Explain the binary search algorithm.

The binary search algorithm is a search algorithm used to find a specific element in a sorted array or list. It works by repeatedly dividing the search space in half until the target element is found or the search space is empty.

Here is the step-by-step process of the binary search algorithm:

1. Start with defining the lower and upper bounds of the search space, which are initially set to the first and last indices of the array, respectively.

2. Calculate the middle index of the search space by taking the average of the lower and upper bounds.

3. Compare the middle element with the target element:
- If the middle element is equal to the target element, the search is successful, and the index of the target element is returned.
- If the middle element is greater than the target element, update the upper bound to be the middle index minus one, and go back to step 2.
- If the middle element is less than the target element, update the lower bound to be the middle index plus one, and go back to step 2.

4. Repeat steps 2 and 3 until the target element is found or the lower bound becomes greater than the upper bound, indicating that the target element is not present in the array.

The binary search algorithm has a time complexity of O(log n), where n is the number of elements in the array. This makes it significantly more efficient than linear search algorithms for large arrays.