Add Kth lexicographic permutation

maths/kth_lexicographic_permutation.py

@@ -0,0 +1,44 @@
+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 and k < factorials[-1] * n
+    ), "k out of bounds"
+
+    permutation = []
+    elements = list(range(n))
+
+    # Find permutation
+    while factorials:
+        factorial = factorials.pop()
+        number = k // factorial
+        permutation.append(elements[number])
+        elements.remove(elements[number])
+        k = k % factorial
+    permutation.append(elements[0])
+
+    return permutation
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+