mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 21:41:08 +00:00
e7a59bfff5
* In place of calculating the factorial several times we can run a loop k times to calculate the combination for example: 5 C 3 = 5! / (3! * (5-3)! ) = (5*4*3*2*1)/[(3*2*1)*(2*1)] =(5*4*3)/(3*2*1) so running a loop k times will reduce the time complexity to O(k) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update maths/combinations.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
61 lines
1.4 KiB
Python
61 lines
1.4 KiB
Python
"""
|
|
https://en.wikipedia.org/wiki/Combination
|
|
"""
|
|
|
|
|
|
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")
|
|
res = 1
|
|
for i in range(k):
|
|
res *= n - i
|
|
res //= i + 1
|
|
return res
|
|
|
|
|
|
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.",
|
|
)
|