Case Study 1 Problem: Merge Sort Merge Sort follows the rule of Divide and Conquer to sort a given set of numbers/elements, recursively, hence consuming less time. Merge sort runs in O(n*log n) time in all the cases. Two functions are involved in this algorithm. The merge() function is used for the merging two halves and the mergesort() function recursively calls itself to divide the array until the size becomes one. Use the array below to perform a Merge Sort. Show all necessary workings. (75, 22, 65, 97, 35, 56, 18, 89} Case Study 2

Quicksort SPLIT (the 2-pointer algorithm covered in class) is applied to the integer array [4,3,5,7,9,2,1], using the first entry as the pivot.  Show the series of item swaps that are performed in the split process, and the array after each of these swaps, up to and including the step of placing the pivot at its correct location. You only need to show the split of the original array, you are not required to continue working on the subarrays after the split.

Python language

DESIGN YOUR OWN SETTING Task: Devise your own setting for storing and searching the data in an array of non-negative integers redundantly. You may just describe the setting without having to give an explicit algorithm to explain the process by which data is stored. You should explain how hardware failures can be detected in your method. Once you have described the setting, include the following to your answer: Write a pseudocode function to describe an algorithm where the stored data can be searched for a value key: if the data is found, its location in the original array should be returned; -1 should be returned if the data is not found; -2 should be returned if there is a data storage error Include a short commentary explaining why your pseudocode works Describe the worst-case and best-case inputs to your search algorithm Derive the worst-case and best-case running times for the search algorithm Derive the Theta notation for the worst-case and best-case running times