sgu194 无源汇带有下界的网络流

#pragma comment(linker, "/STACK:102400000,102400000")
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <sstream>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <string>
#include <time.h>
#include <math.h>
#include <queue>
#include <stack>
#include <set>
#include <map>
using namespace std;
#define INF 0x3f3f3f3f
#define eps 1e-8
#define pi acos(-1.0)
typedef long long ll;
/*
对于有流量上下限的无源的网络流的可行流转化为一般的有源汇点的最大流来做 
(1)添加超级源点S和超级汇点T 
(2)对于原有的边(u,v,l(u,v),c(u,v))(l为流量下限,c为流量上限),添加边(u,v,0,c-l); 
(3)对于每个结点i,记w[i]=sum(l(u,i))-sum(l(i,v)); 
   若w[i]>0,添加边(S,i,w[i]),若w[i]<0,添加边(i,T,-w[i]); 
(4)求解S-T的最大流; 
(5)当且仅当S的出边和T的入边满流,原流量限制的无源网络流可行流有解; 
(6)一组可行流的解为: 
   对于每条流量边(u,v),可行流量为l(u,v)+其构造的图中的流量. 
*/ 

const int maxn=20100;
const int maxm=1002000;
struct Edge{
	int next,to,cap;
	Edge(){};
	Edge(int _next,int _to,int _cap){
		next=_next;to=_to;cap=_cap;
	}
}edge[maxm];
int head[maxn],tol,dep[maxn],gap[maxn];
void addedge(int u,int v,int flow){
    edge[tol]=Edge(head[u],v,flow);head[u]=tol++;
    edge[tol]=Edge(head[v],u,0);head[v]=tol++;
}
void bfs(int start,int end){
    memset(dep,-1,sizeof(dep));
    memset(gap,0,sizeof(gap));
    gap[0]++;int front=0,rear=0,Q[maxn];
    dep[end]=0;Q[rear++]=end;
    while(front!=rear){
        int u=Q[front++];
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;if(dep[v]==-1)
                Q[rear++]=v,dep[v]=dep[u]+1,gap[dep[v]]++;
        }
    }
}
int sap(int s,int t,int N){
	int res=0;bfs(s,t);
	int cur[maxn],S[maxn],top=0,u=s,i;
	memcpy(cur,head,sizeof(head));
	while(dep[s]<N){
		if(u==t){
			int temp=INF,id;
		    for( i=0;i<top;i++)
			   if(temp>edge[S[i]].cap)
				   temp=edge[S[i]].cap,id=i;
		    for( i=0;i<top;i++)
			      edge[S[i]].cap-=temp,edge[S[i]^1].cap+=temp;
		    res+=temp;top=id;u=edge[S[top]^1].to;
		}
		if(u!=t&&gap[dep[u]-1]==0)break;
		for( i=cur[u];i!=-1;i=edge[i].next)
			if(edge[i].cap&&dep[u]==dep[edge[i].to]+1)break;
		if(i!=-1)cur[u]=i,S[top++]=i,u=edge[i].to;
		else{
			int MIN=N;
			for( i=head[u];i!=-1;i=edge[i].next)
				if(edge[i].cap&&MIN>dep[edge[i].to])
					MIN=dep[edge[i].to],cur[u]=i;
			--gap[dep[u]];++gap[dep[u]=MIN+1];
			if(u!=s)u=edge[S[--top]^1].to;
		}
	}
	return res;
}
int w[maxn],l[maxn];
int main()
{
     //freopen("data.in","r",stdin);
     //freopen("data.out","w",stdout);
     int n,m;
	 while(cin>>n>>m){
		 memset(head,-1,sizeof(head));tol=0;
		 memset(w,0,sizeof(w));
		 for(int i=0;i<m;i++){
			 int u,v,c;
			 scanf("%d%d%d%d",&u,&v,&l[i],&c);
			 addedge(u,v,c-l[i]);
			 w[u]-=l[i];
			 w[v]+=l[i];
		 }
		 int sum=0;
		 for(int i=1;i<=n;i++){
			 if(w[i]>0)addedge(0,i,w[i]),sum+=w[i];
			 if(w[i]<0)addedge(i,n+1,-w[i]);
		 }
		 int ans=sap(0,n+1,2*n+10);
		 if(ans!=sum)puts("NO");
		 else{
			 puts("YES");
			 for(int i=0;i<m;i++)printf("%d\n",edge[2*i+1].cap+l[i]);
		 }
	 }
     return 0;
}