Add a recursive merge sort algorithm that accepts an array as input. (#4462)

This is a different recursive implementation of the merge sort algorithm.

* Recursive Merge Sort That Accepts an Array 

Recursive Merge Sort That Accepts an Array

* Add Wikipedia Link

* Fixes naming conventions

* Update sorts/recursive_mergesort_array.py

Co-authored-by: Maxim R. <49735721+mrmaxguns@users.noreply.github.com>

* Update sorts/recursive_mergesort_array.py

Co-authored-by: Maxim R. <49735721+mrmaxguns@users.noreply.github.com>

* Update sorts/recursive_mergesort_array.py

Co-authored-by: Maxim R. <49735721+mrmaxguns@users.noreply.github.com>

* Update sorts/recursive_mergesort_array.py

Co-authored-by: Maxim R. <49735721+mrmaxguns@users.noreply.github.com>

* Update sorts/recursive_mergesort_array.py

Co-authored-by: Maxim R. <49735721+mrmaxguns@users.noreply.github.com>

* Adds black format

* Removes unused variables

* Fixes variable names and adds documentation

* Fixes variable names to use snake_case.

* Removes double #.

* Update sorts/recursive_mergesort_array.py

Co-authored-by: Maxim R. <49735721+mrmaxguns@users.noreply.github.com>

Co-authored-by: Maxim R. <49735721+mrmaxguns@users.noreply.github.com>
Co-authored-by: Benjamin Fein <benfein78@icloud.com>

sorts/recursive_mergesort_array.py

@@ -0,0 +1,64 @@
+"""A merge sort which accepts an array as input and recursively
+splits an array in half and sorts and combines them.
+"""
+
+"""https://en.wikipedia.org/wiki/Merge_sort """
+
+
+def merge(arr: list[int]) -> list[int]:
+    """Return a sorted array.
+    >>> merge([10,9,8,7,6,5,4,3,2,1])
+    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+    >>> merge([1,2,3,4,5,6,7,8,9,10])
+    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+    >>> merge([10,22,1,2,3,9,15,23])
+    [1, 2, 3, 9, 10, 15, 22, 23]
+    >>> merge([100])
+    [100]
+    >>> merge([])
+    []
+    """
+    if len(arr) > 1:
+        middle_length = len(arr) // 2  # Finds the middle of the array
+        left_array = arr[
+            :middle_length
+        ]  # Creates an array of the elements in the first half.
+        right_array = arr[
+            middle_length:
+        ]  # Creates an array of the elements in the second half.
+        left_size = len(left_array)
+        right_size = len(right_array)
+        merge(left_array)  # Starts sorting the left.
+        merge(right_array)  # Starts sorting the right
+        left_index = 0  # Left Counter
+        right_index = 0  # Right Counter
+        index = 0  # Position Counter
+        while (
+            left_index < left_size and right_index < right_size
+        ):  # Runs until the lowers size of the left and right are sorted.
+            if left_array[left_index] < right_array[right_index]:
+                arr[index] = left_array[left_index]
+                left_index = left_index + 1
+            else:
+                arr[index] = right_array[right_index]
+                right_index = right_index + 1
+            index = index + 1
+        while (
+            left_index < left_size
+        ):  # Adds the left over elements in the left half of the array
+            arr[index] = left_array[left_index]
+            left_index = left_index + 1
+            index = index + 1
+        while (
+            right_index < right_size
+        ):  # Adds the left over elements in the right half of the array
+            arr[index] = right_array[right_index]
+            right_index = right_index + 1
+            index = index + 1
+    return arr
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()