Design a divide-and-conquer algorithm in pseudocode for computing the number of levels in a binary tree. (In particular, the algorithm must return 0 and 1 for the empty and single-node trees, respectively.) What is the time efficiency class of your algorithm? The tree node class is as follows: ср class Node { int val; Node* leftchild; Node* rightchild; }

Design a divide-and-conquer algorithm in pseudocode for computing the number of levels in a binary tree. (In particular, the algorithm must return 0 and 1 for the empty and single-node trees, respectively.) What is the time efficiency class of your algorithm? The tree node class is as follows: ср class Node { int val; Node* leftchild; Node* rightchild; }

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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Q5. a. A binary search tree may be balanced or unbalanced based on the arrangement of the nodes of the tree. With you knowledge in Binary search tree:i. Explain the best and worst case scenarios of the time and space complexity of both type of binary trees above.b. Using your knowledge in binary tree traversals, implement the following tree traversing algorithms in either Java or C++, i. inorder, ii. preorder iii. and postorder traversal
Write a C++ program to implement binary search tree (BST). Your program should accept a list ofnumbers from the user (minimum 5) and then build a binary search tree from those numbers.Implement following functions: Serach function: Number is found or not leavesCount: Returns number of leaves in binary tree inorder: Print the contents of tree using inorder traversal Note: Define three files: bst.h, bst.cpp, main.cpp to solve this problem
1.111.Q_7a. A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root. The path sum of a path is the sum of the node's values in the path. Given the root of a binary tree, return the maximum path sum of any non-empty path .Input: root = [1,2,3] Output: 6 Explanation: The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6..tahms.
Below are some statements about binary search trees and red-black trees. Indicate which of these statements is correct. A. A binary search tree with the height ‘h’ can have a maximum of 2 (h + 1) - 1 nodes. B. The height of a binary search tree containing ‘n’ elements can be at most (n-1). C. The time complexity for inserting a new element into a BST tree that contains 'n' elements is in the worst case 0 (log2 n). D. The time complexity for inserting a new element into an AVL tree that contains 'n' elements is at best 0 (log2 n). E. The complexity of the time to insert a new element into a red-black tree containing 'n' elements is in the worst case 0 (log2 n). Group of answer options Only statements B and E are correct. Only statements A, B and E are correct. Only statements B, D and E are correct. Only statements A, B, D and E are correct. Only statements B, C and E are correct.
(a) You have an empty binary search tree. After that, you do the following sequence of insertions:20, 30, 10, 50, 40, 60. Draw the status of the binary search tree after the first 3 insertions, and at the endof all 6 insertions (you only need to show 2 trees). (b) Start now with a binary search tree with a single node containing an unknown key X. You mustchoose the value X so that if you later add the 6 keys in question 1(a) in the same order, you get aperfect tree with 7 nodes. Give a value for X and show the final tree obtained.
Please provide code in Python Language design algorithms for the following operations for a binary tree T: preorder next(p): Return the position visited after p in a preorder traversal of T (or None if p is the last node visited). inorder next(p): Return the position visited after p in an inorder traversal of T(or None if p is the last node visited).
1. How many different binary trees are possible with n nodes? Solution: For example, consider a tree with 3 nodes (n=3). It will have a maximum combination of 5 different trees. 2. Assume that each node has either 0 or 2 children. Given string: I L I L L a. Give the pre order traversal. b. Give the Postorder traversal
In DrRacket: Define the difference between Binary Search Trees and Nodes? A) A Binary Search Tree is a Node, but a Node isn’t always a Binary Search Tree. B) A Node is a Binary Search Tree, but a Binary Search Tree isn’t always a Node. C) Binary Search Trees may contain Nodes, but Nodes cannot contain Binary Search Trees. D) Nodes may contain Binary Search Trees, but Binary Search Trees cannot contain Nodes. E) They are the same thing
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Tl and T2 are two very large binary trees, with Tl much bigger than T2. Create an algorithm to determine if T2 is a subtree of Tl.A tree T2 is a subtree of Tl if there exists a node n in Tl such that the subtree of n is identical to T2. That is, if you cut off the tree at node n, the two trees would be identical.
8_ I need completion of code. Given a binary tree, check whether it is a mirror ofitself (ie, symmetric around its center). For example, this binary tree [1,2,2,3,4,4,3] is symmetric: 1 / \ 2 2 / \ / \3 4 4 3But the following [1,2,2,null,3,null,3] is not: 1 / \ 2 2 \ \ 3 3Note:Bonus points if you could solve it both recursively and iteratively.""" # TC: O(b) SC: O(log n)def is_symmetric(root): if root is None: return True return helper(root.left, root.right) def helper(p, q): if p is None and q is None: return True if p is not None or q is not None or q.val != p.val: return False return helper(p.left, q.right) and helper(p.right, q.left) def is_symmetric_iterative(root): if root is None: return True stack = [[root.left, root.right]] while stack: left, right = stack.pop() # popleft if left is None and right is None: continue. .