Going Home POJ - 2195 （最小费用最大流）

Posted 2021-01-29 zgqblogs

On a grid map there are n little men and n houses. In each unit time, every little man can move one unit step, either horizontally, or vertically, to an adjacent point. For each little man, you need to pay a $1 travel fee for every step he moves, until he enters a house. The task is complicated with the restriction that each house can accommodate only one little man. 

Your task is to compute the minimum amount of money you need to pay in order to send these n little men into those n different houses. The input is a map of the scenario, a ‘.‘ means an empty space, an ‘H‘ represents a house on that point, and am ‘m‘ indicates there is a little man on that point. 

You can think of each point on the grid map as a quite large square, so it can hold n little men at the same time; also, it is okay if a little man steps on a grid with a house without entering that house.

Input

There are one or more test cases in the input. Each case starts with a line giving two integers N and M, where N is the number of rows of the map, and M is the number of columns. The rest of the input will be N lines describing the map. You may assume both N and M are between 2 and 100, inclusive. There will be the same number of ‘H‘s and ‘m‘s on the map; and there will be at most 100 houses. Input will terminate with 0 0 for N and M.

Output

For each test case, output one line with the single integer, which is the minimum amount, in dollars, you need to pay.

Sample Input

2 2
.m
H.
5 5
HH..m
.....
.....
.....
mm..H
7 8
...H....
...H....
...H....
mmmHmmmm
...H....
...H....
...H....
0 0

Sample Output

2
10
28


思路
应该算是这个算法的板子题了，感觉还是只有看自己的代码才是最容易懂的。
cap表示边的容量，w表示费用。

#include<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<map>
#include<set>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<ctime>
#define fuck(x) cout<<#x<<" = "<<x<<endl;
#define ls (t<<1)
#define rs ((t<<1)+1)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int maxn = 1024;
const int inf = 2.1e9;
const ll Inf = 999999999999999999;
const int mod = 1000000007;
const double eps = 1e-6;
const double pi = acos(-1);
int n,m;
char mp[108][108];
struct node
{
    int x,y;
}p1[maxn],p2[maxn];
int Head[maxn],Next[maxn*maxn],v[maxn*maxn],w[maxn*maxn],cap[maxn*maxn],cnt;
int t1,t2;int ans;
void init()
{
    t1=1;cnt=t2=ans=0;
    memset(Head,-1,sizeof(Head));
}

void add(int x,int y,int z,int f){
//    cout<<x<<" "<<y<<" "<<z<<endl;
    v[cnt]=y;
    w[cnt]=z;
    cap[cnt]=f;
    Next[cnt]=Head[x];
    Head[x]=cnt++;

    v[cnt]=x;
    w[cnt]=-z;
    cap[cnt]=0;
    Next[cnt]=Head[y];
    Head[y]=cnt++;
}
bool vis[maxn];
int dis[maxn];
int prevv[maxn],preve[maxn];
int s,t;
bool spfa()
{
    queue<int>q;
    memset(vis,0,sizeof(vis));
    for(int i=1;i<=t;i++){
        dis[i]=inf;
    }

    dis[s]=0;
    q.push(s);
    while(!q.empty()){
        int u=q.front();
        q.pop();
        vis[u]=false;
        for(int k=Head[u];k!=-1;k=Next[k]){
            if(cap[k]&&dis[v[k]]>dis[u]+w[k]){
                dis[v[k]]=dis[u]+w[k];
                prevv[v[k]]=u;
                preve[v[k]]=k;

                if(!vis[v[k]]){
                    vis[v[k]]=true;
                    q.push(v[k]);
                }
            }
        }
    }
//    for(int i=1;i<=t;i++){
//        cout<<dis[i]<<" ";
//    }
//    cout<<endl;
//    getchar();getchar();
    if(dis[t]==inf){return false;}
    else return true;
}
int min_cost_flow()
{
//    fuck("???")
    while(spfa()){
//        cout<<"____"<<endl;
        for(int i=t;i!=s;i=prevv[i]){
            int k=preve[i];
            cap[k]-=1;
            cap[k^1]+=1;
        }
//        cout<<endl;
        ans+=dis[t];
    }

}

int main()
{
//    ios::sync_with_stdio(false);
//    freopen("in.txt","r",stdin);

    while(scanf("%d%d",&n,&m)!=EOF&&(n||m)){
        init();
        for(int i=1;i<=n;i++){
            scanf("%s",mp[i]+1);
            for(int j=1;j<=m;j++){
                if(mp[i][j]==‘m‘){p1[++t1]=node{i,j};}
                else if(mp[i][j]==‘H‘){p2[++t2]=node{i,j};}
            }
        }
        s=1;t=t1+t2+1;
        for(int i=2;i<=t1;i++){
            add(s,i,0,1);
            for(int j=1;j<=t2;j++){
                add(i,j+t1,abs(p1[i].x-p2[j].x)+abs(p1[i].y-p2[j].y),inf);
            }
        }
        for(int i=1;i<=t2;i++){
            add(i+t1,t,0,1);
        }

        min_cost_flow();
        printf("%d
",ans);
    }

    return 0;
}