越流越贵（最小费用最大流）

Posted 2021-10-09 jpphy0

目录

• 问题
• 分析
• 代码

问题

分析

代码

#include<bits/stdc++.h>
using namespace std;
const int MXN = 55, MXE = 510, inf = 0x3f3f3f3f;
int n, m, pre[MXN], dis[MXN], inq[MXN], flow[MXN];
int head[MXN], tot;
struct Edge{int to, nxt, cap, cost;}edge[MXE<<5];
void addEdge(int u, int v, int cap, int cost){
	Edge &e = edge[++tot];
	e.to = v, e.cap = cap, e.cost = cost, e.nxt = head[u], head[u] = tot;
}
void add(int u, int v, int cap, int cost){
	addEdge(u, v, cap, cost), addEdge(v, u, 0, -cost);
}
bool spfa(){
	memset(inq, 0, sizeof inq);
	memset(flow, inf, sizeof flow);
	memset(dis, inf, sizeof dis);
	queue<int> q;
	q.push(1), inq[1] = 1, dis[1] = 0, flow[1] = inf;
	int from, to;
	while(q.size()){
		from = q.front(), q.pop(), inq[from] = 0;
		for(int i = head[from]; ~i; i = edge[i].nxt){
			if(edge[i].cap == 0) continue;
			to = edge[i].to;
			if(dis[to] > dis[from]+edge[i].cost){
				dis[to] = dis[from]+edge[i].cost;
				if(!inq[to]) q.push(to), inq[to] = 1;
				pre[to] = i;
				flow[to] = min(flow[from], edge[i].cap);
			}
		}
	}
	return dis[n] != inf;
}
void update(int s, int t){
	for(int i, now = n; now != s; now = edge[i^1].to)
		i = pre[now], edge[i].cap -= flow[now], edge[i^1].cap += flow[now];
}
int main(){
	int t, u, v, c, maxflow, ans;
	scanf("%d", &t);
	while(t--){
		maxflow = 0, ans = 0, tot = 1;
		memset(head, -1, sizeof head);
		scanf("%d%d", &n, &m);
		for(int i = 1; i <= m; ++i){
			scanf("%d%d%d", &u, &v, &c);
			for(int j = 1; j<= c; ++j) add(u, v, 1, 2*j-1);
		}
		while(spfa()) maxflow += flow[n], ans += flow[n]*dis[n], update(1, n);
		printf("%d %d\\n", maxflow, ans);
	}	
	return 0;
}