Add Binary Search algorithm in Python

python/searching/binary_search.py

@@ -0,0 +1,41 @@
+from typing import List, Optional
+
+def binary_search(arr: List[int], target: int) -> Optional[int]:
+    """
+    Perform binary search on a sorted list of integers.
+
+    Parameters:
+    - arr (List[int]): Sorted list of integers.
+    - target (int): The value to search for.
+
+    Returns:
+    - Optional[int]: Index of target if found, else None.
+    """
+
+    left = 0
+    right = len(arr) - 1
+
+    # Continue searching while the range is valid
+    while left <= right:
+        # Calculate the mid index to avoid integer overflow
+        mid = left + (right - left) // 2
+
+        # Debug: print current search range
+        # print(f"Searching in range [{left}, {right}], mid={mid}")
+
+        # If the middle element is the target, return its index
+        if arr[mid] == target:
+            return mid
+
+        # If the middle element is less than target,
+        # eliminate the left half (including mid)
+        elif arr[mid] < target:
+            left = mid + 1
+
+        # If the middle element is greater than target,
+        # eliminate the right half (including mid)
+        else:
+            right = mid - 1
+
+    # Target was not found in the list
+    return None