Robberies
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 10562 Accepted Submission(s): 3889
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
动态规划
AC代码：
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 10562 Accepted Submission(s): 3889
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
动态规划
AC代码：
//用成功逃走的概率当做价值,银行的总钱数当做背包容量
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
struct node
{
int M;//钱量
float P;//不被抓概率
}dp[110];
float f[10010];//最大的钱量为100*100=10000；
int max(int n,int m)
{return n>m?n:m;}
int main()
{
int i,j,T,n,m,sum;
float x,Psum;
scanf("%d",&T);
while(T--)
{
memset(dp,0,sizeof(dp));
memset(f,0,sizeof(f));
scanf("%f %d",&x,&m);
Psum=1-x;//最小逃脱率，低于这个就逃不了了
sum=0;
for(i=0;i<m;i++)
{
scanf("%d %f",&dp[i].M,&dp[i].P);
sum+=dp[i].M;
dp[i].P=1-dp[i].P;//逃脱率
}
f[0]=1;//抢0块大洋肯定不被抓
for(i=0;i<m;i++)
{
for(j=sum;j>=dp[i].M;j--)
f[j]=max(f[j],f[j-dp[i].M]*dp[i].P);//f[j]表示抢j块大洋的最大的逃脱概率,条件是f[j-q[i].money]可达,也就是之前抢劫过;
}
for(i=sum;i>=0;i--)
{
if(f[i]>=Psum)
{break;}
}
printf("%d\n",i);
}
return 0;
}
