连续最短路算法（Successive Shortest Path）（最小费用最大流）

#include <cstdio>
#include <cstring>
#include <queue>
#include <vector>
#include <algorithm>
using namespace std;
#define N 205
#define INF 0x3f3f3f3f
struct node {
    int x, y;
    node () {}
    node (int x, int y) : x(x), y(y) {}
};
struct Edge {
    int cap, u, v, cost;
    Edge() {}
    Edge(int u, int v, int cap, int cost) : u(u), v(v), cap(cap), cost(cost) {}
}edge[N*N];
vector<node> p, h;
vector<int> G[N];
int tot, dis[N], inq[N], pre[N], S, T;

void AddEdge(int u, int v, int cap, int cost) {
    edge[tot] = Edge(u, v, cap, cost);
    G[u].push_back(tot++);
    edge[tot] = Edge(v, u, 0, -cost);
    G[v].push_back(tot++);
}

int CalDis(int x1, int y1, int x2, int y2) {
    return abs(x1 - x2) + abs(y1 - y2);
}

bool SPFA() {
    memset(inq, 0, sizeof(inq));
    memset(dis, INF, sizeof(dis));
    queue<int> que; que.push(S);
    dis[S] = 0; inq[S] = 1;
    while(!que.empty()) {
        int u = que.front(); que.pop(); inq[u] = 0;
        for(int i = 0; i < G[u].size(); i++) {
            Edge &e = edge[G[u][i]];
            if(e.cap > 0 && dis[e.v] > e.cost + dis[u]) {
            // 当可以增广并且费用更小的时候
                dis[e.v] = e.cost + dis[u];
                pre[e.v] = G[u][i]; // 记录路径
                if(inq[e.v]) continue;
                que.push(e.v); inq[e.v] = 1;
            }
        }
    }
    return dis[T] < INF;
}

void MFMC(int &mincost, int &maxflow) {
    int ans = 0, flow = INF, p;
    // 从汇点沿着此次增广的路径往回走,当找到源点的时候退出
    for(int u = T; u; u = edge[p].u) {
        p = pre[u]; // 找增广的流量
        if(edge[p].cap < flow) flow = edge[p].cap;
    }
    for(int u = T; u; u = edge[p].u) {
        p = pre[u];
        edge[p].cap -= flow; // 更新每条边的流量
        edge[p^1].cap += flow;
        ans += flow * edge[p].cost; // 费用 = 单位费用 * 流量
    }
    mincost += ans, maxflow += flow;
}


int main() {
    int n, m;
    char s[105];
    while(scanf("%d%d", &n, &m), n + m) {
        p.clear(); h.clear();
        for(int i = 0; i < n; i++) {
            scanf("%s", s);
            for(int j = 0; j < m; j++) {
                if(s[j] == 'H') h.push_back(node(i, j));
                if(s[j] == 'm') p.push_back(node(i, j));
            }
        }
        tot = 0; int sz1 = p.size(), sz2 = h.size();
        S = 0, T = sz1 + sz2 + 1;
        for(int i = 0; i <= T; i++) G[i].clear();
        for(int i = 0; i < sz1; i++) // S到man
            AddEdge(S, i + 1, 1, 0);
        for(int i = 0; i < sz2; i++) // house到T
            AddEdge(i + 1 + sz1, T, 1, 0);
        for(int i = 0; i < sz1; i++) {
            for(int j = 0; j < sz2; j++) {
                int c = CalDis(p[i].x, p[i].y, h[j].x, h[j].y);
                AddEdge(i + 1, j + 1 + sz1, 1, c);
            }
        }

        int mincost = 0, maxflow = 0;
        while(SPFA()) MFMC(mincost, maxflow);
        printf("%d
", mincost);
    }
    return 0;
}