Suppose the following array were passed in to a mergesort algorithm: 42 39 87 21| 56 93 43 35 Draw what the array looks like after the first recursive call completes, and then after the second recursive call (immediately before the final call to merge).

Quicksort is a powerful divide-and-conquer sorting algorithm that can be described in just four lines ofpseudocode. The key to Quicksort is the PARTITION(A, p, r) procedure, which inputs elementsptorof array A,and chooses the final element x = A[r] as the pivot element. The output is an array where all elementsto the left ofxare less thanx, and all elements to the right of x are greater than x. In this question, we will use the Lomuto Partition Method from class and assume that the pivot isalwaysthe last (right-most) element of the input array. Question: Let A be an array withn= 2k−1 elements, where k is some positive integer. Determine a formula (in terms of n) for the minimum possible number of total comparisons required by Quicksort, as well as a formula for the maximum possible number of total comparisons required by Quicksort. Use your formulas to show that the running time of Quicksort is O(nlogn) in the best case and O(n2) in the worst case.

Write a program to sort an array of random elements using quicksort as follows: Sort the arrays using pivot as the first element of the array Sort the arrays using pivot as the median of the first, last, and middle elements of the array Sort the arrays using pivot as the first element of the array. However,, when the size of any sub-list reduces to less than 20, sort the sub-list using insertion sort. Sort the array using pivot as the median of the first, last and middle elements of the array. When the size of any sub-list reduces to less than 20, sort the sub-list using insertion sort. Calculate and display the CPU time for each of the preceding four steps. Example of the median of the first, last and middle elements: 1 2 3 4 5 6 7 8 0 (median of 1, 5, 0 is 1) 8 0 1 2 3 4 5 6 7 (median of 8, 3, 7 is 7) To calculate the CPU time, use the header , and clock_t type. You need to cast the duration to float and divide it by CLOCKS_PER_SEC. Depends on the CPU of your computer, your…

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…

Can u answer this please

I need question 2 ans  previous question 1 has been answered

Java: Consider the following algorithm for searching in an unsorted array. If the size of the array is 1, then check if it contains the element to be searched. Otherwise, divide the array into two halves, and  recursively search both halves. Which of (a)–(c) is false? The running time of this algorithm is O(N) The actual running time of this algorithm is likely to be better than sequential search. This is an example of a divide‐and‐conquer algorithm all of the above are true none of the above is true

Use Binary Search, Recursive (Algorithm 2.1) to search for the integer 120 in the following list (array) of integers. Show the actions (execution) step by step. No code needed. Solution: 12 34 37 45 57 82 99 120 134 1. Compute the middle index from initial low (1) and high (9) indices: mid = Continue... A