Explain the working principle of the binary search algorithm and its main stages.

The binary search algorithm is used to find an element in a sorted array. Its principle is based on repeatedly dividing the search area in half and comparing the target value with the middle element of the current range.

Main stages:

1. Define the initial range — usually the entire array (left and right boundaries).
2. Find the index of the middle element of the range.
3. Compare the target value with the middle element:
   • If they are equal, return the index of the found element.
   • If the target is less, narrow the search to the left half (move the right boundary).
   • If greater, narrow to the right half (move the left boundary).
4. Repeat steps 2-3 until the range becomes empty.

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  # element not found