二分图匹配（KM算法）n^3 分类： ACM TYPE 2014-10-01 21:46 98人阅读 评论(0) 收藏

#include <iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
const int maxn = 301;
const int INF = (1<<31)-1;
int w[maxn][maxn];
int lx[maxn],ly[maxn]; //顶标

int linky[maxn];

int visx[maxn],visy[maxn];
int slack[maxn];
int n;
bool find(int x)
{
    visx[x] = true;
    for(int y = 1; y <=n; y++)
    {
        if(visy[y])   continue;
        int t = lx[x] + ly[y] - w[x][y];
        if(t==0)
        {
            visy[y] = true;
            if(linky[y] == -1 || find(linky[y]))
            {
                linky[y] = x;
                return true;        
            }
        }
        else if(slack[y] > t)      slack[y] = t;
    }
    return false;                   
}

int KM()                
{
    int i,j;

    memset(linky,-1,sizeof(linky));
    memset(ly,0,sizeof(ly));
    
    for(i = 1; i <=n; i++)			//初始化顶标 
    {
         lx[i] = -INF;
         for(j = 1; j <=n; j++)
         {
            if(w[i][j] > lx[i])   lx[i] = w[i][j];         	
         }
    }

    for(int x = 1; x <=n; x++)
    {
        for(i = 1; i <=n; i++) 	slack[i] = INF;
        while(true)
        {
            memset(visx,0,sizeof(visx));
            memset(visy,0,sizeof(visy));
            if(find(x))  break;
            int d = INF;
            
            for(i = 1; i <=n; i++)          
            {
                if(!visy[i] && d > slack[i])    d = slack[i];
            }
            for(i = 1; i <=n; i++)
            {
                if(visx[i])    lx[i] -= d;
            }
            for(i = 1; i <=n; i++)
            {
                if(visy[i])	   ly[i] += d;
                else           slack[i] -= d;
            }
        }
    }
    
    int result = 0;
    for(i = 1; i <=n; i++)
    {
	    if(linky[i]>-1)
	    {
	        result += w[linky[i]][i];    	    	
	    }
    }

    return result;
}

int main()
{

    while(scanf("%d",&n)==1)
    {
        int cost;
        for(int i=1;i<=n;i++)
        {
	        for(int j=1;j<=n;j++)
	        {
	            scanf("%d",&cost);
	            w[i][j] = cost;
	        }        	
        }
        printf("%d\n",KM());
    }
    return 0;
}

更新顶标的问题的了

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