Algorithm for Random Elements Input: a group G given by a set of generators S; Output: a sequence of pseudo-random elements of G;

Exercise 1 Given the following recursive version of selection sort:public void recursiveSelectionSort(int a[], int n, int index){if (index == n)return;int k = minIndex(a, index, n-1);if (k != index)swap(a, k, index);recursiveSelectionSort(a, n, index + 1);}minIndex is a separate function that finds the smallest value in the given array “a” from“index” to “n-1” index values.swap is a separate function that swaps elements in the given array “a” between theelements at index “k” and “index” respectively.Assuming these 2 functions work as expected, there may be an error with therecursiveSelectionSort code. Answer the following:1) Design your own set of 8 unsorted integers in an array2) Determine what the given code will produce with your array by describing what thearray looks like with each recursive instance of recursiveSelectionSort3) If the code does have an error, describe the error, where it is, and how you would fixitFor example, if you said your array was [4 2 3 1 5 6 7 8], then…

Number of times you need to assign a value (let say -1) to all elements of a 4-demnsional array A[k, l, m, n] (to initialize it) can be expressed mathematically as product of sets cardinalities   Write a pseudo-code that does this assignment.

A majority element is an element that makes up more than half of the items inan array. Given a positive integers array, find the majority element. If there is no majority element,return -1. Do this in O(N) time and 0(1) space.Input: 1 2 5 9 5 9 5 5 5Output: 5

The optimised bubble sort offers none of the following benefits over conventional sorts for items that have already been sorted.

For each n-element array an, the first element is always what is returned by a[1]. What is true, and what is false?

What is the a(3) term of the sequence {a(n)} where a(n) = 2n - 6?