An algorithm for randomly generating integer partitions of a particular length, in Python?

Question

I\'ve been using the random_element() function provided by SAGE to generate random integer partitions for a given integer (N) that are a particular

Answer 1

I ran into a similar problem when I was trying to calculate the probability of the strong birthday problem.

First off, the partition function explodes when given only modest amount of numbers. You'll be returning a LOT of information. No matter which method you're using N = 10000 and S = 300 will generate ridiculous amounts of data. It will be slow. Chances are any pure python implementation you use will be equally slow or slower. Look to making a CModule.

If you want to try python the approach I took as a combination of itertools and generators to keep memory usage down. I don't seem to have my code handy anymore, but here's a good impementation:

http://wordaligned.org/articles/partitioning-with-python

EDIT:

Found my code:

def partition(a, b=-1, limit=365):
  if (b == -1):
    b = a
  if (a == 2 or a == 3):
    if (b >= a and limit):
      yield [a]
    else:
      return
  elif (a > 3):
    if (a <= b):
      yield [a]
    c = 0
    if b > a-2:
      c = a-2
    else:
      c = b
    for i in xrange(c, 1, -1):
      if (limit):
        for j in partition(a-i, i, limit-1):
          yield [i] + j