DP入门---Robberies

最新推荐文章于 2022-01-13 08:42:39 发布

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最新推荐文章于 2022-01-13 08:42:39 发布

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原文链接：http://www.cnblogs.com/chen9510/p/5509863.html

本文介绍了一个基于01背包算法解决银行抢劫问题的方法，该问题要求在被抓概率不超过给定阈值的情况下，计算出能抢到的最大金额。通过两层循环实现，外层遍历银行，内层使用金额作为状态转移的依据。

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HDU 2955

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

0.04 3

1 0.02

2 0.03

3 0.05

0.06 3

2 0.03

3 0.05

0.10 3

1 0.03

2 0.02

3 0.05

Sample Output

题意：输入T组数据，然后输入P,N P表示被抓的最大上限，N表示银行个数然后输入N家银行的钱数与被抓概率，求在被抓概率小于等于P时，抢的最大钱数。

思路：01背包，第二重循环用抢的钱数表示，里面的值为抢下标对应的钱被抓概率。

代码如下;

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
using  namespace  std;
double dp[10005];
int  main()
{
    int T,N,sum,money[105];
    double P,p[105];
    scanf("%d",&T);
    while(T--)
    {
        sum=0;
        scanf("%lf%d",&P,&N);
        P=1-P;
        for(int i=0; i<N; i++)
        {
            int d;
            double f;
            scanf("%d%lf",&d,&f);
            money[i]=d;
            p[i]=1-f;
            sum+=d;
        }
        memset(dp,0,sizeof(dp));
        dp[0]=1;
        for(int i=0; i<N; i++)
        for(int j=sum; j>=money[i]; j--)
        {
            dp[j]=max(dp[j],dp[j-money[i]]*p[i]);
        }
        for(int i=sum;i>=0;i--)
        if(dp[i]>=P)
        {
            printf("%d\n",i);
            break;
        }
    }
    return  0;
}