UVa 10330

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 = 220;
const int maxm = 40011;
struct Edge{
    int v,cap,flow,next;
}edge[maxm];
int eh[maxn],tot;
bool vist[maxn];
int d[maxn];

void init(){
    tot = 0;
    memset(eh,-1,sizeof(eh));
}
void addedge(int u,int v,int c){
    Edge e = {v,c,0,eh[u]};
    edge[tot] = e;
    eh[u] = tot ++;
}
void add(int u,int v,int c){
    addedge(u,v,c);
    addedge(v,u,0);
}
bool BFS(int s,int t){
    memset(vist,0,sizeof(vist));
    queue<int>Q;
    Q.push(s);
    vist[s] = 1;
    d[s] = 0;
    while(!Q.empty()){
        int u = Q.front();
        Q.pop();
        for(int i=eh[u];i!=-1;i=edge[i].next){
            int v = edge[i].v;
            if(!vist[v] && edge[i].cap > edge[i].flow){
                vist[v] = 1;
                d[v] = d[u] + 1;
                Q.push(v);
                if(v == t)return true;
            }
        }
    }
    return false;
}
int DFS(int u,int t,int avi){
    if(u == t || avi == 0)return avi;
    int flow = 0 ,f;
    for(int i=eh[u];i!=-1;i=edge[i].next){
        int v = edge[i].v;
        if(d[v] == d[u]+1 && (f=DFS(v,t,min(avi,edge[i].cap-edge[i].flow)))>0){
            edge[i].flow += f;
            edge[i^1].flow -= f;
            flow += f;
            avi -= f;
            if(avi == 0)break;
        }
    }
    return flow;
}
int maxFlow(int s,int t){
    int flow = 0;
    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+1,n+i+1,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(0,u,INF);
        }
        while(D--){
            scanf("%d",&u);
            add(n+u,2*n+1,INF);
        }
        printf("%d
",maxFlow(0,2*n+1));
    }
    return 0;
}