Generate sample of 1,000,000 random permutations

Question

I am working with large number of integer permutations. The number of elements in each permutation is K. The element size is 1 byte. I need to generate N unique random permu

Answer 1

I'm a little late, but I think I have a method not shown.

I remembered that their is an algorithm that given the starting order of all K items and an integer index it will generate the index'th permutation of the K items in roughly time proportional to K. Knowing that their K! (factorial) permutations of K items, as long as you can randomly generate an integer between zero and K! you can use the routine to generate N unique random indices in memory then print out the corresponding permutation to disk.

Here is a Python version of the algorithm with N set to 10 and k to 25, although I have used k = 144 successfully:

from math import factorial
from copy import copy
import random

def perm_at_index(items, index):
    '''
    >>> for i in range(10):
            print i, perm_at_index([1,2,3], i)


    0 [1, 2, 3]
    1 [1, 3, 2]
    2 [2, 1, 3]
    3 [2, 3, 1]
    4 [3, 1, 2]
    5 [3, 2, 1]
    6 [1, 2, 3]
    7 [1, 3, 2]
    8 [2, 1, 3]
    9 [2, 3, 1]
    '''

    itms, perm = items[:], []
    itmspop, lenitms, permappend = itms.pop, len(itms), perm.append
    thisfact = factorial(lenitms)
    thisindex = index % thisfact
    while itms:
        thisfact /= lenitms
        thischoice, thisindex = divmod(thisindex, thisfact)
        permappend(itmspop(thischoice))
        lenitms -= 1
    return perm

if __name__ == '__main__':
    N = 10      # Change to 1 million
    k = 25      # Change to 144
    K = ['K%03i' % j for j in range(k)] # ['K000', 'K001', 'K002', 'K003', ...]
    maxperm = factorial(k)              # You need arbitrary length integers for this!
    indices = set(random.randint(0, maxperm) for r in range(N))
    while len(indices) < N:
        indices |= set(random.randint(0, maxperm) for r in range(N - len(indices)))
    for index in indices:
        print (' '.join(perm_at_index(K, index)))

The output of which looks something like this:

K008 K016 K024 K014 K003 K007 K015 K018 K009 K006 K021 K012 K017 K013 K022 K020 K005 K000 K010 K001 K011 K002 K019 K004 K023
K006 K001 K023 K008 K004 K017 K015 K009 K021 K020 K013 K000 K012 K014 K016 K002 K022 K007 K005 K018 K010 K019 K011 K003 K024
K004 K017 K008 K002 K009 K020 K001 K019 K018 K013 K000 K005 K023 K014 K021 K015 K010 K012 K016 K003 K024 K022 K011 K006 K007
K023 K013 K016 K022 K014 K024 K011 K019 K001 K004 K010 K017 K018 K002 K000 K008 K006 K009 K003 K021 K005 K020 K012 K015 K007
K007 K001 K013 K003 K023 K022 K016 K017 K014 K018 K020 K015 K006 K004 K011 K009 K000 K012 K002 K024 K008 K021 K005 K010 K019
K002 K023 K004 K005 K024 K001 K006 K007 K014 K021 K015 K012 K022 K013 K020 K011 K008 K003 K017 K016 K019 K010 K009 K000 K018
K001 K004 K007 K024 K011 K022 K017 K023 K002 K003 K006 K021 K010 K014 K013 K020 K012 K016 K019 K000 K015 K008 K018 K009 K005
K009 K003 K010 K008 K020 K024 K007 K018 K023 K013 K001 K019 K006 K002 K016 K000 K004 K017 K014 K011 K022 K021 K012 K005 K015
K006 K009 K018 K010 K015 K016 K011 K008 K001 K013 K003 K004 K002 K005 K022 K020 K021 K017 K000 K019 K024 K012 K023 K014 K007
K017 K006 K010 K015 K018 K004 K000 K022 K024 K020 K014 K001 K023 K016 K005 K011 K002 K007 K009 K013 K019 K012 K021 K003 K008