{"id":1103,"date":"2019-05-11T16:38:03","date_gmt":"2019-05-11T08:38:03","guid":{"rendered":"https:\/\/mnihyc.com\/blog\/?p=1103"},"modified":"2020-02-09T02:53:53","modified_gmt":"2020-02-08T18:53:53","slug":"yzoj-p2872-poj-1637sightseeing-tour","status":"publish","type":"post","link":"https:\/\/mnihyc.com\/blog\/archives\/1103","title":{"rendered":"YZOJ P2872 [POJ 1637]Sightseeing tour"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P2872 [POJ 1637]Sightseeing tour<\/h1>\n<p style=\"text-align: center;\">Time Limit\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 Memory Limit\uff1a131072KB<\/p>\n<p style=\"text-align: center;\">Difficulty:<span style=\"color: #ff9900;\"> \\(6.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><span style=\"color: #000000;\">Description<\/span><\/h3>\n<\/li>\n<\/ul>\n<p>The city executive board in Lund wants to construct a sightseeing tour by bus in Lund, so that tourists can see every corner of the beautiful city. They want to construct the tour so that every street in the city is visited exactly once. The bus should also start and end at the same junction. As in any city, the streets are either one-way or two-way, traffic rules that must be obeyed by the tour bus. Help the executive board and determine if it\u2019s possible to construct a sightseeing tour under these constraints.<\/p>\n<ul>\n<li>\n<h3><strong>Input<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>On the first line of the input is a single positive integer n, telling the number of test scenarios to follow. Each scenario begins with a line containing two positive integers m and s, \\(1 \\leq m \\leq 200\\), \\(1 \\leq s \\leq 1000\\) being the number of junctions and streets, respectively. The following s lines contain the streets. Each street is described with three integers, \\(x_i\\), \\(y_i\\), and \\(d_i\\), \\(1 \\leq x_i,y_i \\leq m\\), \\(0 \\leq d_i \\leq 1\\), where \\(x_i\\) and \\(y_i\\) are the junctions connected by a street. If \\(d_i=1\\), then the street is a one-way street (going from \\(x_i\\) to \\(y_i\\)), otherwise it\u2019s a two-way street. You may assume that there exists a junction from where all other junctions can be reached.<\/p>\n<ul>\n<li>\n<h3><strong>Output<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>For each scenario, output one line containing the text \u201cpossible\u201d or \u201cimpossible\u201d, whether or not it\u2019s possible to construct a sightseeing tour.<\/p>\n<ul>\n<li>\n<h3><strong>Sample Input<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true\">4\r\n5 8\r\n2 1 0\r\n1 3 0\r\n4 1 1\r\n1 5 0\r\n5 4 1\r\n3 4 0\r\n4 2 1\r\n2 2 0\r\n4 4\r\n1 2 1\r\n2 3 0\r\n3 4 0\r\n1 4 1\r\n3 3\r\n1 2 0\r\n2 3 0\r\n3 2 0\r\n3 4\r\n1 2 0\r\n2 3 1\r\n1 2 0\r\n3 2 0<\/pre>\n<ul>\n<li>\n<h3><strong>Sample Output<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true\">possible\r\nimpossible\r\nimpossible\r\npossible<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Source: POJ 1637<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u6df7\u5408\u56fe\u6b27\u62c9\u56de\u8def\u3002<\/p>\n<p>\u9996\u5148\u628a\u8be5\u56fe\u7684\u65e0\u5411\u8fb9\u4efb\u610f\u5b9a\u5411\uff0c\u8ba1\u7b97\u6bcf\u4e2a\u70b9\u7684\u5165\u5ea6\u548c\u51fa\u5ea6\u3002<\/p>\n<p>\u5982\u679c\u6709\u67d0\u4e2a\u70b9\u51fa\u5165\u5ea6\u4e4b\u5dee\u4e3a<strong>\u5947\u6570<\/strong>\uff0c\u90a3\u4e48\u80af\u5b9a<strong>\u4e0d\u5b58\u5728<\/strong>\u6b27\u62c9\u56de\u8def\u3002\u56e0\u4e3a\u6b27\u62c9\u56de\u8def\u8981\u6c42\u6bcf\u70b9 \\(din=dout\\)\uff0c \u4e5f\u5c31\u662f\u603b\u5ea6\u6570\u4e3a\u5076\u6570\uff0c\u5b58\u5728\u5947\u6570\u5ea6\u70b9\u5fc5\u4e0d\u80fd\u6709\u6b27\u62c9\u56de\u8def\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u6bcf\u4e2a\u70b9\u5165\u5ea6\u548c\u51fa\u5ea6\u4e4b\u5dee\u5747\u4e3a\u5076\u6570\uff0c\u8bbe \\(x=\\frac{\\left| din-dout \\right|}{2}\\) \u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u70b9\uff0c\u53ea\u8981\u5c06 \\(x\\) \u6761\u8fb9\u6539\u53d8\u65b9\u5411\uff08\\(din&gt;dout\\) \u5c31\u662f\u628a\u5165\u8fb9\u53d8\u5411\uff0c\\(dout&gt;din\\) \u5c31\u662f\u628a\u51fa\u8fb9\u53d8\u5411\uff09\uff0c\u5c31\u80fd\u4fdd\u8bc1 \\(din=dout\\) \u3002\u5982\u679c\u6bcf\u4e2a\u70b9\u90fd\u662f \\(din=dout\\)\uff0c\u90a3\u4e48\u8be5\u56fe\u5c31\u662f\u6b27\u62c9\u56de\u8def\u3002<\/p>\n<p>\u95ee\u9898\u8f6c\u5316\u4e3a\uff0c\u6539\u53d8\u4e00\u4e9b\u8fb9\uff0c\u53ef\u4ee5\u8ba9\u6bcf\u4e2a\u70b9 \\(din=dout\\) \u3002<\/p>\n<p>\u9996\u5148\uff0c\u6709\u5411\u8fb9\u4e0d\u80fd\u6539\u53d8\u65b9\u5411\uff0c\u6ca1\u6709\u5efa\u51fa\u6765\u7684\u5fc5\u8981\u3002<\/p>\n<p>\u56e0\u4e3a \\(din, dout\\) \u662f\u628a\u65e0\u5411\u8fb9\u5b9a\u5411\u540e\u7b97\u51fa\u6765\u7684\uff0c\u6240\u4ee5\u56fe\u4e2d\u5e94\u6709\u8fd9\u4e00\u6761\u5b9a\u5411\u540e\u7684\u8fb9\uff0c\u5bb9\u91cf\u4e3a \\(1\\) \u3002<\/p>\n<p>\u65b0\u5efa \\(S,T\\) \uff1a\u5bf9\u4e8e \\(din&gt;dout\\) \u7684\u70b9 \\(u\\)\uff0c\u8fde \\(u \\rightarrow T\\) \u5bb9\u91cf\u4e3a \\(x_u\\) \u7684\u8fb9\uff1b\u5bf9\u4e8e \\(dout&gt;din\\) \u7684\u70b9 \\(v\\) \uff0c\u8fde \\(S \\rightarrow v\\) \u5bb9\u91cf\u4e3a \\(x_v\\) \u7684\u8fb9\u3002<\/p>\n<p>\u7136\u540e\u8dd1\u6700\u5927\u6d41\uff0c\u6ee1\u6d41\u5219\u53ef\u4ee5\u5b58\u5728\u6b27\u62c9\u56de\u8def\u3002<\/p>\n<p>\u6ca1\u6709\u8fde\u63a5 \\(S,T\\) \u7684\u8fb9\u5bb9\u91cf\u4e3a \\(1\\) \uff0c\u6709\u6d41\u91cf\u8868\u793a\u8fd9\u6761\u8fb9\u53cd\u5411\uff1b\u4e0e \\(S, T\\) \u76f8\u8fde\u7684\u8fb9\u8868\u793a\u6709\u5bb9\u91cf\u4e3a \\(x\\) \u6761\u8fb9\u9700\u8981\u53cd\u5411\uff0c\u5224\u65ad\u6ee1\u6d41\u5373\u53ef\u3002<\/p>\n<p><a href=\"https:\/\/wenku.baidu.com\/view\/0ad00abec77da26925c5b01c.html\">https:\/\/wenku.baidu.com\/view\/0ad00abec77da26925c5b01c.html<\/a><\/p>\n<p>&nbsp;<\/p>\n<pre class=\"lang:default decode:true \">#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#define _abs(_a) ((_a)&lt;0?-(_a):(_a))\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[505],gnext[5050],gnode[5050],gflow[5050];\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[505];\r\ninline bool BFS()\r\n{\r\n\tstatic int lst[505];\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[505];\r\nint DFS(register int now,register int mxflow)\r\n{\r\n\tif(now == T)\r\n\t\treturn mxflow;\r\n\t\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\t\r\n\treturn 0;\r\n}\r\n\r\nint din[505],dout[505];\r\n\r\nint main()\r\n{\r\nregister int _T=getnum();\r\nrestart:\r\nwhile(_T--)\r\n{\r\n\tgcnt=0,memset(ghead,0,sizeof(ghead));\r\n\tmemset(din,0,sizeof(din)),memset(dout,0,sizeof(dout));\r\n\tregister int N=getnum(),M=getnum();\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t{\r\n\t\tregister int u=getnum(),v=getnum(),d=getnum();\r\n\t\tdin[v]++,dout[u]++;\r\n\t\tif(!d)\r\n\t\t\tinsertLine(u,v,1);\r\n\t}\r\n\tS=N+1,T=S+1;\r\n\tregister int tout=0;\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tif(_abs(din[i]-dout[i])%2 != 0)\r\n\t\t{\r\n\t\t\tprintf(\"impossible\\n\");\r\n\t\t\tgoto restart;\r\n\t\t}\r\n\t\telse\r\n\t\t\tif(din[i] &gt; dout[i])\r\n\t\t\t\tinsertLine(i,T,(din[i]-dout[i])&gt;&gt;1),tout+=(din[i]-dout[i])&gt;&gt;1;\r\n\t\t\telse if(din[i] &lt; dout[i])\r\n\t\t\t\tinsertLine(S,i,(dout[i]-din[i])&gt;&gt;1);\r\n\t\r\n\tregister int ans=0;\r\n\twhile(BFS())\r\n\t{\r\n\t\tfor(register int i=1;i&lt;=T;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(\"%s\\n\",(ans==tout ? \"possible\" : \"impossible\"));\r\n}\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 P2872 [POJ 1637]Sightseeing tour Time Limit\uff1a1000MS &hellip; <a href=\"https:\/\/mnihyc.com\/blog\/archives\/1103\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P2872 [POJ 1637]Sightseeing tour<\/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-1103","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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