binary search algo

def binary_search(arr, target):
    # Set the start and end indices
    start = 0
    end = len(arr) - 1

    # Keep searching until the start index is greater than the end index
    while start <= end:
        # Calculate the middle index
        mid = (start + end) // 2

        # If the middle element is the target value, return its index
        if arr[mid] == target:
            return mid

        # If the middle element is less than the target value, search the right half of the array
        elif arr[mid] < target:
            start = mid + 1

        # If the middle element is greater than the target value, search the left half of the array
        else:
            end = mid - 1

    # If the target value is not found, return -1
    return -1