Let M(n) be the minimum number of comparisons needed to sort an array A with exactly n ele- ments. For example, M(1) = 0, M(2) = 1, and M(4) = 4. If n is an even number, clearly explain why M(n) = 2M(n/2) + n/2

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.

Question: Given an array of integers, find the maximum sum of contiguous subarray (containing at least one number). Example: Input: [-2,1,-3,4,-1,2,1,-5,4] Output: 6 (Explanation: [4,-1,2,1] has the largest sum = 6)

Given an integer array A[1..n] you are to list the k smallest elements. What method will you use when (i)k=0(1) Explain why you chose the algorithm you chose for parts (i)

Consider sorting n numbers stored in array A[1:n] by first finding the smallestelement of A[1:n] and exchanging it with the element in A[1]. Then find thesmallest element of A[2:n], and exchange it with A[2]. Then find the smallestelement of A[3:n], and exchange it with A[3]. Continue in this manner for thefirst n-1 elements of A. Write pseudocode for this algorithm, which is knownas selection sort. What loop invariant does this algorithm maintain? Why does itneed to run for only the first n-1 elements, rather than for all n elements? Give theworst-case running time of selection sort in big theta notation. Is the best-case runningtime any better?

it's not a programming question.

Given a sorted array of size N and an integer K, find the position at which K is present in the array using binary search. Example 1: Input: N = 5 arr[] = {1 2 3 4 5} K = 4 Output: 3 Explanation: 4 appears at index 3.

Let A be an array, where each of the n elements is a randomly chosen digit between 0 and 9. For example, if n = 12, this array could be A = [3,5,1,0,5,7,9,2,2,8,8,6]. Determine whether Counting Sort or Merge Sort sorts this array faster.

Consider an array of length 5, arr[5] = {9,7,4,2,1}. What are the steps of insertions done while running insertion sort on the array? a) 7 9 4 2 1 4 7 9 2 1 2 4 7 9 1 1 2 4 7 9 b) 9 7 4 1 2 9 7 1 2 4 9 1 2 4 7 1 2 4 7 9 c) 7 4 2 1 9 4 2 1 9 7 2 1 9 7 4 1 9 7 4 2 d) 7 9 4 2 1 2 4 7 9 1 4 7 9 2 1 1 2 4 7 9

an array of integers nums sorted in ascending order, find the startingand ending position of a given target value. If the target is not found in thearray, return [-1, -1]. For example:Input: nums = [5,7,7,8,8,8,10], target = 8Output: [3,5]Input: nums = [5,7,7,8,8,8,10], target = 11Output: [-1,-1].