hdu2955 Robberies （01背包）

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最新推荐文章于 2025-08-12 21:54:14 发布

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本文介绍了一个经典的01背包问题应用实例——“抢银行”问题，并详细解析了如何通过调整背包容量来求解最大收益的同时确保被抓概率低于预设阈值。该问题涉及动态规划中的背包问题及概率计算。

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

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
   

Sample Output

    2 4 6
   

Source

IDI Open 2009

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题意：

抢银行。抢每一个银行被抓的几率为caught[]，互为独立事件，在容忍上限内，抢最多的钱。

01背包，但须要改变一点。须要将能抢来的最多的钱最为背包容量

代码例如以下：

/*此题关键是找到背包的容量和价值*/
#include <cstdio>
#include <cstring>
#define N 10047
int M[N];
double P[N],f[N];
double max(double a,double b)
{
	if(a > b)
		return a;
	return b;
}
int main()
{
	double p;
	int T,n,i,j,sum;
	scanf("%d",&T);
	while(T--)
	{
		sum = 0;
		memset(f,0,sizeof(f));//要对数组进行初始化
		scanf("%lf%d",&p,&n);
		p =1-p;;//成功逃走的概率
		f[0] = 1;//未抢劫一分钱那么逃走的概率就为1
		for(i = 0 ; i < n ; i++)
		{
			scanf("%d%lf",&M[i],&P[i]);
			P[i] = 1-P[i];
			sum+=M[i];//算出银行总钱数
		}
		for(i = 0 ; i < n ; i++)
		{
			for(j = sum ; j >= M[i] ; j--)
			{
				f[j] = max(f[j],f[j-M[i]]*P[i]);
			}//这里的每次成功的概率须要进行乘法运算。由于是两次成功的概率所以是乘法
		}
		for(i = sum ; i >= 0 ; i--)
		{
			if(f[i] >= p)
				break;//找出能够成功逃走而且逃走概率不超过警戒值
		}
		printf("%d\n",i);
	}
	return 0;
}