Binary search is an advanced version of a linear search algorithm. Binary search provides an optimum solution to search for an element.

The list of values have to be arranged in ascending or descending order before applying the Binary search logic. Use Selection sort logic for the sorting.

Selection sort is a sorting algorithm that treats the input as two parts, a sorted part and an unsorted part, and repeatedly selects the proper next value to move from the unsorted part to the end of the sorted part.

Selection sort logic:

The index variable i denotes the dividing point. Elements to the left of i are sorted, and elements including and to the right of i are unsorted. All elements in the unsorted part are searched to find the index of the element with the smallest value. The variable indexSmallest stores the index of the smallest element in the unsorted part. Once the element with the smallest value is found, that element is swapped with the element at location i$.$ Then, the index i is advanced one place to the right, and the process repeats.

Binary search logic:

Let's consider our list has below sorted values and we want to search for an element $45.$

$\{23,45,67,87,98\}$

Get the center element from the array and in this case it is $67.$

Compare the center element with the key element i$.$e$.$; in this case compare $67$ with $45.$

Since the center element is greater than the key element, we're sure that the key element is in the first half of the list of elements because the array has already been sorted.

If the center element is less than the key element, the element is in the second half of the list of elements.

Consider the list of values as either first half or second half and repeat the above steps until the element is found or the entire array of elements is checked.

Sample input and output:Selection Sort Pseudocode:Binary search pseudocode:Write a Java program that implements the selection sort and binary search algorithms. It needs to accept input of greater than $5$ numbers $($any order$),$ sort the numbers, then ask for a key that will be searched via Binary search. If it finds the key, it will display the index in the array and how many binary search rounds it took to complete.