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* Add Catalan number to maths * updating DIRECTORY.md * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
52 lines
1.1 KiB
Python
52 lines
1.1 KiB
Python
"""
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Calculate the nth Catalan number
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Source:
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https://en.wikipedia.org/wiki/Catalan_number
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"""
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def catalan(number: int) -> int:
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"""
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:param number: nth catalan number to calculate
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:return: the nth catalan number
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Note: A catalan number is only defined for positive integers
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>>> catalan(5)
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14
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>>> catalan(0)
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Traceback (most recent call last):
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...
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ValueError: Input value of [number=0] must be > 0
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>>> catalan(-1)
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Traceback (most recent call last):
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...
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ValueError: Input value of [number=-1] must be > 0
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>>> catalan(5.0)
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Traceback (most recent call last):
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...
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TypeError: Input value of [number=5.0] must be an integer
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"""
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if not isinstance(number, int):
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raise TypeError(f"Input value of [number={number}] must be an integer")
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if number < 1:
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raise ValueError(f"Input value of [number={number}] must be > 0")
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current_number = 1
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for i in range(1, number):
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current_number *= 4 * i - 2
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current_number //= i + 1
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return current_number
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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