a. The following array of integers are to be sorted into ascending order: 5 2 11 7 6 13 If selection sort is chosen to sort this array, write the contents of the array each time that the sort algorithm changes it. How many comparison operations and how CR(8) many swaps are performed in the sorting?
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- Q:During each iteration of Quick Sort algorithm, the first element of array is selected as a pivot. The algorithm for Quick Sort is given below. Modify it in such a way that last element of array should be selected as a pivot at each iteration. Also explain the advantages.Consider the following array of int values. [17, 11, 6, 22, -3, 8, 4, 22, 2, 35, -4, 10] Write the contents of the array after 4 passes of the outermost loop of selection sort. Assume selection sort is sorting slots from low-to-high Write the contents of the array during each of the the recursive calls of merge sort.3. Binary search. (a) Suppose we want to check if a sorted sequence A contains an element v. For this, we can use Binary Search. Binary Search compares the value at the midpoint of the sequence A with v and eliminates half of the sequence from further consideration. The Binary Search algorithm repeats this procedure, halving the size of the remaining portion of the sequence each time. Write a recurrence for the running time of Binary search and solve this recurrence. (b) Ternary Search is a generalization of Binary Search that can be used to find an element in an array. It divides the array with n elements into three parts and determines, with two comparisons, which part may contain the value we are searching for. For instance, initially, the array is divided into three thirds by taking mid1 = ["¹] and mid2 = [²(n-¹)]. Write a recurrence for the running time of Ternary search and solve this recurrence.
- 1. Consider an array of 66000 sorted entries. What is the maximum number of comparisonsthat must be made to find any arbitrary value in the array?Let A and B be two integers valued arrays of sizes n1 & n2 respectively. The elements of the two arrays are sorted in increasing order and may contain duplicate elements.It is required to form a list, C, of distinct elements, in increasing order, that are in A but not in B and in B but not in A. (There shall be no duplicate elements in list C.)The two arrays, A & B, can only be traversed once.Example:A: -2, 2, 4, 4, 4, 7, 9, 9, 9, 12, 15,B: 1, 2, 5, 9, 15, 15, 15, 17, 17, 17C: -2, 1, 4, 5, 7, 12, 17Question 17 Aa .You are given a sorted list of n numbers stored in an array A, where n can be arbitrarily large. Now randomly generate a number k and search the number in the list (i.e., in A). Now randomly select two subarrays of A, each of size n^1/2 . Then repeat the same procedure on each of the subarrays. The procedure stops after the subarray sizes become 1. Analyze the time complexity of finding the total number of successful searches in the entire procedure using big O-notation Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this line
- What is the time complexity for the following code/program? 1.5 A binary search works like this: in a sorted array, the search algorithm compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. What is the complexity of binary search? Why?Following is the function for interpolation search. This searching algorithm estimates the position (index) of a key in array based on the elements in the first position and last position in the array, and the length of array. The array must be sorted in ascending order. Suppose array A contains the following 15 elements: A = [1, 3, 3, 10, 17, 22, 22, 22, 24, 25, 26, 27, 27, 28, 28] At first iteration, at which position (index) the element of 24 is estimated in array A? In which part of array (starting index and ending index) the searching should continue? How many iterations the searching are performed until the element of 24 is found? int InterpolationSearch(int x[], int key, int n) { int mid, min = 0, max = n-1; while(x[min] < key && x[max] > key) { mid = min + ((key-x[min])*(max-min)) / (x[max]-x[min]); if(x[mid] < key) min = mid + 1; else if(x[mid] > key) max = mid - 1; else return mid; } if…Consider the algorithm for insertion sort shown below. The input to this algorithm is an array A. You must assume that indexing begins at 1.
- Course: Data structure and algorithms: Topic: Algorithm Complexity: Please solve it o emergency basis: Question 2: Imagine that we want to keep track of friendships between n people. We can do this with an array of size nXn. Each row of the array represents the friends of an individual, with the columns indicating who has that individual as a friend. For example, if person j is a friend of person i, then we place a mark in column j of row i in the array. Likewise, we should also place a mark in column i of row j if we assume that friendship works both ways. What will be the space complexity of this problem.: In searching an element in an array, linear search can be used, even though simple to implement, but not efficient, with only O(n) time complexity. Assuming the array is already in sorted order, modify the search function below, using a better algorithm, so the average time complexity for the search function is O(log n). include <iostream> using namespace std; int search(int al), int s, int v) { 1/ Modify below codes. for (int i = 0; i <s; i++) { if (a[i] = v) return i; return -1; int main() { int intArray:10] = { 5, 7, 8, 9, 10, 12, 13, 15, 20, 34); // Search for element '12' in 10-elements integer array. cout << search(intArray, 10, 12); // '5' will be printed out. // Search for element '35' in 10-elements integer array. cout << search(intArray, 10, 35); // '-1' will be printed out. // Index '-l' means that the element is not found. return 0;Exercise 1:In this problem, we would like to implement a variation of the Bubble Sort algorithm. The algorithm differs from a bubble sort in that it sorts in both directions on each pass through the list. The algorithm is illustrated as in the following figure: For the first step, we perform bubble sort from the index 1 to n (n is thenumber of elements in the array). The next step, we perform a reserved bubble sort from the index n to 1. The process is repeated until all the array is sorted. Propose a pseudo-code to complete the Bubble Sort algorithm. Implement and test this algorithm in C/C++. Analyze and compute the complexity of this algorithm in the best, average and worst scenarios.Exercise 2:Re-implement Exercise 1 using a linear data structure: List, Stack, Queue. Justify your choice of data structure.