mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
37 lines
1.0 KiB
Python
37 lines
1.0 KiB
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.")
|