from __future__ import print_function try: xrange #Python 2 except NameError: xrange = range #Python 3 try: raw_input #Python 2 except NameError: raw_input = input #Python 3 ''' The number of partitions of a number n into at least k parts equals the number of partitions into exactly k parts plus the number of partitions into at least k-1 parts. Subtracting 1 from each part of a partition of n into k parts gives a partition of n-k into k parts. These two facts together are used for this algorithm. ''' def partition(m): memo = [[0 for _ in xrange(m)] for _ in xrange(m+1)] for i in xrange(m+1): memo[i][0] = 1 for n in xrange(m+1): for k in xrange(1, m): memo[n][k] += memo[n][k-1] if n-k > 0: memo[n][k] += memo[n-k-1][k] return memo[m][m-1] if __name__ == '__main__': import sys if len(sys.argv) == 1: try: n = int(raw_input('Enter a number: ')) print(partition(n)) except ValueError: print('Please enter a number.') else: try: n = int(sys.argv[1]) print(partition(n)) except ValueError: print('Please pass a number.')