How does a binary search algorithm work and what is its time complexity?

How Does Binary Search Algorithm Work and What is Its Time Complexity?

In computer science, the binary search algorithm is a method for finding the position of a specific value within a sorted array. The basic idea behind the binary search algorithm is to repeatedly divide the search interval in half until the target value is found or the interval is empty.

How Binary Search Algorithm Works:

1. Compare the target value with the middle element of the array.
2. If the target value is equal to the middle element, the search is successful.
3. If the target value is less than the middle element, continue the search on the left subarray.
4. If the target value is greater than the middle element, continue the search on the right subarray.
5. Repeat the process until the target value is found or the interval is empty.

Time Complexity of Binary Search Algorithm:

The time complexity of the binary search algorithm is O(log n), where n is the number of elements in the array. This is because in each step of the algorithm, the size of the search interval is cut in half. As a result, the binary search algorithm has significantly better performance compared to linear search, which has a time complexity of O(n).