diff --git a/maths/kth_lexicographic_permutation.py b/maths/kth_lexicographic_permutation.py new file mode 100644 index 000000000..1820be727 --- /dev/null +++ b/maths/kth_lexicographic_permutation.py @@ -0,0 +1,40 @@ +def kthPermutation(k, n): + """ + Finds k'th lexicographic permutation (in increasing order) of + 0,1,2,...n-1 in O(n^2) time. + + Examples: + First permutation is always 0,1,2,...n + >>> kthPermutation(0,5) + [0, 1, 2, 3, 4] + + The order of permutation of 0,1,2,3 is [0,1,2,3], [0,1,3,2], [0,2,1,3], + [0,2,3,1], [0,3,1,2], [0,3,2,1], [1,0,2,3], [1,0,3,2], [1,2,0,3], + [1,2,3,0], [1,3,0,2] + >>> kthPermutation(10,4) + [1, 3, 0, 2] + """ + # Factorails from 1! to (n-1)! + factorials = [1] + for i in range(2, n): + factorials.append(factorials[-1] * i) + assert 0 <= k < factorials[-1] * n, "k out of bounds" + + permutation = [] + elements = list(range(n)) + + # Find permutation + while factorials: + factorial = factorials.pop() + number, k = divmod(k, factorial) + permutation.append(elements[number]) + elements.remove(elements[number]) + permutation.append(elements[0]) + + return permutation + + +if __name__ == "__main__": + import doctest + + doctest.testmod()