FAVDICE - Favorite Dice

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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?


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.


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.




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vijay77794: 2016-01-31 18:48:48

AC .................. :)

Mayank Garg: 2016-01-27 09:57:21

Nice concept :D My 300th green !!

coder_shishir: 2015-10-06 08:51:43

my 50th...

Sarthak Munshi: 2015-09-21 14:30:30

double required . float gives WA .

anuveshkothari: 2015-08-26 14:43:04

learned about coupon collector problem

Vars: 2015-08-17 06:50:45

my 100th with a piece of cake... :)

shantanu tripathi: 2015-08-13 22:07:02

learn about the famous "coupon collector prob" to solve this one. :)

Avi Aryan: 2015-07-17 10:35:23

Nice problem. My first problem with "Expected value" stuff. Looking forward to try some more.

BadeMeow: 2015-07-07 14:10:00

AC in one go! My 50th!! :D
Don't forget the double!

SangKuan: 2015-06-21 04:39:03

https://en.wikipedia.org/wiki/Coupon_collector%27s_problem.and use double

Added by:Matthew Reeder
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