Adding Binary Search Algo Based on 2D Arrays

sorts/binarysearch_on_sorted_2d_array.py

@@ -0,0 +1,72 @@
+#!/usr/bin/env python3
+
+
+def binary_search_2d(matrix: list[list[int]], target: int) -> tuple[int, int]:
+    """
+    Searches for a target value in a 2D sorted array.
+
+    The matrix is sorted such that each row is in ascending order, and the
+    first element of each row is greater than the last element of the previous row.
+
+    Args:
+        matrix: A 2D list of integers sorted in ascending order.
+        target: The integer value to search for.
+
+    Returns:
+        A tuple (row_index, col_index) if found, otherwise (-1, -1).
+
+    Raises:
+        ValueError: If matrix is empty or not rectangular.
+
+    >>> binary_search_2d([[1, 3, 5], [7, 9, 11], [12, 13, 15]], 9)
+    (1, 1)
+    >>> binary_search_2d([[1, 3, 5], [7, 9, 11], [12, 13, 15]], 4)
+    (-1, -1)
+    >>> binary_search_2d([], 1)  # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+        ...
+    ValueError: matrix must not be empty
+    >>> binary_search_2d([[1, 2], [3, 4, 5]], 3)  # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+        ...
+    ValueError: matrix must be rectangular
+    """
+    if not matrix or not matrix[0]:
+        raise ValueError("matrix must not be empty")
+
+    rows = len(matrix)
+    cols = len(matrix[0])
+
+    for row in matrix:
+        if len(row) != cols:
+            raise ValueError("matrix must be rectangular")
+
+    left, right = 0, rows * cols - 1
+
+    while left <= right:
+        mid = left + (right - left) // 2
+        mid_value = matrix[mid // cols][mid % cols]
+
+        if mid_value == target:
+            return mid // cols, mid % cols
+        elif mid_value < target:
+            left = mid + 1
+        else:
+            right = mid - 1
+
+    return -1, -1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Example usage
+    matrix = [[1, 3, 5], [7, 9, 11], [12, 13, 15]]
+    target = 9
+    result = binary_search_2d(matrix, target)
+    if result == (-1, -1):
+        print(f"{target} was not found in the matrix.")
+    else:
+        print(f"{target} was found at position {result} in the matrix.")