span class=\"token punctuation\">;<\/span><br \/>\n            R<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">set<\/span><span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v <span class=\"token operator\">:<\/span> dag<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> R<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">|&#061;<\/span> R<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ DAG\u4e2d\u51fa\u5ea6&gt;&#061;2\u7684SCC\u68c0\u67e5\u53ef\u8fbe\u96c6\u4ea4\u96c6<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> c <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> c <span class=\"token operator\">&lt;&#061;<\/span> sc <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token operator\">!<\/span>escaped<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>c<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>dout<span class=\"token punctuation\">[<\/span>c<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            bitset<span class=\"token operator\">&lt;<\/span><span class=\"token number\">5005<\/span><span class=\"token operator\">&gt;<\/span> seen<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v <span class=\"token operator\">:<\/span> dag<span class=\"token punctuation\">[<\/span>c<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>seen <span class=\"token operator\">&amp;<\/span> R<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">any<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> escaped <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n                seen <span class=\"token operator\">|&#061;<\/span> R<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token punctuation\">(<\/span>escaped <span class=\"token operator\">?<\/span> <span class=\"token string\">&#034;Not Trapped&#034;<\/span> <span class=\"token operator\">:<\/span> <span class=\"token string\">&#034;Trapped&#034;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token char\">&#039;\\\\n&#039;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token function\">solve<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><\/p>\n<h3>\u603b\u7ed3<\/h3>\n<p>\u672c\u9898\u5de7\u5999\u5730\u5c06\u201c\u8fb9\u4e0d\u76f8\u4ea4\u8def\u5f84\u201d\u7684\u5224\u5b9a\u8f6c\u5316\u4e3a\u53ef\u8fbe\u96c6\u4ea4\u96c6\u7684\u95ee\u9898&#xff0c;\u907f\u514d\u4e86\u8017\u65f6\u7684\u6700\u5927\u6d41\u8ba1\u7b97\u3002\u6838\u5fc3\u6280\u5de7\u5728\u4e8e&#xff1a;<\/p>\n<li>\u5229\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Tarjan\\\\texttt{Tarjan}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.2222em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Tarjan<\/span><\/span><\/span><\/span><\/span><\/span> \u7f29\u70b9\u5c06\u4e00\u822c\u6709\u5411\u56fe\u8f6c\u5316\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5e76\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u5185\u90e8\u9884\u5148\u8fdb\u884c\u5feb\u901f\u5224\u5b9a\u3002<\/li>\n<li>\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DAG\\\\texttt{DAG}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DAG<\/span><\/span><\/span><\/span><\/span><\/span> \u4e0a\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">bitset\\\\texttt{bitset}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">bitset<\/span><\/span><\/span><\/span><\/span><\/span> \u538b\u7f29\u5b58\u50a8\u53ef\u8fbe\u96c6\u5408&#xff0c;\u4f7f\u5f97\u4ea4\u96c6\u5224\u5b9a\u53ef\u4ee5\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N\/64)O(N\/64)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mord\">\/64<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u7684\u4f4d\u64cd\u4f5c\u5185\u5b8c\u6210&#xff0c;\u6781\u5927\u63d0\u5347\u4e86\u6548\u7387\u3002<\/li>\n<li>\u6ce8\u610f\u5904\u7406\u5e73\u884c\u8fb9\u548c\u8282\u70b9\u6307\u5411\u540c\u4e00 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u7279\u6b8a\u60c5\u51b5&#xff0c;\u786e\u4fdd\u4e0d\u6f0f\u5224\u3002<\/li>\n<p>\u8be5\u89e3\u6cd5\u5145\u5206\u5229\u7528\u4e86\u56fe\u7684\u7ed3\u6784\u6027\u8d28\u548c\u4f4d\u8fd0\u7b97\u52a0\u901f&#xff0c;\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SCC\\\\texttt{SCC}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">SCC<\/span><\/span><\/span><\/span><\/span><\/span> \u7f29\u70b9\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">bitset\\\\texttt{bitset}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">bitset<\/span><\/span><\/span><\/span><\/span><\/span> \u4f18\u5316\u7684\u7ecf\u5178\u5e94\u7528\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9898\u76ee\u63cf\u8ff0<br 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\/>\n\u57ce\u5e02\u5730\u56fe\u662f\u6709\u5411\u56fe&#xff0c;\u8282\u70b9\u8868\u793a<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55,427,4405],"topic":[],"class_list":["post-109458","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-427","tag-4405"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>UVa 11896 Inglorious Gangs - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/109458.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta 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