[40] Illustrate the operations of building a Max-Heap and Heap-Sort on the followingarray: A 16, 20, 10, 5, 13, 8, 7, 4, 25, 3, 6, 12>. For each iteration, use binary trees toshow the intermediate data structures or results.[20] What are its worst-case and best-case running times? Justify your answer.

Step 1: Building a Max-Heap: We start by building a Max-Heap from the given array. A Max-Heap is a…

Answered: [40] Illustrate the operations of…

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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What are the inherent benefits and drawbacks of this (two-dimensional sequence) backing representation? Discuss with respect to implementation, efficiency, and memory usage in general and as compared to an array-based, a linked list-based, and a binary tree-based implementation. (PI 1.2/ABET[1], PI 6.1/ABET[6] , PI 6.2/ABET[6])
(a) What are the best, worst, and average case runtimes for finding the smallest element inan unsorted array? Explain.(b) If you know that a binary tree is full, compare the complexity of finding the number of elements in the binary tree with finding the number of elements in a perfect binarytree. Explain.(c) Hash tables are normally very efficient - often O(1) with a good hash function. However,hash tables are not always the best choice. When would it be better to choose a differentdata representation? Explain.(d) In what cases would an array representation of a binary tree be more efficient thana node representation? Explain.
Given the following list of integers: 12,15,20,25 (a) Apply the BUILDHEAP procedure to this list, in a right-to-left scan. Draw appropriate trees each time the addition of a new element causes changes in the tree structure. (b) Now, sort the list obtained in part(a) in a series of exchange and heapify steps. Once again, draw appropriate trees to illustrate each exchange-heapify step.
Compare the implementations of the dynamic set using different data structures. Fill in the worst- case time complexity of the data structures that are to support the specified operation of the dynamic sets. Use the O notation. Assume that the height of the binary search tree is h = ©(log n) 4. Worst-case time complexity of the dynamic set operations Data Structures Search Insertion Successor Maximum Extract-Max Deletion (w/o search) Binary max heap Sorted array in ascending order Binary search tree
In the BinaryTree abstract data structure, there is a remove() function. a. Explain briefly the purpose of the remove() function. b. The remove() function runs differently depending on the number of subtree on a node. i. Explain briefly, how to estimate the number of substrees given a binary tree node. ii. Give an example in a single sentence to justify that the worst-case time complexity for the remove() is O( n).
Use a triply linked structure as opposed to an array for implementing a priority queue using a heapordered binary tree. Each node will require three links: two to move up the tree and one to move down it. Even if the maximum size of the priority queue is unknown at the outset, your solution should nonetheless provide logarithmic running times for each operation.
Provide an explanation of the search time performance of list, BST (binary search trees), and AVL, each of which has its own distinct difficulties.
You have been given an array of integers that have just been sorted using the QuickSort algorithm. If you treat this array as a complete binary tree, would this array contain a Min Heap? If yes, you must justify your answer by citing the properties of a Min Heap and the way a complete binary tree is stored in an array.If no, you must provide a counterexample.
What are the advantages and disadvantages of this (two-dimensional sequence) backing representation? Discuss implementation, efficiency, and memory consumption in general, as well as comparisons to array-based, linked-list-based, and binary tree-based implementations. (PI 1.2/ABET(1), PI 6.1/ABET(6), PI 6.2/ABET(6))
(a) Describe in brief the Depth-first search in respect of the following characteristics: • Uninformed search • Stack (LIFO) • Deepest Node • Incomplete Not Optimal Time complexity
Consider the initial B+ tree index shown below. The number of pointers in a node is 3. Draw the B+ tree for each of following operations (in total there should be two trees): (1) insert ‘10’; (2) delete ‘17’. (Each of the operations, besides (1), must be performed on the B+ tree drawn for the previous operation and (1) must be performed on the following B+ tree). I need the carrect answer as soon as possible please
Please answer the following, #6 (in bold) . Number 5 is linked to #6, but i only need number 6 NOT 5. Write clearly please. 5. Create a height-balanced binary search tree from the following sorted array. 1 5 9 11 12 13 15 18 19 6. Consider from the previous questions the height balanced binary search trees created from sorted arrays. Creating this balanced tree gives a tree with an efficient search time for any value it holds. If I wanted to find the range of the data (difference between largest and smallest item), how long would it take to do this with the binary search tree? Explain your answer with a single sentence. (Give the answer relative to input size n, but not in Big O notation).

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