题意:
有n个人要回到n间房子里,每间房子只允许一个人,求n个人要走的最小距离和。
分析:
裸的二分图最小权匹配,KM搞之。
代码:
//poj 2195
//sep9
#include <iostream>
using namespace std;
const int maxN=128;
char g[maxN][maxN];
int mx[maxN],my[maxN],hx[maxN],hy[maxN];
int w[maxN][maxN];
int lx[maxN],ly[maxN],linky[maxN];
int visx[maxN],visy[maxN];
int slack[maxN];
int nx,ny;bool find(int x)
{visx[x]=true;for(int y=0;y<ny;++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=0;i<nx;++i)for(j=0,lx[i]=INT_MIN;j<ny;++j)if(w[i][j]>lx[i])lx[i]=w[i][j];for(int x=0;x<nx;++x){for(i=0;i<ny;++i)slack[i]=INT_MAX;while(1){memset(visx,0,sizeof(visx));memset(visy,0,sizeof(visy));if(find(x))break;int d=INT_MAX;for(i=0;i<ny;++i)if(!visy[i]&&slack[i]<d)d=slack[i]; if(d==INT_MAX)return -1;for(i=0;i<nx;++i)if(visx[i])lx[i]-=d;for(i=0;i<ny;++i)if(visy[i])ly[i]+=d;elseslack[i]-=d;}}int result=0;for(i=0;i<ny;++i)if(linky[i]>-1)result+=w[linky[i]][i];return result;
}int main()
{int i,j,n,m;while(scanf("%d%d",&n,&m)==2){if(n==0&&m==0)break;for(i=0;i<n;++i)scanf("%s",g[i]);int mcnt=0,hcnt=0;for(i=0;i<n;++i)for(j=0;j<m;++j)if(g[i][j]=='m'){mx[mcnt]=i;my[mcnt]=j;++mcnt;}else if(g[i][j]=='H'){hx[hcnt]=i;hy[hcnt]=j;++hcnt;} for(i=0;i<mcnt;++i)for(j=0;j<hcnt;++j){w[i][j]=abs(mx[i]-hx[j])+abs(my[i]-hy[j]);w[i][j]=-w[i][j];}nx=ny=mcnt;printf("%d\n",-KM());}return 0;
}