Randomize a List problem

[Albert Chan]

(09-18-2020 03:31 PM)John Keith Wrote:  In most test runs that I did the 2nd permutation was most common, and
the last permutation returned by the program was the least common.

Least common permutations are permutations that RANL *never* produced.
For n-items list, RANL does n! ways, ideal probability of each permutations is 1/n!

Example {1,2,3,4}, out of 4! = 24 ways, RANL produced:
(Out of 24, frequencies of all 1's is ideal, P = 1/24 ≈ 4.17%)

Code:

Pat  Freq
1234    4
1243    4
1324    3
1342    2
1423    3
1432    2
3124    2
3142    1
4123    2
4132    1

RANL generated g = 10 permutations. Missing permutations = 4! - 10 = 14, all having P = 0%
Trivia: 1 cannot be shuffled beyond its neighbors. Those accounted for 12 missing permutations.

Here are RANL missing permutations percentages, for n-items list (smaller is better)

Code:

n    g   missing permutations = 1 - g/n!
3    4   33.33%
4   10   58.33%
5   28   76.67%
6   80   88.89%
7  274   94.56%
8  898   97.77%