HUST 1342 Cheat Secretly 有源汇上下界网络流 最小流
HUST 1342 Cheat Secretly 有源汇上下界网络流 最小流
题意：有N个点M条边的单向无环图，先要求必须走某些边，走到没有出边的点可以转移到任意一个点，问最少转移的次数。
最小流建图
入度为0的连st 流量为 oo
出度为0的连et 流量为 oo
若某边必须走，那么这条边的下界为1，上界为 oo
若某边不走，那么这条边的下界为0，上界为 oo
求最小流
//author: CHC
//First Edit Time: 2015-09-10 13:36
#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=1e+4;
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]!=0;
}
LL Dinic(int st,int et){
LL ans=0;
while(bfs(st,et)){
top=0;
memcpy(cur,head,sizeof(head));
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],ru[MAXN],chu[MAXN],n,m;
int main()
{
int t,cas=0;
scanf("%d",&t);
while(t--){
init();
scanf("%d%d",&n,&m);
int st=0,et=n+1;
memset(du,0,sizeof(du));
memset(ru,0,sizeof(ru));
memset(chu,0,sizeof(chu));
for(int i=0,x,y,v;i<m;i++){
scanf("%d%d%d",&x,&y,&v);
chu[x]++;
ru[y]++;
if(v){
AddEdge(x,y,INF-1);
du[x]-=1;
du[y]+=1;
}
else {
AddEdge(x,y,INF);
}
}
for(int i=1;i<=n;i++){
if(ru[i]==0){
AddEdge(st,i,INF);
}
if(chu[i]==0){
AddEdge(i,et,INF);
}
}
int sst=et+1,eet=et+2;
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(et,st,INF);
LL t=Dinic(sst,eet);
printf("Case #%d: %lld\n",++cas,t);
}
return 0;
}