Added mergesort like for counting inversions between two arrays

Author: aladdinpersson

Algorithms/other/counting_inversions.py

@@ -0,0 +1,41 @@
+def merge_sort(array):
+    total_inversions = 0
+    if len(array) <= 1:
+        return (array,0)
+
+    midpoint = int(len(array) / 2)
+
+    (left, left_inversions) = merge_sort(array[:midpoint])
+    (right, right_inversions) = merge_sort(array[midpoint:])
+    (merged_array, merge_inversions) = merge_and_count(left, right)
+    
+    return (merged_array, left_inversions + right_inversions + merge_inversions)
+
+def merge_and_count(left, right):
+    count_inversions = 0
+    result = []
+    left_pointer = right_pointer = 0
+    left_len = len(left)
+    right_len = len(right)
+
+    while left_pointer < len(left) and right_pointer < len(right):
+        if left[left_pointer] <= right[right_pointer]:
+            result.append(left[left_pointer])
+            left_pointer += 1
+
+        elif right[right_pointer] < left[left_pointer]:
+            count_inversions += (left_len - left_pointer)
+            result.append(right[right_pointer])
+            right_pointer += 1
+
+    result.extend(left[left_pointer:])
+    result.extend(right[right_pointer:])
+
+    return (result, count_inversions)
+
+if __name__ == "__main__":
+    array = [9, 2, 1, 5, 2, 3, 5, 1, 2, 32, 12, 11]
+    print(array)
+
+    result = merge_sort(array)
+    print(result)