FAVDICE - Favorite Dice
BuggyD loves to carry his favorite die around. Perhaps you wonder why it's his favorite? Well, his die is magical and can be transformed into an N-sided unbiased die with the push of a button. Now BuggyD wants to learn more about his die, so he raises a question:
What is the expected number of throws of his die while it has N sides so that each number is rolled at least once?
Input
The first line of the input contains an integer t, the number of test cases. t test cases follow.
Each test case consists of a single line containing a single integer N (1 <= N <= 1000) - the number of sides on BuggyD's die.
Output
For each test case, print one line containing the expected number of times BuggyD needs to throw his N-sided die so that each number appears at least once. The expected number must be accurate to 2 decimal digits.
Example
Input: 2 1 12 Output: 1.00 37.24
hide comments
vijay77794:
2016-01-31 18:48:48
AC .................. :) |
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Mayank Garg:
2016-01-27 09:57:21
Nice concept :D My 300th green !! |
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coder_shishir:
2015-10-06 08:51:43
my 50th... |
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Sarthak Munshi:
2015-09-21 14:30:30
double required . float gives WA . |
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anuveshkothari:
2015-08-26 14:43:04
learned about coupon collector problem |
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Vars:
2015-08-17 06:50:45
my 100th with a piece of cake... :) |
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shantanu tripathi:
2015-08-13 22:07:02
learn about the famous "coupon collector prob" to solve this one. :) |
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Avi Aryan:
2015-07-17 10:35:23
Nice problem. My first problem with "Expected value" stuff. Looking forward to try some more. |
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BadeMeow:
2015-07-07 14:10:00
AC in one go! My 50th!! :D
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SangKuan:
2015-06-21 04:39:03
https://en.wikipedia.org/wiki/Coupon_collector%27s_problem.and use double |
Added by: | Matthew Reeder |
Date: | 2006-10-29 |
Time limit: | 1s |
Source limit: | 30000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: ERL JS-RHINO NODEJS PERL6 VB.NET |
Resource: | Al-Khawarizm 2006 |