hdu 2955 Robberies

Robberies

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 7351    Accepted Submission(s): 2762 

Problem 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

 

Source

IDI Open 2009

 

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gaojie

// 好吧、我对概率真的好弱智  我开始居然是把概率相加了、、、
// 这种情况、为了避开繁杂的讨论 就是利用补集来算了、对立算起来真心更清爽、然后就是O 1 背包了
#include <iostream>
#include <algorithm>
#include <queue>
#include <math.h>
#include <stdio.h>
#include <string.h>
using namespace std;
double dp[10010];
int M[110];
double p[110];
#define epx 0.000000001
int main()
{
    int T,n,V;
    double P;
    int i,j,k;
    scanf("%d",&T);
    while(T--){
        scanf("%lf %d",&P,&n);
        V=0;
       for(i=1;i<=n;i++)
        {
            scanf("%d %lf",&M[i],&p[i]);
            V+=M[i];
        }
        for(i=1;i<=V;i++)
            dp[i]=0;
        dp[0]=1;
        for(i=1;i<=n;i++)
            for(j=V;j>=M[i];j--){
             if(dp[j]<dp[j-M[i]]*(1-p[i]))
                dp[j]=dp[j-M[i]]*(1-p[i]);
            }
       P=1-P;
       for(i=V;i>0;i--)
         if(dp[i]>=P)
            break;
    printf("%d
",i);
    }

    return 0;
}