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- provided code: import java.util.Comparator; /** * Your implementation of various iterative sorting algorithms. */public class Sorting { /** * Implement bubble sort. * * It should be: * in-place * stable * adaptive * * Have a worst case running time of: O(n^2) * And a best case running time of: O(n) * * NOTE: You should implement bubble sort with the last swap optimization. * * You may assume that the passed in array and comparator * are both valid and will never be null. * * @param <T> Data type to sort. * @param arr The array that must be sorted after the method runs. * @param comparator The Comparator used to compare the data in arr. */ public static <T> void bubbleSort(T[] arr, Comparator<T> comparator) { // WRITE YOUR CODE HERE (DO NOT MODIFY METHOD HEADER)! } /** * Implement selection sort. * * It should be: * in-place * unstable…Optimization: make the input as big or as small as possible in Python using Newton and Bisection methods. The second picture below is another example from other problems we did. Please show your codes.Consider the following multiplication problem: Given an integer list (an array) of size n, we want to calculate the product of all numbers in the list and display the result. (a) Define an instance of a problem in general. (b) Specify two different instances of the multiplication problem defined above. (c) What is the solution for each instance in part (b). How did you come up with that solution?
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- 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…I need question 2 ans previous question 1 has been answeredComplete the combinations function to generate all combinations of the characters in the string s with length k recursively