Consider the 3-Merge sort algorithm, which recursively divides an array of length>=3 into 3 subarrays of equal size and sort each of them recursively(via 3-Merge sort) then uses the above merge method to obtain a sorted array. Does 3-Merge sort perfom asymptotically better than the classical Merge Sort algorithm and why?

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.

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For each question, an algorithm will be described that operates on N elements, and your answer should include: (a) a big-O expression that describes the total number of operations in the worst case (for ex- ample, O(N³)) (b) a description of how to achieve the same effect as the algorithm described, but achieved with a better big-O time bound (for example, "use mergesort instead of insertion sort") (c) the big-O time bound for your improved approach. Your improved algorithm does not need to be provably the best possible, but it should have a different and better big-O bound. (It may not be as simple as substituting one named algorithm for another; consider what is redundant about the work done by the existing algorithm.) You don't need to use pseudocode to describe your algorithms - the style used in the problem descriptions is also sufficient for your solutions. You can use pseudocode if you like. Do not write real code. If you wish to use an algorithm described in class, you can name…

Show all steps that recursive merge sort algorithm would perform to sort the list of values [6,9,3,1,8,0,5,7,2] and mark their order of execution.

Very confused about this problem. Any help is appercaited

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.

Even when employing a self-balancing binary search tree to construct binary tree sort, the worst-case time required is O(n log n), making it slower than merge sort.