Homework Answers
Question 1:
Answer: 3.
An AVL tree is a self balancing binary search tree (BST) in which the difference between the heights of left and right subtrees should not be more than one for all nodes.
Height is maximum when each level contains minimal nodes.
Question 2:
Answer: inorder traversal
AVL tree is a self balancing binary search tree. In a binary search tree, all elements in its left sub-tree is less than the root node and all elements in its right subtree is greater than the root node. Each sub-tree itself is a binart search tree. Hence inorder traversal gives elements in sorted order.
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Question 1 1 pts What is the maximum height of any AVL-tree with 7 nodes? Assume...
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n))...
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n)) rotations. (b) A set of numbers are inserted into an empty BST in sorted order and inserted into an empty AVL tree in random order. Listing all elements in sorted order from the BST is O (n), while listing them in sorted order from the AVL tree is O (log(n)). (c) If items are inserted into an empty BST in sorted order, then the...
Answer question 3. Question 1 is for the graph Assume the following questions using the provided...
Answer question 3.
Question 1 is for the graph
Assume the following questions using the provided tree. By postorder traversal, what is the node to visit first? By preorder traversal, what is the node to visit last? By postorder traversal, what is the node to visit after node 5? By preorder traversal, what is the node to visit after node 5? By inorder traversal, what is the node to visit after node 5?
QUESTION 4 The shape of binary tree is unknown (unrelated to the tree defined in problem...
QUESTION 4 The shape of binary tree is unknown (unrelated to the tree defined in problem 3). However, we do have the following information: performing an inorder and a postorder traversals of the tree (containing nine integer nodes with integer values from 1 through 9) yield the following outputs: a) Inorder (LNR): 123456789 b) Postorder (LRN): 1354 2 8 796 Based on the above traversal information, determine the shape of the binary tree. Note that there is no need to...
1. [10 pts.] AVL Trees: Example Operations (a) [5 pts.] Draw the AVL tree that results...
1. [10 pts.] AVL Trees: Example Operations
(a) [5 pts.] Draw the AVL tree that results from inserting key
45 into the following AVL
tree.
(b) [5 pts.] Draw the AVL tree that results from deleting key 70
from the following AVL
tree. NOTE: When deleting a key from an AVL tree, please follow the
textbook approach
of finding the node with the key using the function for standard
binary search trees.
If the key is in the tree and...
2. Write a recursive algorithm which computes the number of nodes in a general tree. 3....
2. Write a recursive algorithm which computes the number of nodes in a general tree. 3. Show a tree achieving the worst-case running time for algorithm depth. 4. Let T be a tree whose nodes store strings. Give an efficient algorithm that computes and prints, for every node v of T, the string stored at v and the height of the subtree rooted at v. Hin Consider 'decorating' the tree, and add a height field to each node (initialized to...
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
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....
(b) You are given the AVL Tree in the figure below. Assume that the nodes are...
(b) You are given the AVL Tree in the figure below. Assume that the nodes are sorted in alphabetical order. E J B D K A F L H Draw the resulting BST after node E is removed. To construct the new BST replace node E with an appropriate node from the left subtree of E. Do not rebalance the resulting tree. Label each node in the resulting tree with its balance factor. (e) Now rebalance the tree from the...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes: • The key T.key is the root node’s key. • The left child T.left is T’s left subtree, which is an AVL tree (possibly E). • The right child T.right is T’s right subtree, which is an AVL tree (possibly E). (a) [5 marks] Write a function RangeCount(T, lo, hi) to count the number of nodes in an...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes The key T.key is the root node's key. The left child T.left is Ts left subtree, which is an AVL tree (possibly E). The right child T.right is T's right subtree, which is an AVL tree (possibly E). (a) 5 marsl Write a function RANGECOUNT(T, lo, hi) to count the number of nodes in an AVL tree with...
Please I need help ASAP Java Programing: Binary Search Tree Fully implement the BST class in Listing 25.4 (on page 961 of the 11th Edition of the text). Design and write a (main) driver program to com...
Please I need help ASAP Java Programing: Binary Search Tree Fully implement the BST class in Listing 25.4 (on page 961 of the 11th Edition of the text). Design and write a (main) driver program to completely test every method in the BST class to ensure the class meets all its requirements. You should read the Listing 25.5: TestBST.java for an idea of what your program should look like. Listing 25.4 BST.java public class BST> extends AbstractTree { protected TreeNode...
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n)) rotations. (b) A set of numbers are inserted into an empty BST in sorted order and inserted into an empty AVL tree in random order. Listing all elements in sorted order from the BST is O (n), while listing them in sorted order from the AVL tree is O (log(n)). (c) If items are inserted into an empty BST in sorted order, then the...
Answer question 3.
Question 1 is for the graph
Assume the following questions using the provided tree. By postorder traversal, what is the node to visit first? By preorder traversal, what is the node to visit last? By postorder traversal, what is the node to visit after node 5? By preorder traversal, what is the node to visit after node 5? By inorder traversal, what is the node to visit after node 5?
QUESTION 4 The shape of binary tree is unknown (unrelated to the tree defined in problem 3). However, we do have the following information: performing an inorder and a postorder traversals of the tree (containing nine integer nodes with integer values from 1 through 9) yield the following outputs: a) Inorder (LNR): 123456789 b) Postorder (LRN): 1354 2 8 796 Based on the above traversal information, determine the shape of the binary tree. Note that there is no need to...
1. [10 pts.] AVL Trees: Example Operations
(a) [5 pts.] Draw the AVL tree that results from inserting key
45 into the following AVL
tree.
(b) [5 pts.] Draw the AVL tree that results from deleting key 70
from the following AVL
tree. NOTE: When deleting a key from an AVL tree, please follow the
textbook approach
of finding the node with the key using the function for standard
binary search trees.
If the key is in the tree and...
2. Write a recursive algorithm which computes the number of nodes in a general tree. 3. Show a tree achieving the worst-case running time for algorithm depth. 4. Let T be a tree whose nodes store strings. Give an efficient algorithm that computes and prints, for every node v of T, the string stored at v and the height of the subtree rooted at v. Hin Consider 'decorating' the tree, and add a height field to each node (initialized to...
(b) You are given the AVL Tree in the figure below. Assume that the nodes are sorted in alphabetical order. E J B D K A F L H Draw the resulting BST after node E is removed. To construct the new BST replace node E with an appropriate node from the left subtree of E. Do not rebalance the resulting tree. Label each node in the resulting tree with its balance factor. (e) Now rebalance the tree from the...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes The key T.key is the root node's key. The left child T.left is Ts left subtree, which is an AVL tree (possibly E). The right child T.right is T's right subtree, which is an AVL tree (possibly E). (a) 5 marsl Write a function RANGECOUNT(T, lo, hi) to count the number of nodes in an AVL tree with...
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