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* Create ncr_combinations.py * Update ncr_combinations.py * Update ncr_combinations.py * Update ncr_combinations.py * Update ncr_combinations.py * updating DIRECTORY.md --------- Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: cclauss <cclauss@users.noreply.github.com>
78 lines
1.8 KiB
Python
78 lines
1.8 KiB
Python
"""
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Generalized combinations (n choose r) calculator for real total and integer choose.
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Wikipedia URL:
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https://en.wikipedia.org/wiki/Binomial_coefficient
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"""
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from math import factorial as math_factorial
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def combinations(total: float, choose: int) -> float:
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"""
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Compute the number of combinations using the formula:
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combinations = total * (total-1) * ... * (total-choose+1) / choose!
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Parameters
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----------
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total : float
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Total number of items. Can be any real number.
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choose : int
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Number of items to select. Must be a non-negative integer.
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Returns
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-------
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float
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The number of combinations.
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Raises
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------
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ValueError
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If choose is not a non-negative integer.
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Examples
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--------
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>>> combinations(5, 2)
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10.0
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>>> combinations(5.5, 2)
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12.375
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>>> combinations(10, 0)
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1.0
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>>> combinations(0, 0)
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1.0
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>>> combinations(5, -1)
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Traceback (most recent call last):
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...
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ValueError: choose must be a non-negative integer
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>>> combinations(5, 2.5)
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Traceback (most recent call last):
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...
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ValueError: choose must be a non-negative integer
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"""
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if not isinstance(choose, int) or choose < 0:
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raise ValueError("choose must be a non-negative integer")
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if choose == 0:
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return 1.0
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numerator = 1.0
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for i in range(choose):
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numerator *= total - i
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denominator = math_factorial(choose)
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return numerator / denominator
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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# Example usage
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total_input = float(input("Enter total (real number): ").strip() or 0)
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choose_input = int(input("Enter choose (non-negative integer): ").strip() or 0)
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print(
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f"combinations({total_input}, {choose_input}) = "
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f"{combinations(total_input, choose_input)}"
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)
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