Answered: Assume we added the following at the…

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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Assume we added the following at the beginning of the Partition algorithm:

middle = ⌊(left t + right)/2⌋;
if A[left] ≤ A[middle] ≤ A[right] OR A[right] ≤ A[middle] ≤ A[left]

swap(A[left t], A[middle]);
if A[middle] ≤ A[right] ≤ A[left] OR A[left] ≤ A[right] ≤ A[middle]

swap(A[left t], A[right]);

such that we pick the pivot to be the median of the leftmost, rightmost and the middle elements, and place it at the leftmost position. The partition algorithm works as before after this modification, i.e., assumes the pivot is in the leftmost position. Construct an example for which quicksort will use Ω(n2) comparisons in this case. (unsorted array)

Expert Solution

Partition Algorithm analysis :

This algorithm partitions the set into the array such that all the elements on the left side are less than the chosen pivot while the right-side element is greater than the pivot.
This algorithm is used as the merger step in the quicksort algorithm.
The quicksort will result in the O(N²) when the input sequence is sorted.
In this case, the partition algorithm will always partition the whole array into the unbalanced tree with one element at one side and the other on another side.
The number of levels, in this case, is N and each level requires O(N), hence total complexity is O(N²)

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