{"id":1078,"date":"2019-05-11T15:22:47","date_gmt":"2019-05-11T07:22:47","guid":{"rendered":"https:\/\/cf.mnihyc.com\/blog\/?p=1078"},"modified":"2020-02-09T02:55:54","modified_gmt":"2020-02-08T18:55:54","slug":"yzoj-p3049-shoi2010minimum-spanning-tree","status":"publish","type":"post","link":"https:\/\/cf.mnihyc.com\/blog\/archives\/1078","title":{"rendered":"YZOJ P3049 [SHOI2010]Minimum Spanning Tree"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3049 [SHOI2010]Minimum Spanning Tree<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a<span style=\"color: #ff9900;\">\\(6.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u6709\u4e00\u4e2a \\(n\\) \u4e2a\u70b9\uff0c\\(m\\) \u6761\u8fb9\u7684\u65e0\u5411\u56fe\uff0c\u6bcf\u6b21\u53ef\u4ee5\u5bf9\u8fd9\u5f20\u56fe\u8fdb\u884c\u64cd\u4f5c\uff1a\u5bf9\u4e8e\u4e00\u6761\u8fb9 \\((u,v)\\)\uff0c\u53ef\u4ee5\u628a\u56fe\u4e2d\u9664\u4e86\u8fd9\u6761\u8fb9\u4ee5\u5916\u7684\u8fb9\uff0c\u6bcf\u4e00\u6761\u7684\u6743\u503c\u90fd\u51cf\u5c11 \\(1\\)\u3002<\/p>\n<p>\u5bf9\u4e8e\u67d0\u4e00\u6761\u7f16\u53f7\u4e3a \\(e\\) \u7684\u8fb9\uff0c\u81f3\u5c11\u9700\u8981\u591a\u5c11\u6b21\u64cd\u4f5c\uff0c\u624d\u80fd\u4fdd\u8bc1\u5176\u80fd\u51fa\u73b0\u5728\u6700\u5c0f\u751f\u6210\u6811\u4e2d\uff1f<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u8f93\u5165\u4e09\u4e2a\u6574\u6570 \\(n\\)\u3001\\(m\\)\u3001\\(e\\)\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\u8f93\u5165 \\(m\\) \u884c\uff0c\u6bcf\u884c\u8f93\u5165\u4e09\u4e2a\u6574\u6570\uff0c\u5176\u4e2d\u7b2c \\(i+1\\) \u884c\u8f93\u5165\u7684\u6574\u6570\u5206\u522b\u4e3a \\(u_i\\)\u3001\\(v_i\\)\u3001\\(w_i\\)\uff0c\u8868\u793a\u65e0\u5411\u56fe\u7684\u8fb9\u7684\u4e24\u4e2a\u7aef\u70b9\u548c\u8fb9\u6743\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u51fa\u4e00\u4e2a\u6574\u6570\u8868\u793a\u7b54\u6848\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true \">5 8 8\r\n5 1 1\r\n5 2 2\r\n5 3 5\r\n5 4 7\r\n1 2 0\r\n2 3 15\r\n2 4 25\r\n1 4 100<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">170<\/pre>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e \\(50\\%\\) \u7684\u6570\u636e\uff0c\\(n \\leq 300\\)\uff0c\\(m \\leq 1000\\) \u3002<\/p>\n<p>\u5bf9\u4e8e \\(100\\%\\) \u7684\u6570\u636e\uff0c\\(n \\leq 2 \\times 10^4\\)\uff0c\\(m \\leq 2 \\times 10^5\\)\uff0c\\(0 \\leq w_i \\leq 2\\times 10^4\\) \u3002<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u8003\u8651 Kruskal \u7b97\u6cd5\uff0c\u8fb9 \\(e\\) \u51fa\u73b0\u5728\u6700\u5c0f\u751f\u6210\u6811\u4e2d\uff0c\u5f53\u4e14\u4ec5\u5f53\u6743\u503c\u6bd4\u5b83\u5c0f\u7684\u8fb9\u5168\u90e8\u52a0\u8fdb\u53bb\u65f6\uff0c\u4ecd\u7136\u4e0d\u80fd\u4f7f\u5f97 \\(e\\) \u7684\u4e24\u7aef\u70b9\u8fde\u901a\u3002<\/p>\n<p>\u6240\u4ee5\u5c31\u6709\u4e86\u4e00\u4e2a\u505a\u6cd5\uff0c\u628a\u6743\u503c\u6bd4\u5b83\u5c0f\u7684\u8fb9\u5168\u90e8\u5f04\u6210\u6bd4\u5b83\u5927\uff0c\u4ee3\u4ef7\u5c31\u662f\u6743\u503c\u7684\u5dee\u503c\uff0c\u8981\u5272\u6389\u6743\u503c\u548c\u5c3d\u91cf\u5c0f\u7684\u4e00\u4e9b\u8fb9\uff0c\u4f7f\u5f97 \\(e\\) \u7684\u4e24\u7aef\u70b9\u4e0d\u8fde\u901a\u3002<\/p>\n<p>\u53d1\u73b0\u8fd9\u662f\u4e00\u4e2a\u6700\u5c0f\u5272\u6a21\u578b\u3002<\/p>\n<p>&nbsp;<\/p>\n<pre class=\"lang:default decode:true \">\/\/ Powered by C4droid with GCCv7.2.0\r\n#include &lt;cstdio&gt;\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;climits&gt;\r\n\r\n#define INFINITE 0x7F7F7F7F\r\n#define _min(_a_,_b_) ((_a_)&lt;(_b_)?(_a_):(_b_))\r\n \r\ninline int getnum()\r\n{\r\n\tregister char c=0;\r\n\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=getchar();\r\n\tregister int a=0;\r\n\twhile(c&gt;='0' &amp;&amp; c&lt;='9')\r\n\t\ta=a*10+c-'0',c=getchar();\r\n\treturn a;\r\n}\r\n \r\n#define GetReverse(_x) ((_x)&amp;1 ? (_x)+1 : (_x)-1)\r\nint gcnt,ghead[20505],gnext[805050],gnode[805050],gflow[805050];\r\ninline void insertLine(register int s,register int t,const int&amp;v)\r\n{\r\n\tgnext[++gcnt]=ghead[s],ghead[s]=gcnt,gnode[gcnt]=t,gflow[gcnt]=v;\r\n\tgnext[++gcnt]=ghead[t],ghead[t]=gcnt,gnode[gcnt]=s,gflow[gcnt]=0;\r\n}\r\n\r\nint S,T;\r\nint dist[20505];\r\ninline bool BFS()\r\n{\r\n\tstatic int lst[20505];\r\n\tregister int front=0,rear=0;\r\n\tmemset(dist,0,sizeof(dist));\r\n\t\r\n\tdist[S]=1,lst[rear++]=S;\r\n\twhile(front&lt;rear)\r\n\t{\r\n\t\tregister int now=lst[front++];\r\n\t\tfor(register int j=ghead[now],t;j;j=gnext[j])\r\n\t\t\tif(gflow[j]&gt;0 &amp;&amp; !dist[t=gnode[j]])\r\n\t\t\t\tdist[t]=dist[now]+1,lst[rear++]=t;\r\n\t}\r\n\treturn dist[T];\r\n}\r\n \r\nint cur[20505];\r\nint DFS(register int now,register int mxflow)\r\n{\r\n\tif(now == T)\r\n\t\treturn mxflow;\r\n\tfor(register int j=cur[now],t;j;j=gnext[j])\r\n\t{\r\n\t\tcur[now]=j,t=gnode[j];\r\n\t\tif(!(gflow[j]&gt;0 &amp;&amp; dist[t]==dist[now]+1))\r\n\t\t\tcontinue;\r\n\t\tregister int nf=DFS(t,_min(mxflow,gflow[j]));\r\n\t\tif(nf)\r\n\t\t{\r\n\t\t\tgflow[j]-=nf;\r\n\t\t\tgflow[GetReverse(j)]+=nf;\r\n\t\t\treturn nf;\r\n\t\t}\r\n\t}\r\n\treturn 0;\r\n}\r\n\r\nint es[205050],et[205050],ew[205050];\r\n\r\nint main()\r\n{\r\n\tregister int N=getnum(),M=getnum(),E=getnum();\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t    es[i]=getnum(),et[i]=getnum(),ew[i]=getnum();\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t    if(i!=E &amp;&amp; ew[i]&lt;=ew[E])\r\n\t    {\r\n\t        insertLine(es[i],et[i],ew[E]-ew[i]+1);\r\n\t        insertLine(et[i],es[i],ew[E]-ew[i]+1);\r\n\t    }\r\n\t\r\n\tS=es[E],T=et[E];\r\n\tregister int ans=0;\r\n\twhile(BFS())\r\n\t{\r\n\t\tfor(register int i=1;i&lt;=N;i++)\r\n\t\t\tcur[i]=ghead[i];\r\n\t\twhile(int nf=DFS(S,INFINITE))\r\n\t\t\tans+=nf;\r\n\t}\r\n\tprintf(\"%d\\n\",ans);\r\n\t\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P3049 [SHOI2010]Minimum Spanning Tree \u65f6\u95f4\u9650\u5236\uff1a1000MS  &hellip; <a href=\"https:\/\/cf.mnihyc.com\/blog\/archives\/1078\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3049 [SHOI2010]Minimum Spanning Tree<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[41,78],"tags":[],"class_list":["post-1078","post","type-post","status-publish","format-standard","hentry","category-proa","category-networkflows"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - 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