D - Going Home POJ - 2195 网络流

#include <cstdio>
#include <cstdlib>
#include <queue>
#include <vector>
#include <iostream>
#include <algorithm>
#include <map>
#include <cstring>
#include <cmath>
#include <string>
#define inf 0x3f3f3f3f
using namespace std;
typedef long long ll;
const int INF = 0x3f3f3f3f;
const int maxn = 1000 + 10;
struct edge
{
    int u, v, c, f, cost;
    edge(int u, int v, int c, int f, int cost) :u(u), v(v), c(c), f(f), cost(cost) {}
};
vector<edge>e;
vector<int>G[maxn];
int a[maxn];//找增广路每个点的水流量
int p[maxn];//每次找增广路反向记录路径
int d[maxn];//SPFA算法的最短路
int inq[maxn];//SPFA算法是否在队列中
int s, t;
void init()
{
    for (int i = 0; i <= maxn; i++)G[i].clear();
    e.clear();
}
void add(int u, int v, int c, int cost)
{
    e.push_back(edge(u, v, c, 0, cost));
    e.push_back(edge(v, u, 0, 0, -cost));
    int m = e.size();
    G[u].push_back(m - 2);
    G[v].push_back(m - 1);
}
bool bellman(int s, int t, int& flow, long long & cost)
{
    memset(d, inf, sizeof(d));
    memset(inq, 0, sizeof(inq));
    d[s] = 0; inq[s] = 1;//源点s的距离设为0，标记入队
    p[s] = 0; a[s] = INF;//源点流量为INF（和之前的最大流算法是一样的）

    queue<int>q;//Bellman算法和增广路算法同步进行，沿着最短路拓展增广路，得出的解一定是最小费用最大流
    q.push(s);
    while (!q.empty())
    {
        int u = q.front();
        q.pop();
        inq[u] = 0;//入队列标记删除
        for (int i = 0; i < G[u].size(); i++)
        {
            edge & now = e[G[u][i]];
            int v = now.v;
            if (now.c > now.f && d[v] > d[u] + now.cost)
                //now.c > now.f表示这条路还未流满（和最大流一样）
                //d[v] > d[u] + e.cost Bellman 算法中边的松弛
            {
                d[v] = d[u] + now.cost;//Bellman 算法边的松弛
                p[v] = G[u][i];//反向记录边的编号
                a[v] = min(a[u], now.c - now.f);//到达v点的水量取决于边剩余的容量和u点的水量
                if (!inq[v]) { q.push(v); inq[v] = 1; }//Bellman 算法入队
            }
        }
    }
    if (d[t] == INF)return false;//找不到增广路
    flow += a[t];//最大流的值，此函数引用flow这个值，最后可以直接求出flow
    cost += (long long)d[t] * (long long)a[t];//距离乘上到达汇点的流量就是费用
    for (int u = t; u != s; u = e[p[u]].u)//逆向存边
    {
        e[p[u]].f += a[t];//正向边加上流量
        e[p[u] ^ 1].f -= a[t];//反向边减去流量 （和增广路算法一样）
    }
    return true;
}
int MincostMaxflow(int s, int t, long long & cost)
{
    cost = 0;
    int flow = 0;
    while (bellman(s, t, flow, cost));//由于Bellman函数用的是引用，所以只要一直调用就可以求出flow和cost
    return flow;//返回最大流，cost引用可以直接返回最小费用
}
struct node
{
    int x, y;
    node(int x=0,int y=0):x(x),y(y){}
};
node peo[110], house[110];
char mp[110][110];
int main()
{
    int n, m;
    while(cin>>n>>m)
    {
        init();
        int cas = 0, tot = 0;
        if (n == 0 && m == 0) break;
        for (int i = 1; i <= n; i++)
        {
            cin >> mp[i] + 1;
            for(int j=1;j<=m;j++)
            {
                if (mp[i][j] == ‘m‘) peo[++cas] = node(i, j);
                if (mp[i][j] == ‘H‘) house[++tot] = node(i, j);
            }
        }
        s = 0, t = cas + tot + 1;
        for (int i = 1; i <= cas; i++) add(s, i, 1, 0);
        for (int i = 1; i <= tot; i++) add(cas + i, t, 1, 0);
        for(int i=1;i<=cas;i++)
        {
            for(int j=1;j<=tot;j++)
            {
                int cost = abs(peo[i].x - house[j].x) + abs(peo[i].y - house[j].y);
                add(i, j + cas, 1, cost);
            }
        }
        ll cost = 0;
        int ans = MincostMaxflow(s, t, cost);
        printf("%lld\n", cost);
    }
    return 0;
}