G(V) = 2 + max(G(Vl) , G(Vr))
G(V) calculate twice the height of node V.
for a Binary search tree to be an AVL tree.
for all nodes v in the tree
get the value of G(vl) and G(vr).
if difference between G(vl) and G(vr) is not more than 2 and also
left and right subtrees are balanced.
Then it is AVL tree.
isAVL(tree):
left = G(tree.left);
right = G(tree.right);
if (abs(left - right) <= 2 and isAVL(tree.left)
and isAVL(tree.right))
return true;
return false;
Suppose you know the value of the recursive function g(v) = 2+max(g(v1), 9(0,)) and g(NULL) =...
3. [5 marks] Suppose T is a binary tree that stores an integer key value in each node. Assume the following notation/operations on a binary tree. » the key T.key is the root node's integer key value . the left child T.left is T's left subtree, which is possibly an empty tree (or null) the right child T.right is T's right subtree, which is possibly an empty tree (or null) (a) Write an efficient algorithm FINDMAxPrODuCT(T) in pseudocode that returns...
2. A regular binary tree is a binary tree whose internal nodes all have two subtrees (left and right). In other words, all their nodes have either zero subtrees (in which case they are leaves) or two subtrees (in which case they are internal nodes). Suppose that you have a boolean function that tells you, for each node of the tree, whether it is a leaf or not (call it: leaf(n), for node n). a) Write a recursive function that...
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....
Answer the following question(s) concerning implementing recursive functions to perform operations on linked lists of nodes arranged as binary trees. For these questions, use the following struct definition for the nodes of the tree (we will not templatize the node here, so you do not have to write template functions for these questions, just assume trees of <int> values): struct BinaryTreeNode { int item; BinaryTreeNode* left; BinaryTreeNode* right; }; ---------------------------------------------- Given a node for a Binary Tree and an (integer)...
please explain each line of code! ( in python
)
1. Write a recursive function that returns the sum of all even integers in a LinkedBinaryTree. Your function should take one parameter, root node. You may assume that the tree only contains integers. You may not call any methods from the LinkedBinaryTree class. Specifically, you should traverse the tree in your function def binary tree even sum (root): Returns the sum of al1 even integers in the binary tree 2....
Problem 2 [35 points (155 15)]: Let Ti and T2 be two binary search trees containing the same elements. In this problem, you will show how to transform Ti into T2 (i.e. Ti is altered to now have the same structure as T2) through a series of rotation operations. (a) Define a binary tree to be a right-going chain if no node in the tree has a left child (in other words, the tree is a linked list formed through...
Write pseudocode for a recursive algorithm for inserting a key
into a binary search tree. The following is the definition
assumed.
right? Write a) pto) You hadt written codes for for a algonithm for inserting a key into a binary seareh tree. The public class BST E extends comparable V prot fected bstNodeE protected class bstNode E V E key V value; ,V> right); bstNode E vright bstNode (E key ngvalue , bstNode«E·V> left . bstNode«E publle void insert (E...
/* * struct for a single node in a binary tree. data contains
the int
* stored in this node. left and right contain pointers to the
left and
* right subtrees respectively. *
* All of the ints stored in the left subtree is smaller than
data.
* All of the ints stored in the right subtree is larger than
data.
*/
struct node {
int data;
struct node *left;
struct node *right;
};
typedef struct node node;
Write...
Hello. I have written the following function to remove a value from a Binary Search Tree using resources my professors gave and stuff I found online. The problem is I don't know how it works and I need to know how it works to finish the rest of the project. public boolean remove(T value){ if(value == null) return false; class RemoveBSTObj{ private boolean found = false; private Node removeBST(Node root, T value){ if(root == null) return root; //IF there is...
Removing Nodes from a Binary Tree in Java This section requires you to complete the following method within BinaryTree.java: public void remove(K key) { } The remove method should remove the key from the binary tree and modify the tree accordingly to maintain the Binary Search Tree Principle. If the key does not exist in the binary tree, no nodes should be removed. In case there is a non-null left child, it should take the place of the removed node....