poj3682 King Arthur's Birthday Celebration （概率）

来源：恒创科技编辑：恒创科技编辑部

2024-02-04 12:11:59

King Arthur's Birthday Celebration

Time Limit:1000MS

Memory Limit:65536K

Total Submissions:2886

Accepted:905

Description

King Arthur is an narcissist who intends to spare no coins to celebrate his comingK-th birthday. The luxurious celebration will start on his birthday and King Arthur decides to let fate tell when to stop it. Every day he will toss a coin which has probabilitypthat it comes up heads and 1-pup tails. The celebration will be on going until the coin has come up heads forKtimes. Moreover, the king also decides to spend 1 thousand coins on the first day's celebration, 3 thousand coins on the second day's, 5 thousand coins on the third day's ... The cost of next day will always be 2 thousand coins more than the previous one's. Can you tell the minister how many days the celebration is expected to last and how many coins the celebration is expected to cost?

Input

The input consists of several test cases.
For every case, there is a line with an integerK( 0 <K≤ 1000 ) and a real numberp(0.1 ≤ p ≤ 1).
Input ends with a single zero.

Output

For each case, print two number -- the expected number of days and the expected number of coins (in thousand), with the fraction rounded to 3 decimal places.

Sample Input

1 1 1 0.5 0

Sample Output

1.000 1.000 2.000 6.000

Source

POJ Founder Monthly Contest – 2008.08.31, Soduku@POJ

解析：ans1=k/p

ans2=k*(k+1)/p/p-k/p

代码：

#include<cstdio>
using namespace std;

int main()
{
  //freopen("1.in","r",stdin);
  int k;  double p;
  while(scanf("%d%lf",&k,&p)&&k!=0)
    {
      printf("%.3f ",k/p);
      printf("%.3f\n",k*(k+1)/p/p-k/p);
  }
  return 0;
}