Challenge:
Input: A list of distinct positive integers within the range \$[1, \text{list-size}]\$.
Output: An integer: the amount of times the list is riffle-shuffled. For a list, this means the list is split in two halves, and these halves are interleaved (i.e. riffle-shuffling the list [1,2,3,4,5,6,7,8,9,10]
once would result in [1,6,2,7,3,8,4,9,5,10]
, so for this challenge the input [1,6,2,7,3,8,4,9,5,10]
would result in 1
).
Challenge rules:
- You can assume the list will only contain positive integers in the range \$[1, \text{list-size}]\$ (or \$[0, \text{list-size}-1]\$ if you choose to have 0-indexed input-lists).
- You can assume all input-lists will either be a valid riffle-shuffled list, or a sorted list which isn't shuffled (in which case the output is
0
). - You can assume the input-list will contain at least three values.
Step-by-step example:
Input: [1,3,5,7,9,2,4,6,8]
Unshuffling it once becomes: [1,5,9,4,8,3,7,2,6]
, because every even 0-indexed item comes first [1, ,5, ,9, ,4, ,8]
, and then all odd 0-indexed items after that [ ,3, ,7, ,2, ,6, ]
.
The list isn't ordered yet, so we continue:
Unshuffling the list again becomes: [1,9,8,7,6,5,4,3,2]
Again becomes: [1,8,6,4,2,9,7,5,3]
Then: [1,6,2,7,3,8,4,9,5]
And finally: [1,2,3,4,5,6,7,8,9]
, which is an ordered list, so we're done unshuffling.
We unshuffled the original [1,3,5,7,9,2,4,6,8]
five times to get to [1,2,3,4,5,6,7,8,9]
, so the output is 5
in this case.
General rules:
- This is code-golf, so shortest answer in bytes wins.
Don't let code-golf languages discourage you from posting answers with non-codegolfing languages. Try to come up with an as short as possible answer for 'any' programming language. - Standard rules apply for your answer with default I/O rules, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs. Your call.
- Default Loopholes are forbidden.
- If possible, please add a link with a test for your code (i.e. TIO).
- Also, adding an explanation for your answer is highly recommended.
Test cases:
Input Output
[1,2,3] 0
[1,2,3,4,5] 0
[1,3,2] 1
[1,6,2,7,3,8,4,9,5,10] 1
[1,3,5,7,2,4,6] 2
[1,8,6,4,2,9,7,5,3,10] 2
[1,9,8,7,6,5,4,3,2,10] 3
[1,5,9,4,8,3,7,2,6,10] 4
[1,3,5,7,9,2,4,6,8] 5
[1,6,11,5,10,4,9,3,8,2,7] 6
[1,10,19,9,18,8,17,7,16,6,15,5,14,4,13,3,12,2,11,20] 10
[1,3,5,7,9,11,13,15,17,19,2,4,6,8,10,12,14,16,18,20] 17
[1,141,32,172,63,203,94,234,125,16,156,47,187,78,218,109,249,140,31,171,62,202,93,233,124,15,155,46,186,77,217,108,248,139,30,170,61,201,92,232,123,14,154,45,185,76,216,107,247,138,29,169,60,200,91,231,122,13,153,44,184,75,215,106,246,137,28,168,59,199,90,230,121,12,152,43,183,74,214,105,245,136,27,167,58,198,89,229,120,11,151,42,182,73,213,104,244,135,26,166,57,197,88,228,119,10,150,41,181,72,212,103,243,134,25,165,56,196,87,227,118,9,149,40,180,71,211,102,242,133,24,164,55,195,86,226,117,8,148,39,179,70,210,101,241,132,23,163,54,194,85,225,116,7,147,38,178,69,209,100,240,131,22,162,53,193,84,224,115,6,146,37,177,68,208,99,239,130,21,161,52,192,83,223,114,5,145,36,176,67,207,98,238,129,20,160,51,191,82,222,113,4,144,35,175,66,206,97,237,128,19,159,50,190,81,221,112,3,143,34,174,65,205,96,236,127,18,158,49,189,80,220,111,2,142,33,173,64,204,95,235,126,17,157,48,188,79,219,110,250]
45
[1,3,5,7,9,2,4,6,8]
is of length 9, but I will add a few more for lengths 7 and 11 perhaps. EDIT: Added the test cases[1,3,5,7,2,4,6] = 2
(length 7) and[1,6,11,5,10,4,9,3,8,2,7] = 6
(length 11). Hope that helps. \$\endgroup\$[1,6,2,7,3,8,4,9,5,10]
or[6,1,7,2,8,3,9,4,10,5]
are possible. In my challenge it does mean that the top card will always remain the top card, so it's indeed a bit of a con-trick.. I've never seen someone irl use only riffle-shuffles to shuffle a deck of cards however. Usually they also use other type of shuffles in between. Anyway, it's too late to change the challenge now, so for the sake of this challenge the top card will always remain the top card after a riffle-shuffle. \$\endgroup\$