**Problem 4: Merge Sort Example and Analysis**---**a) Sorting the List Using Merge Sort**List: \( A = \{ 20, 13, 4, 34, 5, 15, 90, 100, 75, 102, 112, 1 \} \)**Using Merge Sort:**1. **Divide Step:** - Split the list into two halves until each sublist contains a single element: - First Split: \(\{20, 13, 4, 34, 5, 15\}\) and \(\{90, 100, 75, 102, 112, 1\}\) - Continue splitting each half recursively until individual elements are obtained.2. **Conquer (Merge) Step:** - Begin merging the single elements: - Merge \(\{20\}\) and \(\{13\}\) into \(\{13, 20\}\) - Continue merging adjacent sublists in sorted order. - Follow this method recursively for each level up the recursion tree until the sorted list is obtained.**Final Merged List:**\[\{1, 4, 5, 13, 15, 20, 34, 75, 90, 100, 102, 112\}\]---**b) Explanation of the Average Case of Merge Sort**Merge Sort has a time complexity of \(O(n \log n)\) for all cases (best, average, and worst) because the list is always split into two halves, and the merging process for items takes linear time in relation to the number of elements being merged.- **Average Case Analysis:** - Merge Sort divides the problem into smaller subproblems, sorts them, and then merges back the sorted sublists. - Each level of recursion involves partitioning and merging the entire dataset. - The known answer for question 3 serves as a lower-bound estimator, affirming that due to its recursive nature and optimal divide-and-conquer approach, Merge Sort always adheres to a time complexity of \(O(n \log n)\) regardless of the initial distribution of data elements.This ensures efficiency and stability, making Merge Sort a reliable choice for sorting large datasets, as it consistently performs well across different scenarios.

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4- Sort the list A[]={ 20, 13,4, 34, 5, 15, 90, 100, 75, 102, 112, 1} a) Using Merge Sort and show the order that the Merge procedure is performed. b) Explain the average case of Merge Sort. Give a detail explanation of how we can estimate the mean in relationship with the worst and best-case scenarios (hint: use the answer for question 3 as a lower-bound for the average).

4- Sort the list A[]={ 20, 13,4, 34, 5, 15, 90, 100, 75, 102, 112, 1} a) Using Merge Sort and show the order that the Merge procedure is performed. b) Explain the average case of Merge Sort. Give a detail explanation of how we can estimate the mean in relationship with the worst and best-case scenarios (hint: use the answer for question 3 as a lower-bound for the average).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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