One can build a max-heap of n elements in O(n) time. True False Given a binary search tree of n nodes, one can sort the keys therein in O(n) time. True False Consider a comparison based sorting algorithm and its decision tree on n elements. Then, the path from the root to every leaf node in the tree must have N(n log n) edges. True False

One can build a max-heap of n elements in O(n) time. True False Given a binary search tree of n nodes, one can sort the keys therein in O(n) time. True False Consider a comparison based sorting algorithm and its decision tree on n elements. Then, the path from the root to every leaf node in the tree must have N(n log n) edges. True False

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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A worst-case scenario for a binary tree sort that uses a self-balancing binary search tree is O(n log n) time. The merge sort method is much faster than this one.
Similar to a sorted array-based list, one of the main advantages of a binary search is that it is much quicker than a serial search because the data that needs to be searched halves with each step. For example, it is possible to search through 512 values and find the one you want within 9 steps, 1024 values in 10 steps, 2048 in 11 steps, and so on. However, not all tree ADT provides such benefits unless it is balanced. A balanced tree is defined as a tree where the depth of all leaf nodes or nodes with single children differs by no more than one. In other words, the height of a balanced tree is minimized. For this assignment, you will learn how to balance a tree. In this assignment, we will implement several methods to facilitate tree ADT operations, including balancing a tree. Please implement those methods as required in the following steps. /*** Node.java: Node class*/public class Node{private int data;private Node left;private Node right;public Node(int data){this.data =data;…
In the worst-case situation, binary tree sort using a self-balancing binary search tree requires O(n log n) time, which is slower than merge sort.
Suppose you have a binary search tree with 100 nodes and you want to find the node with the maximum value. What is the time complexity of this operation?
Multiple Choice: Select one only: Suppose we cannot use a priority queue (either due to unavailability of libraries, or constraints on operations). If we still want to implement Dijkstra’s algorithm, we must look for the “next closest vertex” by iterating across all vertices and storing distance data on an array, instead of letting the priority queue find this efficiently for us. What would then be the time complexity of this version of Dijkstra’s algorithm without priority queues? a. O(V^2) b. O(V+E) c. O(VE) d. O(VElogV)
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From the below array representation of a binary tree, find the father of node Q? z E xY A N Node H 5 7 8 9 10 | 11 12 13 Index 1 4 6 O a. Y O b. Z O c. E O d. X 3. 2.
A binary tree can be used to sort n elements of an array data. First, create acomplete binary tree, a tree with all leaves at one level, whose height h = (lg n) + 1, and store all elements of the array in the first n leaves. In each empty leaf, store an element E greater than any element in the array.Figure (a) shows an example for data = 8, 20, 41, 7, 2, h = (lg(5)) + 1 = 4,and E = 42. Then, starting from the bottom of the tree, assign to each node the minimum of its two children values, as in Figure (b), so that the smallest element emin in the tree is assigned to the root.If a leaf node is to be removed, this node is replaced by a new node with the same value of its parent node. If a node is added into the tree, it will be a leaf node. Normally a node with value E is replaced with new value. It’s necessary to verify recursively all values of its parent and make any possible modification if necessary so that the tree rules are respected. Implement this tree structure in C/C++ with…
A binary search tree with n keys has a minimum height of log2 n. Choose one: Is it true or false?