What happens if you try to add an element to a Map that has not been created or initialized?

Binary search is an algorithm for finding an element in a sorted array. The principle:

1. Determine the middle element of the array.
2. If the sought element equals the middle, the search is complete.
3. If the sought element is less than the middle, continue in the left half.
4. If greater, in the right half.
5. Repeat the process recursively or iteratively until the element is found or no elements remain.

Example in Python:

def binary_search(arr, target):
    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 -1
# Usage
arr = [1, 3, 5, 7, 9]
print(binary_search(arr, 5))  # Outputs index 2

Binary search is efficient because it halves the search area at each step, providing a complexity of O(log n).