题目
分析:边的容量为上界-下界,d数组保存当前节点下界的入度-岀度的差。为了保证流量的平衡,当di>0是,入度减掉的l比岀度多,所以从超级源点向i连一条容量为di的边,否则,从i向超级汇点连一条容量为-di的边。
然后从SS到ST跑一次最大流即可。
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<queue>
#define MAXN 200
#define MAXM MAXN*MAXN
#define INF 0x7f7f7f7f
using namespace std;
deque<int>q;
void Read(int &x){
char c;
while(c=getchar(),c!=EOF)
if(c>='0'&&c<='9'){
x=c-'0';
while(c=getchar(),c>='0'&&c<='9')
x=x*10+c-'0';
ungetc(c,stdin);
return;
}
}
int d[MAXN+10],n,m,l[MAXM+10],S,T,dist[MAXN+10],num,vd[MAXN+10],flow,tot;
struct node{
int v,cap;
node *next,*back;
}*adj[MAXN+10],edge[MAXM*2+10],*ecnt=edge,*epos[MAXM+10];
void addedge(int u,int v,int cap,int pos){
node *p=++ecnt;
p->v=v;
p->cap=cap;
epos[pos]=p;
p->next=adj[u];
adj[u]=p;
p=p->back=++ecnt;
p->back=ecnt-1;
p->v=u;
p->cap=0;
p->next=adj[v];
adj[v]=p;
}
void read(){
Read(n),Read(m);
T=n+1;
int i,u,v,low,high;
for(i=1;i<=m;i++){
Read(u),Read(v),Read(low),Read(high);
addedge(u,high-low,i);
d[u]-=low;
d[v]+=low;
l[i]=low;
}
for(i=1;i<=n;i++)
if(d[i]>0)
addedge(S,i,d[i],0),tot+=d[i];
else if(d[i]<0)
addedge(i,-d[i],0);
}
int dfs(int u,int augu){
if(u==T)
return augu;
int v,augv=0,delta,mind=num-1;
for(node *p=adj[u];p;p=p->next){
if(p->cap){
v=p->v;
if(dist[u]==dist[v]+1){
delta=min(augu-augv,p->cap);
delta=dfs(v,delta);
augv+=delta;
p->cap-=delta;
p->back->cap+=delta;
if(augu==augv||dist[S]==num)
return augv;
}
mind=min(mind,dist[v]);
}
}
if(!augv){
if(!--vd[dist[u]])
dist[S]=num;
dist[u]=mind+1;
vd[dist[u]]++;
}
return augv;
}
void sap(){
num=T+1;
vd[0]=num;
while(dist[S]<num)
flow+=dfs(S,INF);
}
void print(){
if(flow!=tot)
puts("NO");
else{
puts("YES");
for(int i=1;i<=m;i++)
printf("%d\n",epos[i]->back->cap+l[i]);
}
}
int main()
{
read();
sap();
print();
}