1. Apply both the left-to-right and right-to-left binary exponentiation algorithms to compute a^ 25.
7. For each of the following lists, construct both an AVL tree and a 2-3 tree (use ascending and alphabetical order as applicable): (
a) 3 6 5 1 2 4
(b) A B C D E F
(c) Z Y X W V W
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1. Apply both the left-to-right and right-to-left binary exponentiation algorithms to compute a^ 25. 7. For...
Design and Analysis of Algorithms 1. For each of the following lists, construct an AVL tree by inserting their elements successively, starting with the empty tree. 3, 2, 1, 4, 5, 6, 7 2. Construct a 2-3 tree for the list W, E, L, C, O, M, E, Y, O, U. Use the alphabetical order of the letters and insert them successively starting with the empty tree.
Programming implement and test 3 different algorithms for computing modular exponentiation: 1. Implement a function powerDirect(a, b, m) that takes three integers a, b, and m > 1. The function can compute the modular exponentiation ab modulo m. 2. Implement a function powerMemoryEfficient(a, b, m) that takes three integers a, b, and m > 1. The function can compute the modular exponentiation ab modulo m. This method requires more operations than the first method, because the required memory is substantially...
Data structures C++1- A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height by no more than 1 Out of the following choices, which is the minimum set of nodes, if removed, will make the BST balanced?2- Which of the following is true for Red-Black Trees ? Select all choices that apply! Select one or more: a. For each node in the tree, all paths from that node to any leaf nodes contain...
a. The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y. Construct the tree and determine the output of the PREORDER traversal output. b. One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1....
4. Consider the following subtree of a balanced AVL tree a b AA d X Y d+1 d+2 Now, suppose that subtrees (i.e., subtree X and subtree Y) to be both two levels deeper than its right subtree (i.e., subtree Z) so that we have the following unbalanced AVL tree node at the bottom of subtree Z is deleted, causing its two left a a b d d+1 X d+2 Describe how the AVL tree can be rebalanced. Draw the...
Data structures Exercises: For the following binary tree (Index-Value): 0 1 2 3 4 5 6 7 8 9 A C E G B P D X F H Give the pre-order traversal. Give the post-order traversal. Give the in-order traversal. Determine the height of the tree. Using these values: 8 6 4 3 5 9 2 1 6 Build a binary search tree. Build an AVL Tree. Build a 2-3 Tree. Build a min-heap. Build a max-heap. Apply a...
Public class TreeNode { TreeNode left, right; Int val; } Given a binary tree, print val in level order. Input: 1 2 3 4 5 6 7 Out: 1234567
*****************************In Java***************************************In Java***********************************In Java************************* In this problem, you will implement various algorithms operating on binary search trees. We have provided with you a standard implementation of a generic BST in BinarySearchTree.java. Note that this class is an abstract class, which means that some of its methods are not implemented. In previous assignments, you have implemented interfaces which specified methods that you needed to write. Very similarly, an abstract class is a class with some unimplemented methods (it can be thought...
Data Structures and Algorithms What is the: a. maximum number of levels that a binary search tree with 100 nodes can have? b. minimum number of levels that a binary search tree with 100 nodes can have? c. maximum total number of nodes in a binary tree that has N levels? (Remember that the root is level 0.) d. maximum number of nodes in the Nth level of a binary tree? e. number of ancestors of a node in the...
PYTHON QUESTION... Building a Binary Tree with extended Binary Search Tree and AVL tree. Create a class called MyTree with the methods __init__(x), getLeft(), getRight(), getData(), insert(x) and getHeight(). Each child should itself be a MyTree object. The height of a leaf node should be zero. The insert(x) method should return the node that occupies the original node's position in the tree. Create a class called MyBST that extends MyTree. Override the method insert(x) to meet the definitions of a...