P1344. [USACO4.4] 追查坏牛奶Pollutant Control

\(Solution\)

一个较为模板的最小割，对于第二问，把图的流量变为\(1\)，再跑一边网络流即可

\(Code\)

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int h[50],cur[50],n,m,dep[50],q[50],tot = 1;

struct edge{
	int to,nxt,z;
}e[2005];
void add(int x,int y,int z)
{
	e[++tot] = edge{y,h[x],z},h[x] = tot;
	e[++tot] = edge{x,h[y],0},h[y] = tot;
}
int bfs()
{
	for (int i = 1; i <= n; i++) cur[i] = h[i];
	memset(dep,0,sizeof dep);
	int head = 0,tail = 1;
	q[1] = 1,dep[1] = 1;
	while (head < tail)
	{
		int u = q[++head];
		for (int i = h[u]; i; i = e[i].nxt)
		{
			int v = e[i].to;
			if (dep[v] || e[i].z <= 0) continue;
			dep[v] = dep[u] + 1,q[++tail] = v;
		}
	}
	return dep[n];
}
int dinic(int u,int mn,int fa)
{
	if (u == n || mn <= 0) return mn;
	int flow = 0,sum = 0;
	for (int &i = cur[u]; i; i = e[i].nxt)
	{
		int v = e[i].to;
		if (dep[v] != dep[u] + 1 || v == fa || e[i].z <= 0) continue;
		sum = dinic(v,min(mn,e[i].z),u);
		if (sum <= 0) continue;
		flow += sum,mn -= sum,e[i].z -= sum,e[i ^ 1].z += sum;
		if (mn <= 0) break;
	}
	return flow;
}
int main()
{
	scanf("%d%d",&n,&m);
	for (int i = 1,q,p,c; i <= m; i++) scanf("%d%d%d",&q,&p,&c),add(q,p,c);
	int ans = 0;
	while (bfs()) ans += dinic(1,2147483647,1);
	printf("%d ",ans);
	for (int i = 2; i <= tot; i++)
		if (i & 1) e[i].z = 0; else e[i].z = 1;
	ans = 0;
	while (bfs()) ans += dinic(1,2147483647,1);
	printf("%d\n",ans);
}