Consider a hybrid sorting algorithm that combines Mergesort with Insertion Sort. It uses Mergesort until the number of elements in the input becomes smaller than or equal to 8, after which it switches to Insertion Sort. What is the number of key comparisons performed by this hybrid sorting algorithm in the best case when running on an input array of size n? Briefly justify your answer. You could assume n = 2k, k is more than 3

Consider the following version of insertion sort: Algorithm InsertSort2 (A[0...n − 1])     for i ← 1 to n − 1 do          j ← i − 1          while j ≥ 0 and A[j] > A[j + 1] do               swap(A[j], A[j + 1])               j ← j − 1 What is its time efficiency? How does it compare to the version given in the text?   Apply insertion sort to sort the list E, X, A, M, P, L, E in alphabetical order.   Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix. Algorithm Connected(A[0...n - 1, 0...n - 1])// Input: Adjacency matrix A[0...n - 1, 0...n - 1] of an undirected graph G// Output: 1 (true) if G is connected and 0 (false) if it is notif n = 1 return 1 // one-vertex graph is connected by definitionelseif not Connected(A[0...n - 2, 0...n - 2]) return 0else for j ← 0 to n - 2 doif A[n - 1, j] return 1return 0 Does this algorithm work correctly for every undirected graph with n > 0 vertices? If you answer "yes," indicate the algorithm’s…

In this problem, consider a non-standard sorting algorithm called the Slow Sort. Given anarray A[1 : n] of n integers, the algorithm is as follows: Slow-Sort(A[1 : n]):1. If n < 100, run merge sort (or selection sort or insertion sort) on A.2. Otherwise, run Slow-Sort(A[1 : n −1]), Slow-Sort(A[2 : n]), and Slow-Sort(A[1 : n −1]) again. Question: Prove the correctness of Slow-Sort.

A given implementation of bubble-sort takes on average 1 second to sort an array of 1000 elements. How many seconds do you expect sorting an array of 8000 elements will take? A given implementation of quicksort takes on average 0.1 seconds to sort an array of 1000 elements. How many seconds do you expect sorting an array of 8000 elements will take?

Suppose you have m sorted arrays, each with n elements, and you want to combine them into a single sorted array with mn elements. 1. If you do this by merging the first two arrays, next with the third, then with the fourth, until in the end with the last one. What is the time complexity of this algorithm, in terms of m and n? 2. Give a more efficient solution to this problem, using divide-and-conquer. What is the running time?

In Python: Let n be a (large) positive integer of your choice. We want to know which of the two Quicksort algorithms methods (he Lomuto method and the Hoare method) is superior when sorting arrays containing n elements. To answer this question, you will run Quicksort on 10000 random permutations of [1,2,3, . . . , n], on each of your two Quicksort algorithms.

In this problem, consider a non-standard sorting algorithm called the Slow Sort. Given anarray A[1 : n] of n integers, the algorithm is as follows: Slow-Sort(A[1 : n]):1. If n < 100, run merge sort (or selection sort or insertion sort) on A.2. Otherwise, run Slow-Sort(A[1 : n −1]), Slow-Sort(A[2 : n]), and Slow-Sort(A[1 : n −1]) again. Question: Write a recurrence for Slow-Sort and use the recursion tree method  to solve this recurrenceand find the tightest asymptotic upper bound on the runtime of Slow-Sort.

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].

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.

Show how the binary search algorithm discussed searches for 25 in the sorted listbelow: 4 6 17 25 32 39 41 43 45 49 Here I got  i=4 j=10 m=7 I know that 25<41....but I don't know what to do from here when it's like this. Is it the case where j is moved over to the left? Please help? I'm very confused and not sure if I'm understanding this correctly. Steps would be a great help here!