Implement recursive binary search in Python

DIRECTORY.md

@@ -1323,6 +1323,7 @@
 
 ## [Searches](searches)
   * [Binary Search](searches/binary_search.py)
+  * [Binary Search Recursion](searches/binary_search_recursion.py)
   * [Binary Tree Traversal](searches/binary_tree_traversal.py)
   * [Double Linear Search](searches/double_linear_search.py)
   * [Double Linear Search Recursion](searches/double_linear_search_recursion.py)

searches/binary_search_recursion.py

@@ -0,0 +1,62 @@
+"""
+Pure Python implementation of Recursive Binary Search.
+
+Binary Search is a divide-and-conquer algorithm that works on sorted lists.
+"""
+
+from __future__ import annotations
+
+from collections.abc import Sequence
+from typing import TypeVar
+
+T = TypeVar("T")
+
+
+def binary_search_recursive(
+    arr: Sequence[T],
+    target: T,
+    left: int = 0,
+    right: int | None = None,
+) -> int:
+    """
+    Perform recursive binary search on a sorted sequence.
+
+    :param arr: A sorted sequence of comparable elements
+    :param target: The element to search for
+    :param left: Left boundary of the search interval
+    :param right: Right boundary of the search interval
+    :return: Index of target if found, otherwise -1
+
+    >>> binary_search_recursive([1, 2, 3, 4, 5], 3)
+    2
+    >>> binary_search_recursive([1, 2, 3, 4, 5], 1)
+    0
+    >>> binary_search_recursive([1, 2, 3, 4, 5], 5)
+    4
+    >>> binary_search_recursive([1, 2, 3, 4, 5], 6)
+    -1
+    >>> binary_search_recursive([], 10)
+    -1
+    >>> binary_search_recursive([2, 4, 6, 8], 6)
+    2
+    """
+
+    if right is None:
+        right = len(arr) - 1
+
+    if left > right:
+        return -1
+
+    mid = left + (right - left) // 2
+
+    if arr[mid] == target:
+        return mid
+    if arr[mid] > target:
+        return binary_search_recursive(arr, target, left, mid - 1)
+    return binary_search_recursive(arr, target, mid + 1, right)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()