HDU2955(动态规划背包)

Robberies

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 17877 Accepted Submission(s): 6599

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

30.04 31 0.022 0.033 0.050.06 32 0.032 0.033 0.050.10 31 0.032 0.023 0.05

Sample Output

246
#include<stdio.h>#include<stdlib.h>#include<string.h>float max(float a,float b){return a>b?a:b;}struct Bank{int Money;float Possible;};Bank b[10015];float dp[10015];int main(){int T;float p;int n;int i,j;int sum;scanf("%d",&T);while(T--){sum=0;scanf("%f%d",&p,&n);for(i=0;i<n;i++){scanf("%d%f",&b[i].Money,&b[i].Possible);sum+=b[i].Money;}memset(dp,0,sizeof(dp));dp[0]=1;for(i=0;i<n;i++)for(j=sum;j>=b[i].Money;j--){dp[j]=max(dp[j],dp[j-b[i].Money]*(1-b[i].Possible));}for(j=sum;j>=0;j--){if(dp[j]>1-p){printf("%d\n",j);break;}}}return 0;}


主要是动态转移方程，将录入银行里的总钱数当作背包容量，然后，将每个银行的钱当作重量，不被抓到的概率看作价值，则dp方程中dp数组则为不被抓到的概率下所得到的钱数，最后得到dp数组中最后大于被抓概率情况下已经获得的钱数
dp[j]=max(dp[j],dp[j-b[i].Money]*(1-b[i].Possible));