hdu 2955 Robberies（概率背包）

Posted 2020-09-05 hk lin

Robberies

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 22658    Accepted Submission(s): 8358

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

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对于该题，第一遍拿概率作为背包容量dp（看样例好像最多两位），结果错了。

发觉最多只有1w个银行，于是我选择拿银行数量作为背包容量，然后去求出每个银行数最大逃跑的概率（1-被抓概率）。

接着银行从大到小找一遍，最大的且逃跑概率大于等于逃跑总概率（1-被抓总概率n）的银行数即为答案。

 

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cmath>
#define clr(x) memset(x,0,sizeof(x))
#define MIN 1e-9
using namespace std;
double val[100010];
struct node
{
    int cost;
    double val;
}bank[200];
double d,m;
int T,n,ans,all;
int main()
{
    scanf("%d",&T);
    while(T--)
    {
        scanf("%lf%d",&m,&n);
        all=0;
        m=1-m;
        for(int i=1;i<=n;i++)
        {
            scanf("%d%lf",&bank[i].cost,&bank[i].val);
            all+=bank[i].cost;
        }
        clr(val);
        val[0]=1;
        for(int i=1;i<=n;i++)
            for(int j=all;j>=bank[i].cost;j--)
            {
                if(val[j]<(1-bank[i].val)*val[j-bank[i].cost])
                    val[j]=(1-bank[i].val)*val[j-bank[i].cost];
            }
        for(int i=all;i>=0;i--)
        {
            if(val[i]>=m || m-val[i]<MIN)
            {
                ans=i;
                break;
            }
        }
        printf("%d\n",ans);
    }
    return 0;
}