Python/dynamic_programming/integer_partition.py
Christian Clauss 47a9ea2b0b
Simplify code by dropping support for legacy Python (#1143)
* Simplify code by dropping support for legacy Python

* sort() --> sorted()
2019-08-19 15:37:49 +02:00

33 lines
900 B
Python

'''
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.')