费用流的一般模版

参考博文

struct Edge {
    int v, w, nxt, cost, sy;
}edge[maxn];

char MP[maxn][maxn];
int head[maxn], dis[maxn], vis[maxn], pre[maxn], tot;
int S, T, n, m;

void init() {
    tot = 0;
    T = n * m + 1;
    S = 0;
    memset(head, -1, sizeof(head));
}

void addEdge(int u, int v, int w, int cost) {
    edge[tot].v = v;
    edge[tot].w = w;
    edge[tot].sy = 0;
    edge[tot].cost = cost;
    edge[tot].nxt = head[u];
    head[u] = tot ++;

    edge[tot].v = u;
    edge[tot].w = 0;
    edge[tot].sy = 0;
    edge[tot].cost = -cost;
    edge[tot].nxt = head[v];
    head[v] = tot ++;
}

bool SPFA() {
    memset(dis, INF, sizeof(dis));
    memset(vis, 0, sizeof(vis));
    memset(pre, -1, sizeof(pre));
    queue<int> que;
    que.push(S);
    dis[S] = 0;
    vis[S] = 1;
    pre[S] = -1;
    while(!que.empty()) {
        int u = que.front(); que.pop();
        vis[u] = 0;
        for (int i = head[u]; i + 1; i = edge[i].nxt) {
            if(dis[edge[i].v] > dis[u] + edge[i].cost && edge[i].w > edge[i].sy) {
                dis[edge[i].v] = dis[u] + edge[i].cost;
                pre[edge[i].v] = i;
                if(!vis[edge[i].v]) {
                    vis[edge[i].v] = 1;
                    que.push(edge[i].v);
                }
            }
        }
    }
    if(pre[T] == -1)
        return 0;
    return 1;
}

int MinCostMaxFlow(int &Cost) {
    int Flow = 0, MinFlow = INF;
    Cost = 0;
    while(SPFA()) {
        for (int i = pre[T]; i + 1; i = pre[edge[i ^ 1].v])
            MinFlow = min(MinFlow, edge[i].w - edge[i].sy);//最小流量
        for (int i = pre[T]; i + 1; i = pre[edge[i ^ 1].v]) {
            edge[i].sy += MinFlow;
            edge[i ^ 1].sy -= MinFlow;
            Cost += edge[i].cost * MinFlow;//费用= sigma每条路线的最小流量*花费
        }
        Flow += MinFlow;
    }
    return Flow;//返回最大流
}
int ans = 0;
MinCostMaxFlow(ans);

这是一般的最大流最小费的模版，
如果是最大费最小流的话，把w与cost的位置互换，
如果是最大流最大费的话，把cost的值存负，用最大流最小费的方法求，最后取反即可