网络流 && 费用流 模板

本文深入探讨了网络流算法中的最大流与最小费用最大流问题,提供了详细的算法实现代码,包括Dinic算法的具体步骤,并展示了如何通过最小费用最大流解决实际问题。

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网络最大流
namespace Maxflow {

	const int M = 1e5 + 7;

	int to[M], nxt[M], head[M], beg[M], w[M], e = 1, dis[M];

	void Reset() { Set(head, 0), e = 1; }

	void add(int x, int y, int z) { 
		to[++ e] = y, nxt[e] = head[x], head[x] = e, w[e] = z; 
		if (z) add(y, x, 0);
	}

	bool bfs() {
		queue<int> q; 
		For(i, 1, T) dis[i] = 0;
		dis[S] = 1, q.push(S); 
		for (; !q.empty(); q.pop()) {
			int u = q.front();
			Travel(i, u) if (w[i] && !dis[to[i]])
				dis[to[i]] = dis[u] + 1, q.push(to[i]);
		}
		return dis[T];
	}

	int dfs(int u, int flow) {
		if (u == T || !flow) return flow;
		int used = 0;
		for (int &i = head[u]; i; i = nxt[i])
			if (w[i] && dis[to[i]] == dis[u] + 1) {
				int d = dfs(to[i], min(w[i], flow));
				w[i] -= d, flow -= d;
				w[i ^ 1] += d, used += d;
				if (!flow) break;
			}
		return used;
	}

	int dinic() {
		int res = 0;
		Cpy(beg, head);
		while (bfs()) {
			res += dfs(S, inf);
			Cpy(head, beg);
		}
		return res;
	}

} 

最小费用最大流
#include<bits/stdc++.h>
#define For(i, a, b) for(register int i = a; i <= b; ++ i)
#define go(x, i) for(register int i = head[x]; i; i = nxt[i])
#define inf (0x3f3f3f3f)

using namespace std;

const int maxn = 1e4 + 10, maxm = 1e5 + 10;
int n, m, s, t, cost;

namespace Mincost_Maxflow {
	int to[maxm << 1], head[maxn], nxt[maxm << 1], v[maxm << 1], w[maxm << 1], e = 1;
	int dis[maxn], vis[maxn];

	void add(int x, int y, int z, int val) {
		to[++ e] = y;
		nxt[e] = head[x];
		head[x] = e;
		w[e] = z;
		v[e] = val;
		if(z) add(y, x, 0, -val);
	}

	bool SPFA() {
		queue<int> q;
		memset(dis, inf, sizeof(dis));
		memset(vis, 0, sizeof(vis));
		dis[s] = 0, vis[s] = 1, q.push(s);
		while(!q.empty()) {
			int k = q.front(); q.pop();
			go(k, i) 
				if(w[i] && dis[to[i]] > dis[k] + v[i]) {
					dis[to[i]] = dis[k] + v[i];
					if(!vis[to[i]]) {
						vis[to[i]] = true;
						q.push(to[i]);
					}
				}
			vis[k] = false;
		}
		return dis[t] != inf;
	}

	int dfs(int x, int flow) {
		vis[x] = flow;
		if(x == t || !flow) 
			return flow;
		int used = 0;
		go(x, i) 
			if(dis[to[i]] == dis[x] + v[i] && !vis[to[i]]) {
				int di = dfs(to[i], min(flow, w[i]));
				w[i] -= di, w[i ^ 1] += di;
				flow -= di, used += di, cost += di * v[i];
				if(!flow) break;
			}
		return used;
	}

	int dinic() {
		int res = 0;
		while(SPFA()) {
			vis[t] = true;
			while(vis[t]) {
				memset(vis, 0, sizeof(vis));
				res += dfs(s, inf);
			}
		}
		return res;
	}
}

int main() {
#ifndef ONLINE_JUDGE
	freopen("Mincost_Maxflow.in", "r", stdin);
	freopen("Mincost_Maxflow.out", "w", stdout);
#endif
	int x, y, z, val;
	scanf("%d%d%d%d", &n, &m, &s, &t);
	For(i, 1, m) {
		scanf("%d%d%d%d", &x, &y, &z, &val);
		Mincost_Maxflow::add(x, y, z, val);
	}
	printf("%d ", Mincost_Maxflow::dinic());
	printf("%d\n", cost);
	return 0;
}

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