From 2a8185f159222a31fb66baa220bc6f0c321444b3 Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Mon, 12 Apr 2021 12:03:47 +0200
Subject: [PATCH] Add Python doctests to count-inversions.py (#159)

* Add Python doctests to count-inversions.py

These [doctests](https://docs.python.org/3/library/doctest.html) can be run with `python3 -m doctest -v count-inversions.py`

Our GitHub Actions will also run these doctests.  https://github.com/MakeContributions/DSA/actions

The answer to the last test should be 0, not 2.

@atin Your review please.

* Avoid unnecessary inversions
---
 arrays/python/count-inversions.py | 25 ++++++++++++++++++++-----
 1 file changed, 20 insertions(+), 5 deletions(-)

diff --git a/arrays/python/count-inversions.py b/arrays/python/count-inversions.py
index 16190435..2bbbc5bd 100644
--- a/arrays/python/count-inversions.py
+++ b/arrays/python/count-inversions.py
@@ -2,6 +2,8 @@
 Algorithm Type: Divide & Conquer
 Time Complexity: O(n*log(n))
 """
+numbers = [8, 2, 1, 5, 7, 3, 9, 2, 0, 1]
+
 
 def count_split_inv(arr, left, right):
   split_inv = ridx = lidx = 0
@@ -10,7 +12,7 @@ def count_split_inv(arr, left, right):
   rsize = len(right)
   for i in range(size):
     if lidx != lsize and ridx != rsize:
-      if right[ridx] <= left[lidx]:
+      if right[ridx] < left[lidx]:
         arr[i] = right[ridx]
         ridx += 1
         split_inv += lsize - lidx
@@ -23,9 +25,22 @@ def count_split_inv(arr, left, right):
     elif ridx == rsize:
       arr[i] = left[lidx]
       lidx += 1
-  return split_inv;
+  return split_inv
 
-def count_inversions(arr):
+
+def count_inversions(arr) -> int:
+  """
+  Sort arr and return the number of inversions required.
+
+  >>> numbers
+  [8, 2, 1, 5, 7, 3, 9, 2, 0, 1]
+  >>> count_inversions(numbers)
+  28
+  >>> numbers  # numbers has been sorted!!
+  [0, 1, 1, 2, 2, 3, 5, 7, 8, 9]
+  >>> count_inversions(numbers)
+  0
+  """
   size = len(arr)
   if size == 1:
     return 0
@@ -38,5 +53,5 @@ def count_inversions(arr):
 
   return l_inv + r_inv + split_inv
 
-numbers = [8, 2, 1, 5, 7, 3, 9, 2, 0, 1]
-print(count_inversions(numbers))
+if __name__ == "__main__":
+  print(count_inversions(numbers))