Let A be an array with n = 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.
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Let A be an array with n = 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.
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- Take an array of length n where all the numbers are nonnegative and unique. Find the element inthe array possessing the highest value. Split the element into two parts where the first part containsthe next highest value in the array and the second part holds the required additive entity to get thehighest value. Return the array index value. Consider the negative numbers as well.Input: [4, 8, 6, 3, 2]Output: [4, 6, 2, 6, 3, 2]Let A = [n, n − 1, n − 2, . . . , 3, 2, 1] be an array where the first n positive integers are listed in decreasing order. Determine whether Heapsort or Quicksort sorts this array faster.For this question, assume the Quicksort pivot is always the right-most element.Implement a Binary Search algorithm, and using the results from Exercise 5, show how longthe Binary Search takes (on average) for arrays of size 10, 100, and 1000. (You do not haveto print out the values in the array).
- Let A and B be two arrays of length n, each containing a random permutation of the numbers from 1 to n. An inversion between the two permutations A and B is a pair of values (x, y) where the index of x is less than the index of y in array A, but the index of x is more than the index of y in array B. Design an algorithm which counts the total number of inversions between A and B that runs in O(n log n) time.Please Help me with this Problem Given an unsorted array of size n. Array elements are in the range from 1 to n. One number from set {1, 2,..., n} is missing and one number occurs twice in the array. Find these two numbers.Given an integer n and an array a of length n, your task is to apply the following mutation to a: Array a mutates into a new array b of length n. For each i from 0 to n - 1, b[i] = a[i - 1] + a[i] + a[i + 1]. If some element in the sum a[i - 1] + a[i] + a[i + 1] does not exist, it should be set to 0. For example, b[0] should be equal to 0 + a[0] + a[1].
- Given an array, find the total number of inversions of it. If (i < j) and (A[i] > A[j]), then pair (i, j) is called an inversion of an array A. We need to count all such pairs in the array. For example, Input: A[] = [1, 9, 6, 4, 5] Output: The inversion count is 5 There are 5 inversions in the array: (9, 6), (9, 4), (9, 5), (6, 4), (6, 5)Write a program that reads an array A of N elements containing only 0's and 1's. Your program should find the position of a 0 and replace it with a 1 to get the longest continuous sequence of 1's. Let this position of 0 be called P. Print P if such a 0 exists and print -1 if the original array A contains only 1's. Assume the array indexing starts from 0.Given an array as follows5 4 9 10 2 8 1 3 7 6 Suppose we partition this array using quicksort's partition function and using 5 for the pivot. A) Draw the resulting array after the partition finishes.B) The following is an array which has just been partitioned by the first step of quicksort:3 0 2 4 5 8 7 6 9Give all the elements that could be the pivot? (There may be more than one possibility!) PLEASE HELP WITH PART A AND B AND SHOW WORK!!
- Given two arrays A and B of equal size N, the task is to find if given arrays are equal or not. Two arrays are said to be equal if both of them contain same set of elements, arrangements (or permutation) of elements may be different though.Note : If there are repetitions, then counts of repeated elements must also be same for two array to be equal. Example 1: Input: N = 5 A[] = {1,2,5,4,0} B[] = {2,4,5,0,1} Output: 1.Let A be an array of numbers. In the maximum sub-array problem, your goal is to determine the sub-array A[x . . . y] of consecutive terms for which the sum of the entries is as large as possible. For example, if A = [−2, −3, 4, −1, −2, 1, 5, −3], the maximum sub-array is [4, −1, 2, 1, 5], and the largest possible sum is S = 4 − 1 − 2 + 1 + 5 = 7. Suppose A = [1, 2, −4, 8, 16, −32, 64, 128, −256, 512, 1024, −2048]. Determine S, the largest possible sum of a sub-array of A.A) Starting with a dynamic array of length = 32 and numElements = 30, the length after we execute 90 insert at end operations is [answer]Group of answer choices 120 122 128 none of the above B) In each of the following cases, we start with a dynamic array of length = 128 and numElements = 64. After we execute 30 delete last operations, the number of elements isand the length isAfter we execute 32 delete last operations, the number of elements isand the length isAfter we execute 60 delete last operations, the number of elements isand the length is no hand written
