from typing import List, Optional def binary_search( arr: List[int], target: int ) -> Optional[int]: """ Perform binary search on a sorted array. Args: arr: Sorted list of integers target: Value to search for Returns: Index of target if found, None otherwise Raises: TypeError: If inputs are not of expected types ValueError: If array is empty """ if not isinstance(arr, list): raise TypeError("Expected a list") if not arr: raise ValueError("Array cannot be empty") left, right = 0, len(arr) - 1 while left <= right: mid = (left + right) // 2 if arr[mid] == target: return mid elif arr[mid] < target: left = mid + 1 else: right = mid - 1 return None # Example usage sorted_array = [1, 3, 5, 7, 9, 11, 15, 23] result = binary_search(sorted_array, 7) print(f"Found at index: {result}") # Output: Found at index: 3