hdu 2955 01背包问题

最新推荐文章于 2021-05-16 15:34:08 发布

forpro_yang

最新推荐文章于 2021-05-16 15:34:08 发布

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分类专栏：动态规划文章标签： constraints integer input output less security

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本文介绍了一个经典的01背包问题实例——银行抢劫计划。该问题要求在不超过被抓的概率限制下，计算出能获得的最大金额。通过动态规划的方法求解，考虑了不同银行被抢的可能性及其后果。

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http://acm.hdu.edu.cn/showproblem.php?pid=2955

Robberies

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2406 Accepted Submission(s): 908

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

Sample Output

01背包：

关键方程是f[j]=max( f[j] , f[j-m[i]]*p[i] )

代码：

#include <iostream>
#include <string.h>
#include <stdio.h>
using namespace std;

double max(double a,double b)
{
    return a>b?a:b;
}
int t,n;
int m[110],sum;
double p[110],dp[110*110],q;  //dp[i]表示抢i百万元是不被抓的概率。

int main()
{
    int i,j,k;
    cin>>t;
    while(t--)
    {
        sum=0;
        scanf("%lf%d",&q,&n);
		q=1-q;
        for(i=0;i<n;i++)
        {
            scanf("%d%lf",&m[i],&p[i]);
            sum+=m[i];
        }
        memset(dp,0,sizeof(dp));
        dp[0]=1;
        for(i=0;i<n;i++)
        {
            for(j=sum;j>=m[i];j--)
            {
                dp[j]=max(dp[j],dp[j-m[i]]*(1-p[i]));  //要么抢	j元，要么抢j-m[i]元 ，因为要抢到j元，前提是前面抢i元时没有被抓到，所以是*(1-p[i])
            }
        }
        for(j=sum;j>=0;j--)
        {
            if(dp[j]>=q)
			{
                printf("%d\n",j);
				break;
			}
        }
    }
    return 0;
}