To APPLY binary search on a list of elements, the PREREQUISITE is that the list of elements should be sorted. It is based on the Divide and Conquers Algorithmic paradigm. In the Binary Search Algorithm, we divide the search interval in half periodically to search the sorted list. We begin by creating an interval that spans the entire list. If the search key's value is less than the item in the interval's midpoint, the interval should be narrowed to the lower half. Otherwise, we limit it to the upper half of the page. We check for the value until it is discovered or the interval is empty. Given below is an algorithm describing Binary Search: (Let us assume that the element to be searched is x and the array of elements is sorted in ascending order)

• Step 1: x should be firstly compared to the middle element.
• Step 2: We return the middle element's index if x matches the middle element.
• Step 3: Else If x is greater than the middle element, x can only be found after the middle element in the right half subarray since the array is sorted in the ascending order. As a result, we repeat the process for the right half.
• Step 4: Otherwise, we repeat for the left half (x is SMALLER).
• Step 5: If the interval is empty, we terminate the binary search.

The time complexity of the Binary Search Algorithm is O(log(n)) where n is the size of the list of elements and its space complexity is constant, that is, O(1).