POJ 3308 Paratroopers（最小點權覆蓋）（對數乘轉加）

http://poj.org/problem?id=3308

 

r*c的地圖

每個大炮能夠消滅一行一列的敵人

安裝消滅第i行的大炮花費是ri

安裝消滅第j行的大炮花費是ci

已知敵人座標，同時消滅全部敵人，問最小花費

花費爲全部大炮消費的乘積

 

乘轉加：log（a*b*c）=log（a）+log（b）+log（c）

經典的最小點權覆蓋

源點向行連，列向匯點連

第i行j列有敵人，點i向點j連inf邊

 

最小點權覆蓋=最小割

 

 

#include<cmath>
#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>

using namespace std;

const double inf=2000000000;
const double eps=1e-9;

#define N 201
#define M 701

int src,decc;

int tot;
int front[N],to[M<<1],nxt[M<<1];
double val[M<<1];

int cur[N],lev[N];

queue<int>q;

void add(int u,int v,double cap)
{
    to[++tot]=v; nxt[tot]=front[u]; front[u]=tot; val[tot]=cap;
    to[++tot]=u; nxt[tot]=front[v]; front[v]=tot; val[tot]=0;
}

bool bfs()
{
    for(int i=0;i<=decc;++i) lev[i]=-1,cur[i]=front[i];
    while(!q.empty()) q.pop();
    lev[src]=0;
    q.push(src);
    int now,t;
    while(!q.empty())
    {
        now=q.front();
        q.pop();
        for(int i=front[now];i;i=nxt[i])
        {
            t=to[i];
            if(lev[t]==-1 && val[i]>eps)
            {
                lev[t]=lev[now]+1;
                if(t==decc) return true;
                q.push(t);        
            }
        }
    }
    return false;
}

double dinic(int now,double flow)
{
    if(now==decc) return flow;
    double rest=0,delta;
    int t;
    for(int &i=cur[now];i;i=nxt[i])
    {
        t=to[i];
        if(lev[t]>lev[now] && val[i]>eps)
        {
            delta=dinic(t,min(flow-rest,val[i]));
            if(delta>eps)
            {
                rest+=delta;
                val[i]-=delta; val[i^1]+=delta;
                if(fabs(rest-flow)<eps) break;
            }
        }
    }
    if(fabs(rest-flow)>eps) lev[now]=-1;
    return rest;
}

int main()
{
    int T;
    scanf("%d",&T);
    int n,m,k;
    double x,ans;
    int a,b;
    while(T--)
    {
        scanf("%d%d%d",&n,&m,&k);
        decc=n+m+1;
        tot=1;
        memset(front,0,sizeof(front));
        for(int i=1;i<=n;++i)
        {
            scanf("%lf",&x);
            add(src,i,log(x));
        }
        for(int i=1;i<=m;++i)
        {
            scanf("%lf",&x);
            add(i+n,decc,log(x));
        }
        for(int i=1;i<=k;++i)
        {
            scanf("%d%d",&a,&b);
            add(a,b+n,inf);
        }
        ans=0;
        while(bfs()) ans+=dinic(src,inf);
        printf("%.4lf\n",exp(ans));
    }
}

 

Paratroopers

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 8903		Accepted: 2679

Description

It is year 2500 A.D. and there is a terrible war between the forces of the Earth and the Mars. Recently, the commanders of the Earth are informed by their spies that the invaders of Mars want to land some paratroopers in the m × n grid yard of one their main weapon factories in order to destroy it. In addition, the spies informed them the row and column of the places in the yard in which each paratrooper will land. Since the paratroopers are very strong and well-organized, even one of them, if survived, can complete the mission and destroy the whole factory. As a result, the defense force of the Earth must kill all of them simultaneously after their landing.

In order to accomplish this task, the defense force wants to utilize some of their most hi-tech laser guns. They can install a gun on a row (resp. column) and by firing this gun all paratroopers landed in this row (resp. column) will die. The cost of installing a gun in the ith row (resp. column) of the grid yard is r_i (resp. c_i ) and the total cost of constructing a system firing all guns simultaneously is equal to the product of their costs. Now, your team as a high rank defense group must select the guns that can kill all paratroopers and yield minimum total cost of constructing the firing system.

Input

Input begins with a number T showing the number of test cases and then, T test cases follow. Each test case begins with a line containing three integers 1 ≤ m ≤ 50 , 1 ≤ n ≤ 50 and 1 ≤ l ≤ 500 showing the number of rows and columns of the yard and the number of paratroopers respectively. After that, a line with m positive real numbers greater or equal to 1.0 comes where the ith number is r_i and then, a line with n positive real numbers greater or equal to 1.0 comes where the ith number is c_i. Finally, l lines come each containing the row and column of a paratrooper.

Output

For each test case, your program must output the minimum total cost of constructing the firing system rounded to four digits after the fraction point.

Sample Input

1
4 4 5
2.0 7.0 5.0 2.0
1.5 2.0 2.0 8.0
1 1
2 2
3 3
4 4
1 4

Sample Output

16.0000