Answered: Describe how to efficiently execute…

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

I want to input k sorted lists and merge them into one sorted list, but it takes much Θ(kn) time using the simple method.
(a) Describe how to efficiently execute using Min Heap

Expert Solution

Step 1

Min Heap

It must hold the properties of complete binary tree.
The value (or data contained) in each node of a tree must be equal or smaller than the values of the children of that internal node.

Step 2

The straight-forward (or simple) method for k sorted lists of size n each

Create an output list with size n * k and then copy all the items (or elements) into the output list by picking the smallest of the top items in each list, repeatedly. This will take (k−1) comparisons per item, hence total time is O(k·n). The output list must be a sorted list that holds all the items of the input k sorted lists.

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