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).
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- Finish the splitOdd10 using recursion to determine if the elements of an array can be split into two groups such that the sum of one group is a non-zero multiple of 10 and the sum of the other group is oddThe question below is about Quicksort. Consider the array of ten integers #(55 54 61 79 40 65 70 40 54 38 1. Write again the array of ten integers (this will facilitate marking your answer, in case you write it on a separate paper). 2. What would be the contents of the array immediately before the first recursive call to quicksort? In your answer, trace the algorithm by showing the contents of the array each time an array element is swapped.Outline, but do not implement, a recursive solution for sorting an array of numbers. Hint: First sort the subarray without the initial element.
- (a) Write a method public static void insert(int[] a, int n, int x) that inserts x in order among the first n elements of a, assuming these elements are arranged in ascending order. Do NOT use arraylists. x is the last element in a. n does not include x. (b) Using the insert method from Part (a), write a recursive implementation of Insertion Sort.The sorted values array contains the sixteen integers 1, 2, 3, 13, 13, 20, 24, 25, 30, 32, 40, 45, 50, 52, 57, 60. How many recursive calls are made by our binarySearch method given an initial invocation of binarySearch(45, 0, 15)? A. 3. B. 1. C. 4 D. 2. E. 0 A recursive definition is a definition (choose the best answer): A. that is recursive. B. in which something is defined in smaller terms of itself. C. which uses a mathematical equation. D. where a base case is defined. E. that repeats itself. Recursion is implemented by the system: A. using run time storage allocation. B. using static storage allocation. C. using a single static "stack frame". D. using compile time storage allocation.For a recursive binary search, put the following code in the correct order by dragging each line to the correct place. 1 2 A 5 60 7 8 ⠀ :::: if (right >= left) { if (array [mid] == item) return mid; int binarySearch(int array [], int left, int right, int item) { return binarySearch(array, left, mid - 1, item); if (array [mid] > item) return binary Search(array, mid+ 1, right, item); int mid=1+ (right - left) / 2; return -1; }
- // MergeSortTest.java// Sorting an array with merge sort.import java.security.SecureRandom;import java.util.Arrays; public class MergeSortTest { // calls recursive sortArray method to begin merge sorting public static void mergeSort(int[] data) { sortArray(data, 0, data.length - 1); // sort entire array } // splits array, sorts subarrays and merges subarrays into sorted array private static void sortArray(int[] data, int low, int high) { // test base case; size of array equals 1 if ((high - low) >= 1) { // if not base case int middle1 = (low + high) / 2; // calculate middle of array int middle2 = middle1 + 1; // calculate next element over // split array in half; sort each half (recursive calls) sortArray(data, low, middle1); // first half of array sortArray(data, middle2, high); // second half of array // merge two sorted arrays after split calls…Write a Program to implement binary search using recursion.For a Given array of Size 100, do the following implementations - 1. Write a program to implement the Modified version of the bubble sort algorithm so that it terminates the outer loop when it detects that the array is sorted. Compare the running time of the modified algorithm with Original Bubble sort. 2. Implement Quick sort ( both iterative and recursive). Calculate the run time complexity of both the implementation and compare their performance in terms of best, average and worst time complexity.
- Assume you have a sorted list of 100 pre-sorted elements and a recursive implementation of Quicksort. How many calls to Quicksort are made in order to fully sort it. Assume that the algorithm makes the recursive Quicksort calls before checking if it has an array of size 1 (see https://www.geeksforgeeks.org/quick-sort/ for specific pseudo code or the textbook Introduction to Algorithms 3rd Edition page 171). 85 101 50 103 199 Assume you have the following array: 40, 20, 15, 40, 90, 60, 50, 70. Which of the following elements, if selected as the pivot, would give you the most unequal sub-arrays to be sorted using quicksort? 30, 70 20, 15 40, 90 90, 70 90, 15 Assume you have the following array: 40, 20, 15, 40, 90, 60, 50, 70. Which of the following elements, if selected as the pivot, would give you the most unequal sub-arrays to be sorted using quicksort? 30, 70 20, 15 40, 90 90, 70 90, 15 Assume we have the array 4,10,3,5,1,2,5,6,1,2,3. What are the swaps that will occur after we…In the Recursive Binary Search shown below, there are two base cases: Line 10: the search is exhausted without a finding a value that matches the key Line 16: the search finds a value that matches the key 1 public class RecursiveBinarySearch { 2 public static int binarySearch(int[] list, int key) { 3 int low = 0; 4 int high = list.length - 1; 5 return binarySearch(list, key, low, high); 6 } 7 8 private static int binarySearch(int[] list, int key, 9 int low, int high) { 10 if (low > high) // The list has been exhausted without a match 11 return -low - 1; 12 13 int mid = (low + high) / 2; 14 if (key < list[mid]) 15 return binarySearch(list, key, low, mid - 1); 16 else if (key == list[mid]) 17 return mid; 18 else 19 return binarySearch(list, key, mid + 1, high); 20 } 21 22 public static void main(String[] args) { 23 int[] list = {3, 5, 7, 8, 12, 17,…With the Binary Search algorithm, the algorithm can be developed by the loop-based form as well as a recursive form. Which of the following is not true? O If the item is not found, the loop version returns when the range bounds reach, but the recursive version finishes when the recursive depth is more than half the initial search range. The search range starts with the whole array, and only the recursive version can work on a subrange passed through arguments. O Both forms of the program divide the search range repeatedly in half. O If the item is found, the loop version returns from the entire method, whereas the recursive version returns from one level of recursion.