POJ3308.md

二分图最小权覆盖 先取对数，然后最小割

#include<cstdio>
#include<cstring>
#include<iostream>
#include<cmath>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<string>
#include<algorithm>
#include<stack>
using namespace std;
void ____(){ ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); }
const int MAXN = 1111;
const int INF = 0x3f3f3f3f;
#define S 0
#define T MAXN - 1
struct EDGE{
    int to, rev;
    double cap;
    EDGE(){}
    EDGE(int _to, double _cap, int _rev){ to = _to; cap = _cap; rev = _rev; }
};
vector<EDGE> G[MAXN];
int n,m,l,rk[MAXN],iter[MAXN];
double x[MAXN],y[MAXN];
void ADDEDGE(int u, int v, double cap){
    G[u].push_back(EDGE(v,cap,(int)G[v].size()));
    G[v].push_back(EDGE(u,0,(int)G[u].size()-1));
}
bool bfs(){
    memset(iter,0,sizeof(iter));
    memset(rk,0,sizeof(rk));
    rk[S] = 1;
    queue<int> que;
    que.push(S);
    while(!que.empty()){
        int u = que.front();
        que.pop();
        for(int i = 0; i < (int)G[u].size(); i++){
            EDGE &e = G[u][i];
            if(!e.cap || rk[e.to]) continue;
            rk[e.to] = rk[u] + 1;
            que.push(e.to);
        }
    }
    return rk[T] != 0;
}
double dfs(int u, double f){
    if(u==T) return f;
    for(int i = 0; i < (int)G[u].size(); i++){
        EDGE &e = G[u][i];
        if(!e.cap || rk[e.to]!=rk[u] + 1) continue;
        double d = dfs(e.to,min(f,e.cap));
        if(d){
            e.cap -= d;
            G[e.to][e.rev].cap += d;
            return d;
        }
    }
    return 0;
}
double Dinic(){
    double flow = 0;
    while(bfs()){
        double d = dfs(S,INF);
        while(d){
            flow += d;
            d = dfs(S,INF);
        }
    }
    return flow;
}
void solve(){
    scanf("%d %d %d",&n,&m,&l);
    for(int i = 1; i <= n; i++) scanf("%lf",&x[i]);
    for(int i = 1; i <= m; i++) scanf("%lf",&y[i]);
    for(int i = 0; i <= n+m; i++) G[i].clear();
    G[T].clear();
    for(int i = 1; i <= n; i++) ADDEDGE(S,i,log(x[i]));
    for(int i = 1; i <= m; i++) ADDEDGE(i+n,T,log(y[i]));
    for(int i = 1; i <= l; i++){
        int u, v;
        scanf("%d %d",&u,&v);
        ADDEDGE(u,v+n,INF);
    }
    printf("%.4f\n",exp(Dinic()));
}
int main(){
    int t;
    for(scanf("%d",&t); t; t--) solve();
    return 0;
}