Python/dynamic_programming/integer_partition.py at master · israelptr/Python · GitHub

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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

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 range(m)] for _ in range(m+1)]

for i in range(m+1):

memo[i][0] = 1

for n in range(m+1):

for k in range(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(input('Enter a number: ').strip())

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.')

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