From 47d17951b830f23fe7cddffa9c24431c29cfea74 Mon Sep 17 00:00:00 2001
From: Kiril Bangachev <51961981+KirilBangachev@users.noreply.github.com>
Date: Fri, 13 Sep 2019 07:13:55 -0400
Subject: [PATCH] Add Kth lexicographic permutation (#1179)

* Add Kth lexicographic permutation

Function that computes the kth lexicographic permtation of 0,1,2,...,n-1 in O(n^2) time

* Update kth_lexicographic_permutation.py

Addressed requested changes
---
 maths/kth_lexicographic_permutation.py | 40 ++++++++++++++++++++++++++
 1 file changed, 40 insertions(+)
 create mode 100644 maths/kth_lexicographic_permutation.py

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()