Given an 8-element array: A = {x1, x2, X3, X4, X5, X6, 27, x8}, we would like to find its 3rd smallest element. It is known that x₁ and xs are the two extreme elements: max and min, but we do not know which one is the max and which one is the min. It is also known that x4 and 5 are the two medians: left-median and right-median. What is the minimum number of comparisons you need to find the 3rd smallest element of the original array?

Given an 8-element array: A = {x1, x2, X3, X4, X5, X6, 27, x8}, we would like to find its 3rd smallest element. It is known that x₁ and xs are the two extreme elements: max and min, but we do not know which one is the max and which one is the min. It is also known that x4 and 5 are the two medians: left-median and right-median. What is the minimum number of comparisons you need to find the 3rd smallest element of the original array?

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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Question

Given an 8-element array: A = {x1, X2, X3, X4, X5, X6, 7, x8}, we would like to find
its 3rd smallest element. It is known that x₁ and 8 are the two extreme elements:
max and min, but we do not know which one is the max and which one is the min.
It is also known that x4 and x5 are the two medians: left-median and right-median.
What is the minimum number of comparisons you need to find the 3rd smallest
element of the original array?
Ans:

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