mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
e3fa014a5a
* updating DIRECTORY.md
* Fix ruff
* Fix
* Fix
* Fix
* Revert "Fix"
This reverts commit 5bc3bf3422.
* find_max.py: noqa: PLR1730
---------
Co-authored-by: MaximSmolskiy <MaximSmolskiy@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
78 lines
2.0 KiB
Python
78 lines
2.0 KiB
Python
"""
|
|
Bell numbers represent the number of ways to partition a set into non-empty
|
|
subsets. This module provides functions to calculate Bell numbers for sets of
|
|
integers. In other words, the first (n + 1) Bell numbers.
|
|
|
|
For more information about Bell numbers, refer to:
|
|
https://en.wikipedia.org/wiki/Bell_number
|
|
"""
|
|
|
|
|
|
def bell_numbers(max_set_length: int) -> list[int]:
|
|
"""
|
|
Calculate Bell numbers for the sets of lengths from 0 to max_set_length.
|
|
In other words, calculate first (max_set_length + 1) Bell numbers.
|
|
|
|
Args:
|
|
max_set_length (int): The maximum length of the sets for which
|
|
Bell numbers are calculated.
|
|
|
|
Returns:
|
|
list: A list of Bell numbers for sets of lengths from 0 to max_set_length.
|
|
|
|
Examples:
|
|
>>> bell_numbers(0)
|
|
[1]
|
|
>>> bell_numbers(1)
|
|
[1, 1]
|
|
>>> bell_numbers(5)
|
|
[1, 1, 2, 5, 15, 52]
|
|
"""
|
|
if max_set_length < 0:
|
|
raise ValueError("max_set_length must be non-negative")
|
|
|
|
bell = [0] * (max_set_length + 1)
|
|
bell[0] = 1
|
|
|
|
for i in range(1, max_set_length + 1):
|
|
for j in range(i):
|
|
bell[i] += _binomial_coefficient(i - 1, j) * bell[j]
|
|
|
|
return bell
|
|
|
|
|
|
def _binomial_coefficient(total_elements: int, elements_to_choose: int) -> int:
|
|
"""
|
|
Calculate the binomial coefficient C(total_elements, elements_to_choose)
|
|
|
|
Args:
|
|
total_elements (int): The total number of elements.
|
|
elements_to_choose (int): The number of elements to choose.
|
|
|
|
Returns:
|
|
int: The binomial coefficient C(total_elements, elements_to_choose).
|
|
|
|
Examples:
|
|
>>> _binomial_coefficient(5, 2)
|
|
10
|
|
>>> _binomial_coefficient(6, 3)
|
|
20
|
|
"""
|
|
if elements_to_choose in {0, total_elements}:
|
|
return 1
|
|
|
|
elements_to_choose = min(elements_to_choose, total_elements - elements_to_choose)
|
|
|
|
coefficient = 1
|
|
for i in range(elements_to_choose):
|
|
coefficient *= total_elements - i
|
|
coefficient //= i + 1
|
|
|
|
return coefficient
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|