题解报告Robberies（概率dp）
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
Output
2 4 6
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。
思路：
正确的方程是:f[j]=max(f[j],f[j-q[i].money]*q[i].v) 其中,f[j]表示抢金额为j的最大的逃脱概率,条件是f[j-q[i].money]可达,也就是之前抢劫过;
始化为:f[0]=1,其余初始化为-1 (抢0块钱肯定不被抓，逃脱概率为1)
代码：
#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
double dp[10000+5];
double p[105];
int w[105];
int main()
{
int T;
scanf("%d",&T);
while(T--)
{
memset(dp,0,sizeof(dp));
int n,sum=0;
double maxp;
scanf("%lf%d",&maxp,&n);
for(int i = 1;i<=n;i++)
scanf("%d%lf",&w[i],&p[i]),sum+=w[i];
dp[0]=1;
for(int i = 1;i<=n;i++)
for(int j = sum;j>=w[i];j--)
dp[j]=max(dp[j],dp[j-w[i]]*(1-p[i]));
int ans = 0;
for(int j = 0;j<=sum;j++)
if((1-dp[j]) -maxp<1e-6 )
ans = max(ans,j);
printf("%d\n",ans);
}
return 0;
}