hdoj Robberies 2955 （機率Dp&&01背包） 好題

Robberies

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 17580    Accepted Submission(s): 6494

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
  
  
   //題意：
  
  
   先給你小偷被抓的機率m與它準備去偷的銀行的個數n。
  
  
   然後給你n個銀行中每個銀行的錢數和偷這個銀行被抓的機率，求出小偷最多能偷多少錢。
  
  
   //轉換：
  
  
   将n個銀行的總錢數看做是背包容量，将成功逃跑的機率（1-m）作為目标，進行01背包就可求出。
  
  
   Hait：重在轉化....
  
  
          
#include<stdio.h>
#include<string.h>
double max(double a,double b)
{
	return a>b?a:b;
}
int a[110];
double dp[10010],b[110];
int main()
{
	int t;
	int n,i,j,k,sum;
	double m,num;
	scanf("%d",&t);
	while(t--)
	{
		scanf("%lf%d",&m,&n);
		m=1-m;
		sum=0;
		for(i=1;i<=n;i++)
		{
			scanf("%d%lf",&a[i],&num);
			b[i]=1-num;
			sum+=a[i];
		}
		memset(dp,0,sizeof(dp));
		dp[0]=1;
		for(i=1;i<=n;i++)
		{
			for(j=sum;j>=a[i];j--)
			{
				dp[j]=max(dp[j],dp[j-a[i]]*b[i]);
			}
		}
		for(i=sum;i>=0;i--)
		{
			if(dp[i]>=m)
			{
				printf("%d\n",i);
				break;
			}
		}
	}
	return 0;
}