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35 lines
664 B
Python
35 lines
664 B
Python
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from __future__ import print_function
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'''
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Counting Summations
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Problem 76
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It is possible to write five as a sum in exactly six different ways:
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4 + 1
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3 + 2
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3 + 1 + 1
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2 + 2 + 1
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2 + 1 + 1 + 1
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1 + 1 + 1 + 1 + 1
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How many different ways can one hundred be written as a sum of at least two positive integers?
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'''
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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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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:
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memo[n][k] += memo[n-k-1][k]
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return (memo[m][m-1] - 1)
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print(partition(100))
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