Day 12: Fix nits, add runtime analysis and follow up link to Python permutations

Author: thatguyintech

day22/README.md

@@ -43,9 +43,23 @@ the permutations, like this:
 [3, 2, 1]
 ```
 
+This solution is `O((spots for the first elem to go in) * (num perms of the remaining list))`
+where `(num perms of the remaining list)` is equal to
+`(spots for the first elem to go in) * (num perms of the remaining list)` recursively.
+So the runtime is `O(n!)`.
+
 ## Code
 
 [Python](permutations.py)
 
 ## Follow up
 
+This procedure has already been implemented in Python's built-in library:
+
+```python
+from itertools import permutations
+
+permutations([1, 2, 3])
+```
+
+https://docs.python.org/2/library/itertools.html#itertools.permutations

day22/permutations.py

@@ -1,20 +1,19 @@
 def permutations(arr):
     allPermutations = list()
 
-    if len(arr) <= 1:
-        return [arr]
+    if len(arr) < 1:
+        return [[]]
     else:
         for i in xrange(len(arr)):
             for permutation in permutations(arr[1:]):
-                # when i is 0, arr[0:1] is at the beginning of this list
                 allPermutations.append(permutation[:i] + arr[0:1] + permutation[i:])
 
-    return sorted(allPermutations)
+    return allPermutations
 
 def main():
     assert permutations([1]) == [[1]]
     assert permutations([1,2]) == [[1, 2], [2, 1]]
-    assert permutations([1,2,3]) == [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
+    assert permutations([1,2,3]) == [[1, 2, 3], [1, 3, 2], [2, 1, 3], [3, 1, 2], [2, 3, 1], [3, 2, 1]]
 
 if __name__ == "__main__":
     main()