Could you help me the following questions?Sara and her friends said they have discovered a way to get O(1) category performance for both insert and remove in a priority queue. Their description of the data structure and algorithms is as follows:They use an array implementation for the priority queueThe index of the array represents the rank of an element – e.g. an element whose rank is 50 will be placed at index 49Each element is the head node to a linked list – if a new element is inserted into the priority queue with the same rank as another element already in the queue, the new element is added to the linked list at its headExample: If an element “X” with rank 25 exists at index 24, and a new element “Y” also has a rank of 25, the linked list at index 24 is “Y” then “X”When remove is performed, the element at the highest index is removed. If there is more than one node at that index, the node at the head of the linked list there is removedBased on this description of the data structure, you determine that their idea that this is O(1) for both insert and remove is incorrect. Explain your reasoning and be sure to at least include the following:Describe at least 2 scenarios where the actual order is not O(1) for either insert and/or removeState what the actual orders are for both in that worst case scenario

A priority queue is an abstract data type that behaves similarly to the normal queue except that…

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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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Could you help me the following questions?

Sara and her friends said they have discovered a way to get O(1) category performance for both insert and remove in a priority queue. Their description of the data structure and algorithms is as follows:

They use an array implementation for the priority queue
The index of the array represents the rank of an element – e.g. an element whose rank is 50 will be placed at index 49
Each element is the head node to a linked list – if a new element is inserted into the priority queue with the same rank as another element already in the queue, the new element is added to the linked list at its head
1. Example: If an element “X” with rank 25 exists at index 24, and a new element “Y” also has a rank of 25, the linked list at index 24 is “Y” then “X”
When remove is performed, the element at the highest index is removed. If there is more than one node at that index, the node at the head of the linked list there is removed

Based on this description of the data structure, you determine that their idea that this is O(1) for both insert and remove is incorrect. Explain your reasoning and be sure to at least include the following:

Describe at least 2 scenarios where the actual order is not O(1) for either insert and/or remove
State what the actual orders are for both in that worst case scenario

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