Add Meta Binary Search algorithm

searches/meta_binary_search.py

@@ -0,0 +1,74 @@
+"""
+Meta Binary Search (One-Sided Binary Search)
+
+Meta Binary Search is a variation of binary search that uses
+bit manipulation to determine the index of the target element
+in a sorted array. Instead of repeatedly dividing the search
+space like traditional binary search, it constructs the index
+bit by bit from the most significant bit to the least.
+
+Time Complexity: O(log n)
+Space Complexity: O(1)
+
+Reference:
+https://www.geeksforgeeks.org/meta-binary-search-one-sided-binary-search/
+"""
+
+
+def meta_binary_search(arr: list[int], target: int) -> int:
+    """
+    Perform Meta Binary Search on a sorted list.
+
+    The algorithm determines the index by checking bits from
+    the most significant bit down to the least significant bit.
+
+    Parameters
+    ----------
+    arr : list[int]
+        A sorted list of integers where the search will be performed.
+    target : int
+        The element to search for.
+
+    Returns
+    -------
+    int
+        Index of the target element if found, otherwise -1.
+
+    Examples
+    --------
+    >>> meta_binary_search([2, 4, 6, 8, 10], 6)
+    2
+    >>> meta_binary_search([2, 4, 6, 8, 10], 7)
+    -1
+    >>> meta_binary_search([], 5)
+    -1
+    """
+
+    n = len(arr)
+    if n == 0:
+        return -1
+
+    # Step 1: Find the Most Significant Bit position
+    max_idx = n - 1
+    msb_pos = 0 if max_idx == 0 else max_idx.bit_length() - 1
+
+    idx = 0  # Initialize index before using it!
+
+    # Step 2: Iterate from MSB down to LSB
+    for i in range(msb_pos, -1, -1):
+        new_idx = idx | (1 << i)
+
+        if new_idx < n and arr[new_idx] <= target:
+            idx = new_idx
+
+    # Step 3: Final verification
+    if idx < n and arr[idx] == target:
+        return idx
+    return -1
+
+
+if __name__ == "__main__":
+    example_array = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
+
+    print(meta_binary_search(example_array, 14))  # Expected output: 6
+    print(meta_binary_search(example_array, 5))  # Expected output: -1