Python/maths/combinations.py
Tianyi Zheng d25187eb7f
Remove type cast in combinations algorithm (#7607)
* Remove commented-out print statements in algorithmic functions

* Encapsulate non-algorithmic code in __main__

* Remove unused print_matrix function

* Remove print statement in __init__

* Remove print statement from doctest

* Encapsulate non-algorithmic code in __main__

* Modify algorithm to return instead of print

* Encapsulate non-algorithmic code in __main__

* Refactor data_safety_checker to return instead of print

* updating DIRECTORY.md

* updating DIRECTORY.md

* Apply suggestions from code review

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* updating DIRECTORY.md

* Remove int cast and change float division to int division

* Move new-line chars

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
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2022-10-25 22:34:46 +02:00

59 lines
1.4 KiB
Python

"""
https://en.wikipedia.org/wiki/Combination
"""
from math import factorial
def combinations(n: int, k: int) -> int:
"""
Returns the number of different combinations of k length which can
be made from n values, where n >= k.
Examples:
>>> combinations(10,5)
252
>>> combinations(6,3)
20
>>> combinations(20,5)
15504
>>> combinations(52, 5)
2598960
>>> combinations(0, 0)
1
>>> combinations(-4, -5)
...
Traceback (most recent call last):
ValueError: Please enter positive integers for n and k where n >= k
"""
# If either of the conditions are true, the function is being asked
# to calculate a factorial of a negative number, which is not possible
if n < k or k < 0:
raise ValueError("Please enter positive integers for n and k where n >= k")
return factorial(n) // (factorial(k) * factorial(n - k))
if __name__ == "__main__":
print(
"The number of five-card hands possible from a standard",
f"fifty-two card deck is: {combinations(52, 5)}\n",
)
print(
"If a class of 40 students must be arranged into groups of",
f"4 for group projects, there are {combinations(40, 4)} ways",
"to arrange them.\n",
)
print(
"If 10 teams are competing in a Formula One race, there",
f"are {combinations(10, 3)} ways that first, second and",
"third place can be awarded.",
)