HDU_2955_背包问题

Description

The aspiring Roy the Robber has seen a lot of American movies, and knows that the bad guys usually gets caught in the end, often because they become too greedy. He has decided to work in the lucrative business of bank robbery only for a short while, before retiring to a comfortable job at a university. 


For a few months now, Roy has been assessing the security of various banks and the amount of cash they hold. He wants to make a calculated risk, and grab as much money as possible. 


His mother, Ola, has decided upon a tolerable probability of getting caught. She feels that he is safe enough if the banks he robs together give a probability less than this.

 

Input

The first line of input gives T, the number of cases. For each scenario, the first line of input gives a floating point number P, the probability Roy needs to be below, and an integer N, the number of banks he has plans for. Then follow N lines, where line j gives an integer Mj and a floating point number Pj . 
Bank j contains Mj millions, and the probability of getting caught from robbing it is Pj .

 

Output

For each test case, output a line with the maximum number of millions he can expect to get while the probability of getting caught is less than the limit set. 

Notes and Constraints 
0 < T <= 100 
0.0 <= P <= 1.0 
0 < N <= 100 
0 < Mj <= 100 
0.0 <= Pj <= 1.0 
A bank goes bankrupt if it is robbed, and you may assume that all probabilities are independent as the police have very low funds.

 

Sample Input

 3
0.04 3
1 0.02
2 0.03
3 0.05
0.06 3
2 0.03
2 0.03
3 0.05
0.10 3
1 0.03
2 0.02
3 0.05 

 

Sample Output

 2
4
6 

 

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
#define MAX_N 105
//最多可以抢这么多钱
#define MAX_M 10005
int money[MAX_N];
//dp[i][j]表示抢前i家银行抢的j万元时的最大的被捕几率（对应最小的逃跑几率）
double dp[MAX_N][MAX_M];
//被抓的概率
double possibility[MAX_N];
int n;
int M;
//被抓的概率
double total;
int t,k;
int main()
{
   //freopen("背包E.txt", "r",stdin);
   scanf("%d",&t);
   k=t;
    while(t--)
    {
       scanf("%lf %d",&total,&n);

       M=0;
       for(int i=0;i<n;i++)
       {
           scanf("%d %lf",money+i,possibility+i);
           M += money[i];
       }

       void solve();
       solve();
    }
   return 0;
}

void solve()
{
    fill(dp[0],dp[0]+M+1,0);
    dp[0][0]=1;
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<=M;j++)
        {
            if(j<money[i])
            {
                dp[i+1][j]=dp[i][j];
            }
            else{

                dp[i+1][j]=max(dp[i][j],dp[i][j-money[i]]*(1-possibility[i]));
           
            }

        }
    }
    int res=0;
    for(int i=0;i<=M;i++)
    {
        //逃跑的机率要大于等于（1-total）
        if(dp[n][i]>=(1-total))
            res=i;
    }
    printf("%d\n",res);

}