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maths/combinations.py
60 строк
1 KB
SubhranShu2332
In place of calculating the factorial several times we can run a loop k times to calculate the combination (#10051)
08 окт 2023, 22:17
Не верифицирован
08 окт 2023, 22:17
e7a59bf
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""" 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.", )