km算法

http://acm.hdu.edu.cn/showproblem.php?pid=2255

km模板，二分图最优匹配，复杂度O(n^3)

http://www.cnblogs.com/jackge/archive/2013/05/03/3057028.html

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int N=310;
const int INF=0x3f3f3f3f;
int n,nx,ny;
int linker[N],lx[N],ly[N],slack[N];  
int visx[N],visy[N],w[N][N];
int DFS(int x)
{
    visx[x]=1;
    for(int y=1;y<=ny;y++){
        if(visy[y])
            continue;
        int tmp=lx[x]+ly[y]-w[x][y];
        if(tmp==0){
            visy[y]=1;
            if(linker[y]==-1 || DFS(linker[y])){
                linker[y]=x;
                return 1;
            }
        }else if(slack[y]>tmp){ 
            slack[y]=tmp;
        }
    }
    return 0;
}
int KM()
{
    int i,j;
    memset(linker,-1,sizeof(linker));
    memset(ly,0,sizeof(ly));
    for(i=1;i<=nx;i++)      
        for(j=1,lx[i]=-INF;j<=ny;j++)
            if(w[i][j]>lx[i])
                lx[i]=w[i][j];
    for(int x=1;x<=nx;x++){
        for(i=1;i<=ny;i++)
            slack[i]=INF;
        while(1){
            memset(visx,0,sizeof(visx));
            memset(visy,0,sizeof(visy));
            if(DFS(x))  
                break;  
            int d=INF;
            for(i=1;i<=ny;i++)
                if(!visy[i] && d>slack[i])
                    d=slack[i];
            for(i=1;i<=nx;i++)
                if(visx[i])
                    lx[i]-=d;
            for(i=1;i<=ny;i++) 
                if(visy[i])
                    ly[i]+=d;
                else
                    slack[i]-=d;
        }
    }
    int res=0;
    for(i=1;i<=ny;i++)
        if(linker[i]!=-1)
            res+=w[linker[i]][i];
    return res;
}
int main()
{
    while(~scanf("%d",&n))
    {
        nx=ny=n;
        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++)
                scanf("%d",&w[i][j]);
        int ans=KM();
        printf("%d\n",ans);
    }    
    return 0;
}