hdu 2955 Robberies

题目：

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

思路：

题意：Roy想要抢劫银行，每家银行多有一定的金额和被抓到的概率，知道Roy被抓的最大概率P，求Roy在被抓的情况下，抢劫最多。

我们需要将处理被抓到概率，转化为求不被抓概率，不被抓概率是每一个逃跑概率的乘积，如果是处理被抓概率太麻烦。

那么问题转化在不被抓的情况下(被抓的概率小于给定值p时安全)能抢得的最大钱数。
dp[j]表示在抢到钱为j时，不被抓概率。

 dp[j]=max(dp[j],dp[j-Mj[i]]*(1-Pj[i]));

代码：

#include<iostream>
#include<stdio.h>
#include<stdlib.h>
#include<algorithm>
#include<string.h>
using namespace std;
double dp[10005];
int Mj[105];
double Pj[105];
int main()
{
    int T,N,total;
    double P;
    scanf("%d",&T);
    while (T--){
        scanf("%lf%d",&P,&N);
        memset(dp,0,sizeof(dp));
        total = 0;
        for (int i = 0; i < N; i++){
            scanf("%d %lf",&Mj[i],&Pj[i]);
            total += Mj[i];
        }
        dp[0] = 1;
        for (int i = 0; i < N; i++){
            for (int j = total; j >= Mj[i]; j--){
                dp[j] = max(dp[j],dp[j-Mj[i]]*(1-Pj[i]));
            }
        }
        for (int i = total; i >= 0; i--){
            if (dp[i]>(1 - P)){
                printf("%d\n",i);
                break;
            }
        }
    }
    return 0;
}