最小费用最大流

网络流的最后一步。之前已经写了最大流的Dinic，SAP，EK这三种算法。

#include "stdafx.h"
#include <iostream>
#include <algorithm>
#include <queue>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <functional>

#define MAXN 5050
#define INF 0x3f3f3f3f
#define P pair<int,int>

using namespace std;

struct edge
{
    int to, cap, cost, rev;
};

int n, m, s, t;
int u, v, c, w;
int maxFlow, minCost;

vector<edge> G[MAXN];
int h[MAXN];
int dist[MAXN], prevv[MAXN], preve[MAXN];

void addedge(int from, int to, int cap, int cost)
{
    edge temp1 = { to, cap, cost, (int)G[to].size() };
    edge temp2 = { from, 0, -cost, (int)G[from].size() - 1 };
    G[from].push_back(temp1);
    G[to].push_back(temp2);
}

//Dijkstra算法实现
void MCMF(int s, int t, int f)
{
    fill(h + 1, h + 1 + n, 0);
    while (f > 0)
    {
        priority_queue<P, vector<P>, greater<P> > D;
        memset(dist, INF, sizeof dist);
        dist[s] = 0; D.push(P(0, s));
        while (!D.empty())
        {
            P now = D.top(); D.pop();
            if (dist[now.second] < now.first) continue;
            int v = now.second;
            for (int i = 0; i<(int)G[v].size(); ++i)
            {
                edge &e = G[v][i];
                if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to])
                {
                    dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
                    prevv[e.to] = v;
                    preve[e.to] = i;
                    D.push(P(dist[e.to], e.to));
                }
            }
        }
        if (dist[t] == INF) break;
        for (int i = 1; i <= n; ++i) h[i] += dist[i];
        int d = f;
        for (int v = t; v != s; v = prevv[v])
            d = min(d, G[prevv[v]][preve[v]].cap);
        f -= d; maxFlow += d;
        minCost += d * h[t];
        for (int v = t; v != s; v = prevv[v])
        {
            edge &e = G[prevv[v]][preve[v]];
            e.cap -= d;
            G[v][e.rev].cap += d;
        }
    }
}

int _tmain(int argc, _TCHAR* argv[])
{

    cout << "节点数为："; cin >> n;
    cout << "边数为："; cin >> m;
    cout << "源点编号为："; cin >> s;
    cout << "汇点编号为："; cin >> t;

    cout << "输入 " << m << " 条边的信息：" << endl;
    while (m--)
    {
        cout << "起点："; cin >> u;
        cout << "终点："; cin >> v;
        cout << "容量："; cin >> c;
        cout << "费用："; cin >> w;
        cout << "-----------------" << endl;
        addedge(u, v, c, w);
    }

    MCMF(s, t, INF);

    cout << "最大流为：" << maxFlow << endl;
    cout << "最小费用为" << minCost << endl;
    cout << endl;

    system("pause");
    return 0;
}