Generating all tuples (Python)

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This is a simple example of the tuples generation algorithm, written in Python.

see The Art of Computer Programming (TAOCP) Volume 4 Fascicle 2, Generating All Tuples and Permutations (2005), ISBN 0-201-85393-0

Algorithm M

The generation function is genTuplesM as below:

  • Input parameter: we list the limits on each bit into a list as an input
  • Output: generating all possible tuples
def genTuplesM(lst):
  return reduce(lambda prev, b: [xs + [i] for xs in prev for i in range(1,b+1)], lst, [[]])

Alternatively, using product() in Python 2.6 and later:

import itertools
def genTuplesM(lst):
  return itertools.product(*[range(1,b+1) for b in lst]) # returns an iterator


Just load the file in Python, execute it and you will get the result.

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