UVA 1658 Admiral——拆点法+最小费最大流

对于边u->v的处理方法是先建立边u->u+n，权值为0， 然后建立边u+n->v权值为c，这样可以避免一个点经过多次的情况

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 2 * 1e3 + 10;

struct Edge {
    int from, to, cap, flow, cost;
    Edge (int u, int v, int c, int f, int w) : from(u), to(v), cap(c), flow(f), cost(w) {}
};

struct MCMF {
    int n, m;
    vector<Edge> edges;
    vector<int> G[maxn];
    int inq[maxn], d[maxn], p[maxn], a[maxn];

    void init(int x) {
        n = x;
        edges.clear();
        for (int i = 0; i <= n; i++) G[i].clear();
    }

    void addedge(int from, int to, int cap, int cost) {
        edges.push_back(Edge(from, to, cap, 0, cost));
        edges.push_back(Edge(to, from, 0, 0, -cost));
        m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    }

    bool BellmanFord(int s, int t, int &flow, long long &cost) {
        memset(inq, 0, sizeof(inq));
        for (int i = 0; i <= n; i++) d[i] = INF;
        inq[s] = 1, d[s] = 0, p[s] = 0, a[s] = INF;
        queue<int> q; q.push(s);
        while (!q.empty()) {
            int u = q.front(); q.pop();
            inq[u] = 0;
            for (int i = 0; i < G[u].size(); i++) {
                Edge &e = edges[G[u][i]];
                if (e.cap > e.flow && d[e.to] > d[u] + e.cost) {
                    d[e.to] = d[u] + e.cost;
                    p[e.to] = G[u][i];
                    a[e.to] = min(a[u], e.cap - e.flow);
                    if (!inq[e.to]) { q.push(e.to); inq[e.to] = 1; }
                }
            }
        }
        if (d[t] == INF) return false;
        flow += a[t];
        cost += (long long)d[t] * (long long)a[t];
        for (int u = t; u != s; u = edges[p[u]].from) {
            edges[p[u]].flow += a[t];
            edges[p[u]^1].flow -= a[t];
        }
        return true;
    }

    int mincostmaxflow(int s, int t, long long &cost) {
        int flow = 0; cost = 0;
        while (BellmanFord(s, t, flow, cost));
        return flow;
    }
};

int main() {
    MCMF mcmf;
    int n, m;
    while (~scanf("%d %d", &n, &m)) {
        mcmf.init(n<<1);
        for (int i = 2; i <= n - 1; i++) mcmf.addedge(i, i + n, 1, 0);
        mcmf.addedge(1, n + 1, 2, 0);
        mcmf.addedge(n, n<<1, 2, 0);
        for (int i = 0; i < m; i++) {
            int u, v, cost; scanf("%d %d %d", &u, &v, &cost);
            mcmf.addedge(u + n, v, 1, cost);
        }
        long long cost = 0;
        mcmf.mincostmaxflow(1, n<<1, cost);
        cout << cost << endl;
    }
    return 0;
}