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* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
41 lines
1.1 KiB
Python
41 lines
1.1 KiB
Python
def kth_permutation(k, n):
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"""
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Finds k'th lexicographic permutation (in increasing order) of
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0,1,2,...n-1 in O(n^2) time.
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Examples:
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First permutation is always 0,1,2,...n
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>>> kth_permutation(0,5)
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[0, 1, 2, 3, 4]
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The order of permutation of 0,1,2,3 is [0,1,2,3], [0,1,3,2], [0,2,1,3],
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[0,2,3,1], [0,3,1,2], [0,3,2,1], [1,0,2,3], [1,0,3,2], [1,2,0,3],
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[1,2,3,0], [1,3,0,2]
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>>> kth_permutation(10,4)
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[1, 3, 0, 2]
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"""
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# Factorails from 1! to (n-1)!
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factorials = [1]
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for i in range(2, n):
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factorials.append(factorials[-1] * i)
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assert 0 <= k < factorials[-1] * n, "k out of bounds"
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permutation = []
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elements = list(range(n))
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# Find permutation
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while factorials:
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factorial = factorials.pop()
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number, k = divmod(k, factorial)
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permutation.append(elements[number])
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elements.remove(elements[number])
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permutation.append(elements[0])
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return permutation
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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