Going Home HDU - 1533 费用流

http://acm.hdu.edu.cn/showproblem.php?pid=1533

给一个网格图,每两个点之间的匹配花费为其曼哈顿距离,问给每个的"$m$"匹配到一个"$H$"的最小花费

思路:

实际上应该是一道KM匹配的题,不过也可以转化为费用流

建立附加源汇点,$m$连接源点,$H$连接汇点,其余建立$num(H)*num(m)$条边,容量为1,费用为曼哈顿距离,跑一边费用流就行....

#include <bits/stdc++.h>
#define ll long long
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pp pair<int,int>
#define rep(ii,a,b) for(int ii=a;ii<=b;ii++)
#define	per(ii,a,b) for(int ii=a;ii>=b;ii--)
#define show(x) cout<<#x<<"="<<x<<endl
#define show2(x,y) cout<<#x<<"="<<x<<" "<<#y<<"="<<y<<endl
#define show3(x,y,z) cout<<#x<<"="<<x<<" "<<#y<<"="<<y<<" "<<#z<<"="<<z<<endl
#define showa(a,b) cout<<#a<<'['<<b<<"]="<<b[a]<<endl
using namespace std;
const int maxn=1e5+10;
const int maxm=1e6+10;
const int INF=0x3f3f3f3f;
int casn,n,m,k;
struct node {
	int pre,to,cap,cost,next;
}e[maxm];
int head[maxn],nume,inq[maxn],sum,ans;
int q[maxn],pre[maxn],dis[maxn];
int num[maxn],ss,tt;
inline void addx(int a,int b,int c,int d){
	e[++nume]={a,b,c,d,head[a]};
	head[a]=nume;
}
inline void add(int a,int b,int c,int d){
	addx(a,b,c,d);addx(b,a,0,-d);
}
bool spfa(int s=ss,int t=tt){
	for(int i=0;i<=t;i++)dis[i]=INF;
	dis[s]=q[0]=s;
	int top=0,end=1;
	while(top!=end){
		int now=q[top++];top%=maxn;
		for(int i=head[now];i;i=e[i].next){
      int to=e[i].to;
			if(e[i].cap&&dis[to]>dis[now]+e[i].cost){
				pre[to]=i;
				dis[to]=dis[now]+e[i].cost;
				if(!inq[to]){
					inq[e[i].to]=true;
          if(dis[to]<dis[q[top]]){
            top=(top==0)?maxn-1:top-1;
		  		  q[top]=to;
					}else{
						q[end++]=to;end%=maxn;
					}
				}
			}
		}
		inq[now]=false;
	}
	return dis[t]!=INF;
}

void dfs(int s=ss,int t=tt){
	int flow=INF;
	for(int i=pre[t];i;i=pre[e[i].pre]) flow=min(flow,e[i].cap);
	for(int i=pre[t];i;i=pre[e[i].pre]) {
		e[i].cap-=flow;
		e[i^1].cap+=flow;
		ans+=e[i].cost*flow;
	}
}
int hh[123][2];
int mm[123][2];
int main(){
//#define test
#ifdef test
	freopen("in.txt","r",stdin);freopen("out.txt","w",stdout);
#endif
	IO;
  while(cin>>n>>m,n+m){
    nume=1;
    int cnt1=0,cnt2=0;
    char ch;
    memset(head,0,sizeof head);
    nume=1;
    for(int i=1;i<=n;i++){
      for(int j=1;j<=m;j++){
        cin>>ch;
        if(ch=='m') {
          mm[++cnt1][0]=i;
          mm[cnt1][1]=j;
        }
        if(ch=='H') {
          hh[++cnt2][0]=i;
          hh[cnt2][1]=j;
        }
      }
    }
    ss=0,tt=cnt1+cnt2+1;
    for(int i=1;i<=cnt1;i++){
      add(ss,i,1,0);
      for(int j=1;j<=cnt2;j++){
        add(i,j+cnt1,1,abs(hh[j][0]-mm[i][0])+abs(hh[j][1]-mm[i][1]));
      }
    }
    for(int i=1;i<=cnt2;i++){
      add(i+cnt1,tt,1,0);
    }
    ans=0;
    while(spfa())dfs();
    cout<<ans<<endl;
  }
#ifdef test
	fclose(stdin);fclose(stdout);system("out.txt");
#endif
	return 0;
}