网络流模板

最大流

EdmondKard

洛谷 P3376 【模板】网络最大流
#include<bits/stdc++.h>
using namespace std;

inline int read(){
	int s=0,f=1;
	char ch=getchar();
	while(!isdigit(ch)){
		if(ch=='-') f=-1;
		ch=getchar();
	}
	while(isdigit(ch)){
		s=s*10+int(ch-'0');
		ch=getchar();
	}
	return s*f;
}

const int N=5e3+10;

int n,m,s,t;
int head[N],nxt[N<<1],edge[N<<1],ver[N<<1],k=1;

void add(int x,int y,int z){
	ver[++k]=y,edge[k]=z;
	nxt[k]=head[x],head[x]=k;
	return ;
}

int pre[N],flow[N];

bool bfs(){
	queue<int>q;
	fill(pre,pre+1+n,0);
	pre[s]=-1;
	flow[s]=0x3f3f3f3f;
	q.push(s);
	while(q.size()){
		int x=q.front();
		q.pop();
		for(int i=head[x];i;i=nxt[i]){
			if(!edge[i]) continue;
			if(pre[ver[i]]) continue;
			pre[ver[i]]=i;
			flow[ver[i]]=min(flow[x],edge[i]);
			if(ver[i]==t) return 1;
			q.push(ver[i]);
		}
	}
	return 0;
}

void EdmondKard(){
	long long ans=0;
	while(bfs()){
		ans+=flow[t];
		for(int i=t;i!=s;i=ver[pre[i]^1]){
			edge[pre[i]]-=flow[t];
			edge[pre[i]^1]+=flow[t];
		}
	}
	printf("%lld",ans);
	return ;
}

int main(){
	n=read(),m=read(),s=read(),t=read();
	int u,v,w;
	for(int i=1;i<=m;++i){
		u=read(),v=read(),w=read();
		add(u,v,w);
		add(v,u,0);
	}
	EdmondKard();
	return 0;
}

Dinic

洛谷 P3376 【模板】网络最大流
#include<bits/stdc++.h>
using namespace std;

inline int read(){
	int s=0,f=1;
	char ch=getchar();
	while(!isdigit(ch)){
		if(ch=='-') f=-1;
		ch=getchar();
	}
	while(isdigit(ch)){
		s=s*10+int(ch-'0');
		ch=getchar();
	}
	return s*f;
}

const int N=5e3+10;
const int Inf=0x3f3f3f3f;

int n,m,s,t;
int head[N],nxt[N<<1],edge[N<<1],ver[N<<1],k=1;

void add(int x,int y,int z){
	ver[++k]=y,edge[k]=z;
	nxt[k]=head[x],head[x]=k;
	return ;
}

int lv[N],c[N];

bool bfs(){
	queue<int>q;
	fill(lv,lv+1+n,0);
	lv[s]=1;
	q.push(s);
	while(q.size()){
		int x=q.front();
		q.pop();
		for(int i=head[x];i;i=nxt[i]){
			if(!edge[i]) continue;
			if(lv[ver[i]]) continue;
			lv[ver[i]]=lv[x]+1;
			q.push(ver[i]);
		}
	}
	return lv[t];
}

int dfs(int x,int f){
	if(x==t) return f;
	int sum=0;
	for(int i=c[x];i && f;i=nxt[i]){
		c[x]=i;
		if(!edge[i]) continue;
		if(lv[ver[i]]!=lv[x]+1) continue;
		int d=dfs(ver[i],min(f,edge[i]));
		sum+=d;
		f-=d;
		edge[i]-=d;
		edge[i^1]+=d;
	}
	return sum;
}

void Dinic(){
	long long ans=0;
	while(bfs()){
		for(int i=1;i<=n;++i)
			c[i]=head[i];
		ans+=dfs(s,Inf);
	}
	printf("%lld",ans);
	return ;
}

int main(){
	n=read(),m=read(),s=read(),t=read();
	int u,v,w;
	for(int i=1;i<=m;++i){
		u=read(),v=read(),w=read();
		add(u,v,w);
		add(v,u,0);
	}
	Dinic();
	return 0;
}

费用流

EdmondKard

点击查看代码
#include<bits/stdc++.h>
using namespace std;

const int N=1e5+10;

int n,m,s,t;

inline int read(){
	int s=0,f=1;
	char ch=getchar();
	while(!isdigit(ch)){
		if(ch=='-') f=-1;
		ch=getchar();
	}
	while(isdigit(ch)){
		s=s*10+int(ch-'0');
		ch=getchar();
	}
	return s*f;
}

int head[N],ver[N],nxt[N],flow[N],cost[N];
int pre[N],last[N],fl[N],tot=1;
int dist[N],vis[N];

void add(int a,int b,int c,int d){
	ver[++tot]=b,flow[tot]=c,cost[tot]=d;
	nxt[tot]=head[a],head[a]=tot;
	return ;
}

int ans_f=0,ans_c=0;

queue<int>q;

bool Spfa(int st,int ed){
	memset(dist,0x3f3f3f,sizeof(dist));
	memset(fl,0x3f3f3f,sizeof(fl));
	memset(vis,0,sizeof(vis));
	q.push(st);
	vis[st]=1,dist[st]=0,pre[ed]=-1;
	while(q.size()){
		int x=q.front();
		q.pop();
		vis[x]=0;
		for(int i=head[x];i!=-1;i=nxt[i])
			if(flow[i]>0 && dist[ver[i]]>dist[x]+cost[i]){
				dist[ver[i]]=dist[x]+cost[i];
				pre[ver[i]]=x;
				last[ver[i]]=i;
				fl[ver[i]]=min(fl[x],flow[i]);
				if(!vis[ver[i]]){
					vis[ver[i]]=1;
					q.push(ver[i]);
				}
			}
	}
	return pre[ed]!=-1;
} 

int main(){
	memset(head,-1,sizeof(head));
	tot=-1;
	n=read(),m=read(),s=read(),t=read();
	int u,v,w,c;
	while(m--){
		u=read(),v=read(),w=read(),c=read();
		add(u,v,w,c);
		add(v,u,0,-c);
	}
	while(Spfa(s,t)){
		int x=t;
		ans_f+=fl[t];
		ans_c+=fl[t]*dist[t];
		while(x!=s){
			flow[last[x]]-=fl[t];
			flow[last[x]^1]+=fl[t];
			x=pre[x];
		}
	}
	printf("%d %d\n",ans_f,ans_c);
	return 0;
}
posted @ 2022-07-15 21:32  Star_LIcsAy  阅读(50)  评论(0)    收藏  举报