有上下界网络流

Posted 2020-08-09 BBChq

sgu194：

//无源汇上下界网络流，求最大流。
/*
每条边add(u,v,up[i]-dn[i])
每个点out[i]=∑dn[i,v];in[i]=∑dn[v,i];
每个点in[i]-out[i]>0 add(s,i, in[i]-out[i]),否则add(i,t,out[i]-in[i]);
判断与st相连的边是否满流即可。
*/

#include<cstdio>
#include<cstring>
#include<cctype>
#include<algorithm>
using namespace std;
#define rep(i,s,t) for(int i=s;i<=t;i++)
#define dwn(i,s,t) for(int i=s;i>=t;i--)
#define clr(x,c) memset(x,c,sizeof(x))
#define qwq(x) for(edge *o=head[x];o;o=o->next)
int read(){
	int x=0;char c=getchar();
	while(!isdigit(c)) c=getchar();
	while(isdigit(c)) x=x*10+c-‘0‘,c=getchar();
	return x;
}
const int nmax=205;
const int maxn=8e4+5;
const int inf=0x7f7f7f7f;
struct edge{
	int to,cap;edge *next,*rev;
};
edge es[maxn],*pt=es,*head[nmax];
void add(int u,int v,int d){
	pt->to=v;pt->cap=d;pt->next=head[u];head[u]=pt++;
	pt->to=u;pt->cap=0;pt->next=head[v];head[v]=pt++;
	head[u]->rev=head[v];head[v]->rev=head[u];
}
edge *cur[nmax],*p[nmax];
int cnt[nmax],h[nmax];
int maxflow(int s,int t,int n){
	cnt[0]=n;int flow=0,a=inf,x=s;edge *e;
	while(h[s]<n){
		for(e=cur[x];e;e=e->next) if(e->cap>0&&h[x]==h[e->to]+1) break;
		if(e){
			a=min(a,e->cap);cur[x]=p[e->to]=e;x=e->to;
			if(x==t){
				while(x!=s) p[x]->cap-=a,p[x]->rev->cap+=a,x=p[x]->rev->to;
				flow+=a,a=inf;
			}
		}else{
			if(!--cnt[h[x]]) break;
			h[x]=n;
			for(e=head[x];e;e=e->next) if(e->cap>0&&h[x]>h[e->to]+1) cur[x]=e,h[x]=h[e->to]+1;
			cnt[h[x]]++;
			if(x!=s) x=p[x]->rev->to;
		}
	}
	return flow;
}
int out[nmax],in[nmax],dn[maxn];
bool work(int s,int t,int n,int m){
	maxflow(s,t,n);
	qwq(s) if(o->cap) return 0;
	qwq(t) if(o->cap!=out[o->to]-in[o->to]) return 0;
	puts("YES");
	pt=es+1;rep(i,1,m) printf("%d\n",dn[i]+pt->cap),pt+=2;
	return 1;
}
int main(){
	int n=read(),m=read(),u,v,d,tp;
	rep(i,1,m){
		u=read(),v=read(),dn[i]=read();tp=read();
		add(u,v,tp-dn[i]);in[v]+=dn[i];out[u]+=dn[i];
	}
	rep(i,1,n){
		if(in[i]-out[i]>0) add(0,i,in[i]-out[i]);
		else add(i,n+1,out[i]-in[i]);
	}
	if(!work(0,n+1,n+2,m)) puts("NO");
	return 0;
}