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* pre-commit: Upgrade psf/black for stable style 2023 Updating https://github.com/psf/black ... updating 22.12.0 -> 23.1.0 for their `2023 stable style`. * https://github.com/psf/black/blob/main/CHANGES.md#2310 > This is the first [psf/black] release of 2023, and following our stability policy, it comes with a number of improvements to our stable style… Also, add https://github.com/tox-dev/pyproject-fmt and https://github.com/abravalheri/validate-pyproject to pre-commit. I only modified `.pre-commit-config.yaml` and all other files were modified by pre-commit.ci and psf/black. * [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>
58 lines
1.4 KiB
Python
58 lines
1.4 KiB
Python
"""
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https://en.wikipedia.org/wiki/Combination
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"""
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from math import factorial
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def combinations(n: int, k: int) -> int:
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"""
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Returns the number of different combinations of k length which can
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be made from n values, where n >= k.
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Examples:
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>>> combinations(10,5)
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252
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>>> combinations(6,3)
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20
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>>> combinations(20,5)
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15504
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>>> combinations(52, 5)
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2598960
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>>> combinations(0, 0)
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1
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>>> combinations(-4, -5)
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...
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Traceback (most recent call last):
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ValueError: Please enter positive integers for n and k where n >= k
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"""
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# If either of the conditions are true, the function is being asked
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# to calculate a factorial of a negative number, which is not possible
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if n < k or k < 0:
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raise ValueError("Please enter positive integers for n and k where n >= k")
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return factorial(n) // (factorial(k) * factorial(n - k))
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if __name__ == "__main__":
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print(
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"The number of five-card hands possible from a standard",
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f"fifty-two card deck is: {combinations(52, 5)}\n",
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)
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print(
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"If a class of 40 students must be arranged into groups of",
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f"4 for group projects, there are {combinations(40, 4)} ways",
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"to arrange them.\n",
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)
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print(
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"If 10 teams are competing in a Formula One race, there",
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f"are {combinations(10, 3)} ways that first, second and",
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"third place can be awarded.",
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)
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