Answered: Consider the following variant of…

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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Consider the following variant of Mergesort. If the array has more thantwo elements, it recursively sorts the first two-third and the last one-third. Then, it mergesthe first two-third with the last one-third. If the array has at most two elements, then ittrivially sorts the array. For completeness, here is the pseudocode for sorting the arrayA[l..r].

Write a recurrence relation for the worst-case running time of Newsort. Solve the recurrencerelation to obtain aΘ-bound on the running time of the algorithm, in terms of the lengthnof the array. You must use the tree method to solve the recurrence. You may also ignorefloors and ceilings in your calculations.

Input: A, l,r
Result: A sorted in ascending order
1 if r – l+1= 2 and A[l] > A[r] then
swap(A[C], A[r])
exit
4 if r – l +1> 2 then
m+ [(r – l + 1)/3]
NewSort(A, l, l + 2m – 1)
NewSort(A, l + 2m, r)
Merge(A, l, l+ 2m – 1,r)
6
7

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