mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
4d0a8f2355
* optimized recursive_bubble_sort
* Fixed doctest error due whitespace
* reduce loop times for optimization
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
41 lines
1.1 KiB
Python
41 lines
1.1 KiB
Python
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()
|