网络最大流

本文搬运自本人高中时期CSDN博客，若图片加载不出来，可到原文查看：https://blog.csdn.net/zhangtingxiqwq/article/details/132091032

< Zoj3229 Shoot the Bullet|东方文花帖|【模板】有源汇上下界最大流 - 洛谷 >

  1. 先bfs分层

2.dfs增广，当前弧优化

  1. 重复以上步骤
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#include<bits/stdc++.h>
using namespace std;
#define int long long
inline int read(){int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;
ch=getchar();}while(ch>='0'&&ch<='9'){x=(x<<1)+
(x<<3)+(ch^48);ch=getchar();}return x*f;}
#define Z(x) (x)*(x)
#define pb push_back
//#define M
//#define mo
#define N 500010
struct node {
	int x, y, z, n; 
}d[N];
int n, m, i, j, k;
int h[N], H[N], dep[N]; 
int u, v, w, S, T, ans; 
queue<int>q; 
 
void cun(int x, int y, int z) {
//	printf("%lld %lld %lld\n", x, y, z); 
	d[++k].x=x; d[k].y=y; d[k].z=z; 
	 d[k].n=h[x]; h[x]=k;
}
 
int bfs() {
	while(!q.empty()) q.pop(); 
	memset(dep, -1, sizeof(dep)); 
	memcpy(h, H, sizeof(H)); 
	dep[S]=1; q.push(S); 
	while(!q.empty()) {
		u=q.front(); q.pop(); 
//		printf("%d %d\n", u, h[u]); 
		for(int g=h[u]; g; g=d[g].n) {
			v=d[g].y; w=d[g].z; 
//			printf("%lld %lld\n", v, w); 
			if(w<=0 || dep[v]!=-1) continue; 
			dep[v]=dep[u]+1; q.push(v); 
		}
	}
//	printf("--------------%lld\n", dep[T]); 
	return dep[T]!=-1; 
}
 
int dfs(int x, int w) {
	if(x==T) return w;
	if(!w) return 0; 
	int ans=0, s; 
	for(int &i=h[x]; i; i=d[i].n) {
		int y=d[i].y, z=d[i].z;  
		if(dep[y]!=dep[x]+1) continue; 
		if(z<=0) continue; 
		s=dfs(y, min(w, z)); ans+=s; w-=s; 
		d[i].z-=s; d[i^1].z+=s; 
		if(!w) break;  
	}
	return ans; 
}
 
signed main()
{
//	freopen("in.txt", "r", stdin);
//	freopen("out.txt", "w", stdout);
//	srand(time(NULL));
//	T=read();
//	while(T--) {
//
//	}
	n=read(); m=read(); S=read(); T=read(); 
	for(i=1, k=1; i<=m; ++i) {
		u=read(); v=read(); w=read(); 
		cun(u, v, w); cun(v, u, 0); 
	}
	memcpy(H, h, sizeof(h)); 
	while(bfs()) ans+=dfs(S, 1e18); 
	printf("%lld", ans); 
	return 0;
}

如果加了当前弧优化，dfs中循环里直接返回或最后返回复杂度是一样的。