网络流模板

以P3376 【模板】网络最大流为例

EK

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
#define inf 0x3f3f3f3f
using namespace std;
int n,m,s,t;
long long ans;
struct ed {
	int to,next;
	int val;
} edge[200005];
int tot=1,head[1005];
void add(int u,int v,int w) {
	edge[++tot].to=v;
	edge[tot].next=head[u];
	edge[tot].val=w;
	head[u]=tot;
}
int p[1005],e[1005];
bool vis[1005];
bool bfs() {
	memset(vis,false,sizeof(vis));
	queue<int>q;
	q.push(s);
	vis[s]=true;
	while(!q.empty()) {
		int u=q.front();
		q.pop();
		for(int i=head[u]; i; i=edge[i].next) {
			int v=edge[i].to,w=edge[i].val;
			if(!vis[v]&&w>0) {
				p[v]=u,e[v]=i;
				if(v==t)return true;
				q.push(v);
				vis[v]=true;
			}
		}
	}
	return false;
}
void EK() {
	while(bfs()) {
		int flow=inf;
		for(int i=t; i!=s; i=p[i])flow=min(flow,edge[e[i]].val);
		for(int i=t; i!=s; i=p[i]) {
			edge[e[i]].val-=flow;
			edge[e[i]^1].val+=flow;
		}
		ans+=flow;
	}
}
int main() {
	scanf("%d%d%d%d",&n,&m,&s,&t);
	for(int i=1; i<=m; i++) {
		int u,v,w;
		scanf("%d%d%d",&u,&v,&w);
		add(u,v,w),add(v,u,0);
	}
	EK();
	printf("%lld",ans);
	return 0;
}

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用时：551ms

Dinic

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
#define inf 0x3f3f3f3f
using namespace std;
int n,m,s,t;
long long ans;
struct ed {
	int to,next,val;
} edge[200005];
int tot=1,head[1005];
void add(int u,int v,int w) {
	edge[++tot].to=v;
	edge[tot].next=head[u];
	edge[tot].val=w;
	head[u]=tot;
}
int d[1005];
bool vis[1005];
int cur[1005];
bool bfs() {
	memcpy(cur,head,sizeof(head));
	memset(d,inf,sizeof(d));
	queue<int>q;
	q.push(s);
	vis[s]=true;
	d[s]=0;
	while(!q.empty()) {
		int u=q.front();
		q.pop();
		vis[u]=false;
		for(int i=head[u]; i; i=edge[i].next) {
			int v=edge[i].to,w=edge[i].val;
			if(d[v]>d[u]+1&&w) {
				d[v]=d[u]+1;
				if(!vis[v]) {
					vis[v]=true;
					q.push(v);
				}
			}
		}
	}
	return d[t]!=inf;
}
int dfs(int u,int flow) {
	if(u==t) {
		ans+=flow;
		return flow;
	}
	int used=0;
	for(int i=cur[u]; i; i=edge[i].next) {
		cur[u]=i;
		int v=edge[i].to,w=edge[i].val;
		if(d[v]==d[u]+1&&w>0) {
			int rlow=dfs(v,min(flow-used,w));
			if(rlow) {
				used+=rlow;
				edge[i].val-=rlow;
				edge[i^1].val+=rlow;
				if(used==flow)break;
			}
		}
	}
	return used;
}
void Dinic(){
	while(bfs())dfs(s,inf);
}
int main() {
	scanf("%d%d%d%d",&n,&m,&s,&t);
	for(int i=1; i<=m; i++) {
		int u,v,w;
		scanf("%d%d%d",&u,&v,&w);
		add(u,v,w),add(v,u,0);
	}
	Dinic();
	printf("%lld",ans);
	return 0;
}

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用时：101ms

ISAP

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
#define inf 0x3f3f3f3f
using namespace std;
int n,m,s,t;
long long ans;
struct ed {
	int to,next,val;
} edge[200005];
int tot=1,head[1005];
void add(int u,int v,int w) {
	edge[++tot].to=v;
	edge[tot].next=head[u];
	edge[tot].val=w;
	head[u]=tot;
}
int d[1005],g[1005];
bool vis[1005];
void bfs() {
	d[t]=0,g[d[t]]++;
	queue<int>q;
	q.push(t);
	vis[t]=true;
	while(!q.empty()) {
		int u=q.front();
		q.pop();
		for(int i=head[u]; i; i=edge[i].next) {
			int v=edge[i].to;
			if(!vis[v]) {
				d[v]=d[u]+1,g[d[v]]++;
				q.push(v);
				vis[v]=true;
			}
		}
	}
}
int cur[1005];
int dfs(int u,int flow) {
	if(u==t) {
		ans+=flow;
		return flow;
	}
	int used=0;
	for(int i=cur[u]; i; i=edge[i].next) {
		cur[u]=i;
		int v=edge[i].to,w=edge[i].val;
		if(d[v]+1==d[u]&&w>0) {
			int rlow=dfs(v,min(flow-used,w));
			if(rlow) {
				used+=rlow;
				edge[i].val-=rlow;
				edge[i^1].val+=rlow;
				if(used==flow)return used;
			}
		}
	}
	g[d[u]]--;
	if(g[d[u]]==0)d[s]=n+1;
	g[++d[u]]++;
	return used;
}
void ISAP() {
	bfs();
	while(d[s]<n){
		memcpy(cur,head,sizeof(head));
		dfs(s,inf);
	}
}
int main() {
	scanf("%d%d%d%d",&n,&m,&s,&t);
	for(int i=1; i<=m; i++) {
		int u,v,w;
		scanf("%d%d%d",&u,&v,&w);
		add(u,v,w),add(v,u,0);
	}
	ISAP();
	printf("%lld",ans);
	return 0;
}

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用时：48ms