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8f81c460fe
* Made improvements to combinations.py * Update maths/combinations.py Co-authored-by: Du Yuanchao <shellhub.me@gmail.com> * Function now raises an error when given invalid input * Update maths/combinations.py Co-authored-by: Du Yuanchao <shellhub.me@gmail.com>
59 lines
1.4 KiB
Python
59 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 int(factorial(n) / ((factorial(k)) * (factorial(n - k))))
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if __name__ == "__main__":
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print(
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"\nThe number of five-card hands possible from a standard",
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f"fifty-two card deck is: {combinations(52, 5)}",
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)
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print(
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"\nIf 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.\n",
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)
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