Fix kth lexicographic permutation

maths/kth_lexicographic_permutation.py

@@ -1,10 +1,10 @@
 def kth_permutation(k, n):
     """
     Finds k'th lexicographic permutation (in increasing order) of
-    0,1,2,...n-1 in O(n^2) time.
+    0,1,2,...,n-1 in O(n^2) time.
 
     Examples:
-    First permutation is always 0,1,2,...n
+    First permutation is always 0,1,2,...,n-1
     >>> kth_permutation(0,5)
     [0, 1, 2, 3, 4]
 
@@ -14,23 +14,32 @@ def kth_permutation(k, n):
     >>> kth_permutation(10,4)
     [1, 3, 0, 2]
     """
-    # Factorails from 1! to (n-1)!
+    # Factorials from 1! to (n-1)!
+    if not isinstance(k, int) or not isinstance(n, int):
+        raise TypeError("k and n must be integers")
+
+    if n < 1:
+        raise ValueError("n must be a positive integer")
+
     factorials = [1]
     for i in range(2, n):
         factorials.append(factorials[-1] * i)
-    assert 0 <= k < factorials[-1] * n, "k out of bounds"
+
+    max_k = factorials[-1] * n  # equals n!
+    if not (0 <= k < max_k):
+        raise ValueError("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])
+        index, k = divmod(k, factorial)
+        permutation.append(elements[index])
+        elements.pop(index)
 
+    permutation.append(elements[0])
     return permutation