HDOJ 2955

Robberies

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 8206    Accepted Submission(s): 3100

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

 

Recommend

gaojie

 

这题是个变形的01背包。因为代价为浮点数，故不能按正常情况去背，于是可以用金钱作为代价，dp【i】表示得到i元钱的最大逃跑概率，最后去求大于总的逃跑概率能得到的最大钱数即可。

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <map>
#include <string>
#include <stack>
#include <cctype>
#include <vector>
#include <queue>
#include <set>
#include <iomanip>

using namespace std;
//#define Online_Judge
#define outstars cout << "***********************" << endl;
#define clr(a,b) memset(a,b,sizeof(a))
#define lson l , mid  , rt << 1
#define rson mid + 1 , r , rt << 1|1
#define FOR(i , x , n) for(int i = (x) ; i < (n) ; i++)
#define FORR(i , x , n) for(int i = (x) ; i <= (n) ; i++)
#define REP(i , x , n) for(int i = (x) ; i > (n) ; i--)
#define REPP(i ,x , n) for(int i = (x) ; i >= (n) ; i--)

#define mk make_pair
const int MAXN = 10000 + 50;
const int maxw = 100 + 20;
const int MAXNNODE = 1000 +10;
const long long LLMAX = 0x7fffffffffffffffLL;
const long long LLMIN = 0x8000000000000000LL;
const int INF = 0x7fffffff;
const int IMIN = 0x80000000;
#define eps 1e-8
#define mod 10007
typedef long long LL;
const double PI = acos(-1.0);
typedef double D;
typedef pair<int , int> pii;
const D e = 2.718281828459;
D dp[MAXN];///得到i元时逃跑的概率
int value[120] ;
D cost[120];
int main()
{
    //ios::sync_with_stdio(false);
#ifdef Online_Judge
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
#endif // Online_Judge
    int T;
    cin  >> T;
    while(T--)
    {
        int n ;
        D m ;
        D x;
        scanf("%lf%d" , &x  ,&n );

        m = 1 - x;
        int sum = 0;
        FOR(i ,0 , n)
        {
            scanf("%d%lf" ,&value[i] , &x);
            cost[i] = 1 - x;
            sum += value[i];
        }
        clr(dp , 0);
        dp[0] = 1;
//        cout <<  ' '  << sum << endl;
        FOR(i ,0 , n)
        {
                REPP(j ,  sum , value[i])
                {
                    if(dp[j] < dp[j - value[i]] * cost[i])dp[j] = dp[j - value[i]] * cost[i];
                }
        }
//        FORR(i , 0 , sum)cout << dp[i] << endl;
        REPP(i , sum , 0)
            if(m <= dp[i])
            {
                printf("%d\n" , i);
                break;
            }

    }
    return 0;
}