24 hour archive: Problem
2141  So you want to be a 2naire? 2141  So you want to be a 2naire? 2141  So you want to be a 2naire?
Statistics  Sub: 12  AC: 6  AC%: 50,00  Score: 4,35 
Created by  2005 Waterloo Local Contest 
Added by  ymondelo20 (20121113) 
Limits 
Total Time: 5000 MS

Test Time:
2000 MS
Memory: 62 MB  Output: 64 MB  Size:
29 KB

Enabled languages  
Available in 
Description
The player starts with a prize of $1, and is asked a sequence of n questions. For each question, he may quit and keep his prize. Answer the question. If wrong, he quits with nothing. If correct, the prize is doubled, and he continues with the next question.
After the last question, he quits with his prize. The player wants to maximize his expected prize. Once each question is asked, the player is able to assess the probability p that he will be able to answer it. For each question, we assume that p is a random variable uniformly distributed over the range t .. 1.
After the last question, he quits with his prize. The player wants to maximize his expected prize. Once each question is asked, the player is able to assess the probability p that he will be able to answer it. For each question, we assume that p is a random variable uniformly distributed over the range t .. 1.
The player starts with a prize of $1, and is asked a sequence of n questions. For each question, he may quit and keep his prize. Answer the question. If wrong, he quits with nothing. If correct, the prize is doubled, and he continues with the next question.
After the last question, he quits with his prize. The player wants to maximize his expected prize. Once each question is asked, the player is able to assess the probability p that he will be able to answer it. For each question, we assume that p is a random variable uniformly distributed over the range t .. 1.
After the last question, he quits with his prize. The player wants to maximize his expected prize. Once each question is asked, the player is able to assess the probability p that he will be able to answer it. For each question, we assume that p is a random variable uniformly distributed over the range t .. 1.
The player starts with a prize of $1, and is asked a sequence of n questions. For each question, he may quit and keep his prize. Answer the question. If wrong, he quits with nothing. If correct, the prize is doubled, and he continues with the next question.
After the last question, he quits with his prize. The player wants to maximize his expected prize. Once each question is asked, the player is able to assess the probability p that he will be able to answer it. For each question, we assume that p is a random variable uniformly distributed over the range t .. 1.
After the last question, he quits with his prize. The player wants to maximize his expected prize. Once each question is asked, the player is able to assess the probability p that he will be able to answer it. For each question, we assume that p is a random variable uniformly distributed over the range t .. 1.
Input specification
Input is a number of lines, each with two numbers: an integer 1 <= n <= 30, and a real 0 <= t <= 1. Input is terminated by a line containing 0 0. This line should not be processed.
Input is a number of lines, each with two numbers: an integer 1 <= n <= 30, and a real 0 <= t <= 1. Input is terminated by a line containing 0 0. This line should not be processed.
Input is a number of lines, each with two numbers: an integer 1 <= n <= 30, and a real 0 <= t <= 1. Input is terminated by a line containing 0 0. This line should not be processed.
Output specification
For each input n and t, print the player's expected prize, if he plays the best strategy. Output should be rounded up to two decimal places.
For each input n and t, print the player's expected prize, if he plays the best strategy. Output should be rounded up to two decimal places.
Input is a number of lines, each with two numbers: an integer 1 <= n <= 30, and a real 0 <= t <= 1. Input is terminated by a line containing 0 0. This line should not be processed.
Sample input
1 0.5
1 0.3
2 0.6
24 0.25
0 0
Sample output
1.50
1.36
2.56
230.14
Hint(s)
http://coj.uci.cu/24h/
http://coj.uci.cu/24h/
http://coj.uci.cu/24h/