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examine a new Merge sort algorithm.

examine a new Merge sort algorithm.

Database System Concepts
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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**Merging and Merge Sort Algorithm** **11.** **(a)** Demonstrate how to merge (not mergesort) three ordered lists, each of size \( n/3 \), with at most a total of \( \frac{5}{3}n \) comparisons. **(b)** Examine a novel merge sort algorithm where the parameter \( A \) in \( (A, n) \) represents a list of numbers to be sorted, and \( n \) denotes the total length of list \( A \). **Procedure `mergeSort(A, n)`:** 1. **If** \( n = 1 \), **then** return \( A \) 2. **Else** - Divide \( A \) into three lists of equal size: \( B \), \( C \), \( D \). - \( B := \text{mergesort}(B, n/3) \) - \( C := \text{mergesort}(C, n/3) \) - \( D := \text{mergesort}(D, n/3) \) - Return `merge(B, C, D)`. 3. **End** **Objective:** Set up and solve a recurrence relation to determine the worst-case number of comparison operations performed by this algorithm.
Transcribed Image Text:**Merging and Merge Sort Algorithm** **11.** **(a)** Demonstrate how to merge (not mergesort) three ordered lists, each of size \( n/3 \), with at most a total of \( \frac{5}{3}n \) comparisons. **(b)** Examine a novel merge sort algorithm where the parameter \( A \) in \( (A, n) \) represents a list of numbers to be sorted, and \( n \) denotes the total length of list \( A \). **Procedure `mergeSort(A, n)`:** 1. **If** \( n = 1 \), **then** return \( A \) 2. **Else** - Divide \( A \) into three lists of equal size: \( B \), \( C \), \( D \). - \( B := \text{mergesort}(B, n/3) \) - \( C := \text{mergesort}(C, n/3) \) - \( D := \text{mergesort}(D, n/3) \) - Return `merge(B, C, D)`. 3. **End** **Objective:** Set up and solve a recurrence relation to determine the worst-case number of comparison operations performed by this algorithm.
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