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

Binary search is an efficient algorithm for finding an element in a sorted array. Its principle is to repeatedly divide the search area in half and compare the target value with the middle element.

Main steps:

1. Define initial search boundaries: left and right indices.
2. Find the middle index: mid = (left + right) // 2.
3. Compare the target with the element at mid.
   • If equal, return mid.
   • If the target is less, move the right boundary to mid - 1.
   • If greater, move the left boundary to mid + 1.
4. Repeat steps 2-3 until left exceeds right.

If the element is not found, return -1, for example.

Python example:

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