题意:有n个节点m根水管的网络,每根水管有个水流的限制,问最少要多少水流能满足整个网络。

最小流
代码:

//author: CHC
//First Edit Time: 2015-09-10 10:45
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <set>
#include <vector>
#include <map>
#include <queue>
#include <set>
#include <algorithm>
#include <limits>
using namespace std;
typedef long long LL;
const int MAXN=110;
const int MAXM=1e+5;
const int INF = numeric_limits<int>::max();
const LL LL_INF= numeric_limits<LL>::max();
struct Edge {
int to,ci,next;
Edge(){}
Edge(int _to,int _ci,int _next):to(_to),ci(_ci),next(_next){}
}e[MAXM];
int head[MAXN],tot;
void init(){
memset(head,-1,sizeof(head));
tot=0;
}
void AddEdge(int u,int v,int ci0,int ci1=0){
e[tot]=Edge(v,ci0,head[u]);
head[u]=tot++;
e[tot]=Edge(u,ci1,head[v]);
head[v]=tot++;
}
int dis[MAXN],sta[MAXN],top,cur[MAXN];
bool bfs(int st,int et){
memset(dis,0,sizeof(dis));
dis[st]=1;
queue <int> q;q.push(st);
while(!q.empty()){
int now=q.front();q.pop();
for(int i=head[now];~i;i=e[i].next)
if(e[i].ci&&!dis[e[i].to]){
dis[e[i].to]=dis[now]+1;
q.push(e[i].to);
}
}
return dis[et];
}
LL Dinic(int st,int et){
LL ans=0;
while(bfs(st,et)){
top=0;
memcpy(cur,head,sizeof(cur));
int u=st,i;
while(1){
if(u==et){
int pos,minn=INF;
for(i=0;i<top;i++){
if(minn>e[sta[i]].ci){
minn=e[sta[i]].ci;
pos=i;
}
}
for(i=0;i<top;i++){
e[sta[i]].ci-=minn;
e[sta[i]^1].ci+=minn;
}
top=pos;
u=e[sta[top]^1].to;
ans+=minn;
}
for(i=cur[u];~i;cur[u]=i=e[i].next)
if(e[i].ci&&dis[u]+1==dis[e[i].to])break;
if(cur[u]!=-1){
sta[top++]=cur[u];
u=e[cur[u]].to;
}
else {
if(top==0)break;
dis[u]=0;
u=e[sta[--top]^1].to;
}
}
}
return ans;
}
int du[MAXN],n,m,num[MAXM],base[MAXM];
int main()
{
while(~scanf("%d%d",&n,&m)){
memset(du,0,sizeof(du));
init();
for(int i=0,x,y,ci,v;i<m;i++){
scanf("%d%d%d%d",&x,&y,&ci,&v);
num[i]=tot;
if(!v){
AddEdge(x,y,ci);
base[i]=0;
}
else {
AddEdge(x,y,0);
du[x]-=ci;du[y]+=ci;
base[i]=ci;
}
}
int sst=0,eet=n+1;
LL ctot=0;
for(int i=1;i<=n;i++)
if(du[i]>0)AddEdge(sst,i,du[i]),ctot+=du[i];
else AddEdge(i,eet,-du[i]);
LL ans=Dinic(sst,eet);
AddEdge(n,1,INF);
//ans+=Dinic(sst,eet);
LL t=Dinic(sst,eet);
if(ans+t!=ctot)puts("Impossible");
else {
//ans=Dinic(1,n);
//printf("%d\n",e[tot-1].ci);
printf("%I64d\n",t);
for(int i=0;i<m-1;i++){
printf("%d ",base[i]+e[num[i]^1].ci);
}
printf("%d\n",base[m-1]+e[num[m-1]^1].ci);
}
}
return 0;
}