P3381 【模板】最小费用最大流 题解 最小费用最大流SSP算法模板

题目链接：https://www.luogu.com.cn/problem/P3381

解题思路：完全来自 oi.wiki

代码对应我之前写的 最大流Dinic模板 + oi.wiki 上 基于dinic的修改。

示例程序：

#include <bits/stdc++.h>
using namespace std;
const int maxn = 5e3 + 5, maxm = 1e5 + 5, inf = 0x3f3f3f3f;

struct Edge {
    int v, w, c, nxt;
} edge[maxm];
int n, m, s, t, head[maxn], ecnt;

void init() {
    ecnt = 0;
    fill(head+1, head+n+1, -1);
}

void add_edge(int u, int v, int w, int c) {
    edge[ecnt] = { v, w, c, head[u] }; head[u] = ecnt++;
    edge[ecnt] = { u, 0, -c, head[v] }; head[v] = ecnt++;
}

int dis[maxn], cur[maxn], sum_cost;
bool vis[maxn];

bool spfa() {
    queue<int> que;
    fill(dis, dis+n+1, inf);
    dis[s] = 0;
    vis[s] = true;
    que.push(s);
    while (!que.empty()) {
        int u = que.front();
        que.pop();
        vis[u] = false;
        for (int i = head[u]; ~i; i = edge[i].nxt) {
            auto &[v, w, c, nxt] = edge[i];
            if (w > 0 && dis[u] + c < dis[v]) {
                dis[v] = dis[u] + c;
                if (!vis[v]) {
                    vis[v] = true;
                    que.push(v);
                }
            }
        }
    }
    return dis[t] < inf;
}

int dfs(int u, int flow) {
    if (u == t)
        return flow;
    vis[u] = true;
    int ans = 0;
    for (int &i = cur[u]; ~i && ans < flow; i = edge[i].nxt) {
        auto &[v, w, c, nxt] = edge[i];
        if (!vis[v] && w > 0 && dis[v] == dis[u] + c) {
            int f = dfs(v, min(w, flow - ans));
            if (f > 0) {
                ans += f;
                sum_cost += f * c;
                edge[i].w -= f;
                edge[i^1].w += f;
            }
        }
    }
    vis[u] = false;
    return ans;
}

int dinic() {
    int ans = 0;
    while (spfa()) {
        copy(head+1, head+n+1, cur+1);
        int f = dfs(s, inf);
        ans += f;
    }
    return ans;
}

int main() {
    cin >> n >> m >> s >> t;
    init();
    for (int i = 0, u, v, w, c; i < m; i++) {
        cin >> u >> v >> w >> c;
        add_edge(u, v, w, c);
    }
    int max_flow = dinic();
    cout << max_flow << " " << sum_cost << "\n";
    return 0;
}