UVa 10330 - Power Transmission(最大流--拆点)

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1271

题目：普通的网络流模型加多了一个每个节点的流量限制。

刚开始的时候是直接找增广路，顺便更新节点的容量，但是证明不了其正确性，WA了，大概这种做法是错的。

正解：将每个点拆成两个点，并且这两个点构成的边的容量是该点容量，这样就保证流过的流量不大于该点容量。

 /*
  *Author:       Zhaofa Fang
  *Created time: 2013-07-16-20.00
  *Language:     C++
  */
 #include <cstdio>
 #include <cstdlib>
 #include <sstream>
 #include <iostream>
 #include <cmath>
 #include <cstring>
 #include <algorithm>
 #include <string>
 #include <utility>
 #include <vector>
 #include <queue>
 #include <map>
 #include <set>
 using namespace std;

 typedef long long ll;
 #define DEBUG(x) cout<< #x << ':' << x << endl
 #define FOR(i,s,t) for(int i = (s);i <= (t);i++)
 #define FORD(i,s,t) for(int i = (s);i >= (t);i--)
 #define REP(i,n) for(int i=0;i<(n);i++)
 #define REPD(i,n) for(int i=(n-1);i>=0;i--)
 #define PII pair<int,int>
 #define PB push_back
 #define MP make_pair
 #define ft first
 #define sd second
 #define lowbit(x) (x&(-x))
 #define INF (1<<30)
 #define eps 1e-8

 const int maxn = ;
 const int maxm = ;
 struct Edge{
     int v,cap,flow,next;
 }edge[maxm];
 int eh[maxn],tot;
 bool vist[maxn];
 int d[maxn];

 void init(){
     tot = ;
     memset(eh,-,sizeof(eh));
 }
 void addedge(int u,int v,int c){
     Edge e = {v,c,,eh[u]};
     edge[tot] = e;
     eh[u] = tot ++;
 }
 void add(int u,int v,int c){
     addedge(u,v,c);
     addedge(v,u,);
 }
 bool BFS(int s,int t){
     memset(vist,,sizeof(vist));
     queue<int>Q;
     Q.push(s);
     vist[s] = ;
     d[s] = ;
     while(!Q.empty()){
         int u = Q.front();
         Q.pop();
         for(int i=eh[u];i!=-;i=edge[i].next){
             int v = edge[i].v;
             if(!vist[v] && edge[i].cap > edge[i].flow){
                 vist[v] = ;
                 d[v] = d[u] + ;
                 Q.push(v);
                 if(v == t)return true;
             }
         }
     }
     return false;
 }
 int DFS(int u,int t,int avi){
     if(u == t || avi == )return avi;
     int flow =  ,f;
     for(int i=eh[u];i!=-;i=edge[i].next){
         int v = edge[i].v;
         if(d[v] == d[u]+ && (f=DFS(v,t,min(avi,edge[i].cap-edge[i].flow)))>){
             edge[i].flow += f;
             edge[i^].flow -= f;
             flow += f;
             avi -= f;
             if(avi == )break;
         }
     }
     return flow;
 }
 int maxFlow(int s,int t){
     int flow = ;
     while(BFS(s,t)){
         flow += DFS(s,t,INF);
     }
     return flow;
 }
 int main(){
     //freopen("in","r",stdin);
     //freopen("out","w",stdout);
     int n;
     while(~scanf("%d",&n)){
         int u,v,c,m;
         init();
         REP(i,n){
             scanf("%d",&c);
             add(i+,n+i+,c);
         }
         scanf("%d",&m);
         while(m--){
             scanf("%d%d%d",&u,&v,&c);
             add(n+u,v,c);
         }
         int B,D;
         scanf("%d%d",&B,&D);
         while(B--){
             scanf("%d",&u);
             add(,u,INF);
         }
         while(D--){
             scanf("%d",&u);
             add(n+u,*n+,INF);
         }
         printf("%d\n",maxFlow(,*n+));
     }
     return ;
 }