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