BYU15W_4 - Game Calculator
A game is played where two armies face each other. Each turn, every unit in both armies either scores a hit or a miss. Each army then removes a number of units equal to the number of hits scored by the opposing army. The game is over when at the end of a turn, one army does not have any more units. If both armies run out of units on the same turn, the game is a draw. The probability of any one unit scoring a hit is determined at the beginning of the game and remains constant.
The goal is to determine the probability of army A winning, army B winning, or the game ending in a draw.
Example
If the probability of scoring a hit is 0.3, army A has 2 units, and army B has 1 unit, then A has a 0.86839 chance of winning, B has a 0.09213 chance of winning and there is a 0.03948 chance of a draw.
Input
The first line contains a single positive integer T, representing the number of test cases. T test cases follow. Each test case is two lines long. The first line of each test case contains a single decimal number H. The second line contains two positive integers A and B, representing the number of units in each army.
Limits
0 < H <= 1
0 < A, B <= 1,000,000
Output
For each test case, output a single line containing three decimal numbers representing the chance of A winning, B winning and ending in a draw, respectively. Each number should rounded to exactly 5 decimal places.
Example
Input: 2 0.3 2 1 0.854 8 8 Output: 0.86839 0.09213 0.03948 0.38532 0.38532 0.22936
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ttuanho:
2017-07-14 16:56:52
Min_25
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Min_25:
2016-06-11 21:24:41
When H = 0.976 and A = B = 1, the probability of a draw is exactly 0.953125, and it can be rounded to 0.95312 or 0.95313.
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Added by: | BYU Admin |
Date: | 2015-03-28 |
Time limit: | 1s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: ASM64 |