A recursive insertion sort (#1683)

* A recursive insertion sort

* added doctests and typehints

sorts/recursive_insertion_sort.py

@@ -0,0 +1,72 @@
+"""
+A recursive implementation of the insertion sort algorithm
+"""
+
+from typing import List
+
+def rec_insertion_sort(collection: List, n: int):
+    """
+    Given a collection of numbers and its length, sorts the collections
+    in ascending order
+
+    :param collection: A mutable collection of comparable elements
+    :param n: The length of collections
+
+    >>> col = [1, 2, 1]
+    >>> rec_insertion_sort(col, len(col))
+    >>> print(col)
+    [1, 1, 2]
+
+    >>> col = [2, 1, 0, -1, -2]
+    >>> rec_insertion_sort(col, len(col))
+    >>> print(col)
+    [-2, -1, 0, 1, 2]
+
+    >>> col = [1]
+    >>> rec_insertion_sort(col, len(col))
+    >>> print(col)
+    [1]
+    """
+    #Checks if the entire collection has been sorted
+    if len(collection) <= 1 or n <= 1:
+        return
+
+
+    insert_next(collection, n-1)
+    rec_insertion_sort(collection, n-1)
+
+def insert_next(collection: List, index: int):
+    """
+    Inserts the '(index-1)th' element into place
+
+    >>> col = [3, 2, 4, 2]
+    >>> insert_next(col, 1)
+    >>> print(col)
+    [2, 3, 4, 2]
+
+    >>> col = [3, 2, 3]
+    >>> insert_next(col, 2)
+    >>> print(col)
+    [3, 2, 3]
+
+    >>> col = []
+    >>> insert_next(col, 1)
+    >>> print(col)
+    []
+    """
+    #Checks order between adjacent elements
+    if index >= len(collection) or collection[index - 1] <= collection[index]:
+        return
+
+    #Swaps adjacent elements since they are not in ascending order
+    collection[index - 1], collection[index] = (
+    collection[index], collection[index - 1]
+    )
+
+    insert_next(collection, index + 1)
+
+if __name__ == "__main__":
+    numbers = input("Enter integers seperated by spaces: ")
+    numbers = [int(num) for num in numbers.split()]
+    rec_insertion_sort(numbers, len(numbers))
+    print(numbers)