﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:trackback="http://madskills.com/public/xml/rss/module/trackback/" xmlns:wfw="http://wellformedweb.org/CommentAPI/" xmlns:slash="http://purl.org/rss/1.0/modules/slash/"><channel><title>C++博客-心無雜念的空白-文章分类-算法模板</title><link>http://www.cppblog.com/lshain/category/18266.html</link><description>Beyond this world...</description><language>zh-cn</language><lastBuildDate>Thu, 01 Dec 2011 03:22:21 GMT</lastBuildDate><pubDate>Thu, 01 Dec 2011 03:22:21 GMT</pubDate><ttl>60</ttl><item><title>KM算法 模板</title><link>http://www.cppblog.com/lshain/articles/150835.html</link><dc:creator>Lshain</dc:creator><author>Lshain</author><pubDate>Wed, 13 Jul 2011 03:47:00 GMT</pubDate><guid>http://www.cppblog.com/lshain/articles/150835.html</guid><description><![CDATA[<p>/******************************************************<br />Kuhn－Munkras算法流程： <br />(1)初始化可行顶标的值 ；<br />(2)用匈牙利算法寻找完备匹配； <br />(3)若未找到完备匹配则修改可行顶标的值 ；<br />(4)重复(2)(3)直到找到相等子图的完备匹配为止 。<br />*******************************************************/<br />#define MAXINT&nbsp;&nbsp;(int)((1u&lt;&lt;31) - 1)<br />#define MININT&nbsp;&nbsp;(int)(-MAXINT - 1)<br />#define MAX(x, y)&nbsp;((x) &gt; (y) ? (x) : (y))<br />#define MIN(x, y)&nbsp;((x) &lt; (y) ? (x) : (y))<br />#define N&nbsp;&nbsp;&nbsp;(500)</p>
<p>int n;<br />bool x[N], y[N];&nbsp;//是否检测标志<br />int lx[N], ly[N];&nbsp;//lx[],ly[] 可行顶标，何谓&#8220;可行顶标&#8221;，即人为限制每次DFS各边应达到的权，当然要尽量大<br />int cost[N][N];&nbsp;&nbsp;//weight[][] 二分图边权<br />int match[N];&nbsp;&nbsp;//match[] 标记y[]所连接的x[]</p>
<p>/** 找增广路径，看各边能否达到可行顶标，标记*/<br />bool dfs(int v){<br />&nbsp;int i = 0;<br />&nbsp;int temp = 0;<br />&nbsp;x[v] = true;<br />&nbsp;for(i = 1; i &lt;= n; i++){<br />&nbsp;&nbsp;if(!y[i] &amp;&amp; (lx[v] + ly[i]) == cost[v][i]){<br />&nbsp;&nbsp;&nbsp;y[i] = true;<br />&nbsp;&nbsp;&nbsp;temp = match[i];<br />&nbsp;&nbsp;&nbsp;match[i] = v;<br />&nbsp;&nbsp;&nbsp;if(temp == 0 || dfs(temp)){<br />&nbsp;&nbsp;&nbsp;&nbsp;return true;<br />&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;match[i] = temp;<br />&nbsp;&nbsp;}<br />&nbsp;}<br />&nbsp;return false;<br />}</p>
<p>int KM(){<br />&nbsp;int i = 0;<br />&nbsp;int j = 0;<br />&nbsp;int k = 0;<br />&nbsp;int d = 0;<br />&nbsp;int sum = 0;<br />&nbsp;fill(lx + 1, lx + 1 + n, MININT);<br />&nbsp;fill(ly + 1, ly + 1 + n, 0);<br />&nbsp;fill(match + 1, match + 1 + n, 0);<br />&nbsp;for(i = 1; i &lt;= n; i++){<br />&nbsp;&nbsp;for(j = 1; j &lt;= n; j++){<br />&nbsp;&nbsp;&nbsp;/** 初始化可行顶标，既是&#8220;人为&#8221;规定，当然应该越大越好*/<br />&nbsp;&nbsp;&nbsp;lx[i] = MAX(lx[i], cost[i][j]);<br />&nbsp;&nbsp;}<br />&nbsp;}<br />&nbsp;/** KM过程*/<br />&nbsp;for(i = 1;i &lt;= n; i++){<br />&nbsp;&nbsp;do{<br />&nbsp;&nbsp;&nbsp;fill(x + 1, x + 1 + n, false);<br />&nbsp;&nbsp;&nbsp;fill(y + 1, y + 1 + n, false);<br />&nbsp;&nbsp;&nbsp;if(dfs(i)){<br />&nbsp;&nbsp;&nbsp;&nbsp;break;<br />&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;d = MAXINT;<br />&nbsp;&nbsp;&nbsp;for(j = 1; j &lt;= n; j++){<br />&nbsp;&nbsp;&nbsp;&nbsp;if(x[j]){<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for(k = 1; k &lt;= n; k++){<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if(!y[k]){<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;d = MIN(d, ((lx[j] + ly[k]) - cost[j][k]));<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;/** 某些边无法匹配，说明&#8220;人为&#8221;规定的权太大，故减为比它小的最大权*/<br />&nbsp;&nbsp;&nbsp;for(j = 1; j &lt;= n; j++){<br />&nbsp;&nbsp;&nbsp;&nbsp;if(x[j]){<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;lx[j] -= d;<br />&nbsp;&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;&nbsp;if(y[j]){<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ly[j] += d;<br />&nbsp;&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;&nbsp;}<br />&nbsp;&nbsp;}while(1);<br />&nbsp;}<br />&nbsp;sum = 0;<br />&nbsp;for(i = 1; i &lt;= n; i++){<br />&nbsp;&nbsp;sum += cost[match[i]][i];<br />&nbsp;}<br />&nbsp;return sum;<br />}</p>   <img src ="http://www.cppblog.com/lshain/aggbug/150835.html" width = "1" height = "1" /><br><br><div align=right><a style="text-decoration:none;" href="http://www.cppblog.com/lshain/" target="_blank">Lshain</a> 2011-07-13 11:47 <a href="http://www.cppblog.com/lshain/articles/150835.html#Feedback" target="_blank" style="text-decoration:none;">发表评论</a></div>]]></description></item></channel></rss>