Answered: Can we use a binary searh instead to…

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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Observe that the while loop of lines 6–8 of the Insertion-Sort procedure given in class uses a linear search to scan (backward) through the sorted subarray A[1..j − 1]. Can we use a binary searh instead to im- prove the overall worst-case running time of insertion sort to Θ(n lg n)?

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Step 1

Insertion sort

Insertion sort is one of the sorting methods where the sorted array is created by inserting one element at a time in its proper position. The array elements are compared with each other in a linear way and then arranged simultaneously in a specific order.
In insertion sort, the best case is the case when all array elements are already sorted as the T(n) function will become a linear in 'n' whereas in the worst case, array elements are in reverse sorted order then function T(n) will become a quadratic in 'n'. Hence, the best-case runtime complexity is O(n) and worst-case runtime complexity is O(n²) for n number of array elements.

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