mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
d96029e13d
* added doctests * added doctests * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Add doctests to integer_partition.py * Update minimum_partition.py --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
62 lines
1.7 KiB
Python
62 lines
1.7 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.
|
|
* https://en.wikipedia.org/wiki/Partition_(number_theory)
|
|
* https://en.wikipedia.org/wiki/Partition_function_(number_theory)
|
|
"""
|
|
|
|
|
|
def partition(m: int) -> int:
|
|
"""
|
|
>>> partition(5)
|
|
7
|
|
>>> partition(7)
|
|
15
|
|
>>> partition(100)
|
|
190569292
|
|
>>> partition(1_000)
|
|
24061467864032622473692149727991
|
|
>>> partition(-7)
|
|
Traceback (most recent call last):
|
|
...
|
|
IndexError: list index out of range
|
|
>>> partition(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
IndexError: list assignment index out of range
|
|
>>> partition(7.8)
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: 'float' object cannot be interpreted as an integer
|
|
"""
|
|
memo: list[list[int]] = [[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.")
|