Table of Contents
What is the range of balance factor?
The balance factor of any node of an AVL tree is in the integer range [-1,+1]. If after any modification in the tree, the balance factor becomes less than −1 or greater than +1, the subtree rooted at this node is unbalanced, and a rotation is needed.
What is the maximum height of an AVL tree with P nodes Mcq?
4. What is the maximum height of an AVL tree with p nodes? Explanation: Consider height of tree to be ‘he’, then number of nodes which totals to p can be written in terms of height as N(he)=N(he-1)+1+N(he-2).
How do you find the balance factor of a node?
Balance factor of a node is the difference between the heights of the left and right subtrees of that node. The balance factor of a node is calculated either height of left subtree – height of right subtree (OR) height of right subtree – height of left subtree.
How do you find unbalanced nodes in AVL tree?
To check whether it is left left case or not, compare the newly inserted key with the key in left subtree root. If balance factor is less than -1, then the current node is unbalanced and we are either in Right Right case or Right Left case.
Why AVL tree is called height balanced tree?
called AVL trees after their Russian inventors Adelson-Velskii and Landis. (height balanced) heights of left and right subtrees are within 1. (BST) values in left subtree are smaller than root value, which is smaller than the values in the right subtree.
What is the maximum height of an AVL tree with P nodes log p log p )/ 2 PP 2?
Question 5
| A | true |
|---|---|
| B | false |
What is the balance factor of an AVL tree?
An AVL tree is a balanced binary search tree. In an AVL tree, balance factor of every node is either -1, 0 or +1. Balance factor of a node is the difference between the heights of the left and right subtrees of that node.
What is the depth of a node in an AVL tree?
The depth of a node is 1 more then the depth of it’s deepest child. You can do this quite simply with recursion. -1, 0, and +1 are the three balance state of an AVL tree. The balance factor is left height – right height of the tree.
What is the difference between binary tree and AVL tree?
In other words, a binary tree is said to be balanced if the height of left and right children of every node differ by either -1, 0 or +1. In an AVL tree, every node maintains an extra information known as balance factor. The AVL tree was introduced in the year 1962 by G.M. Adelson-Velsky and E.M. Landis.
How do you find the balance factor of a tree?
To calculate the balance factor of a node in an AVL tree we need to find the height of its left subtree and the height of its right subtree. Then we subtract the height of right subtree from the height of its left subtree: balancefactor = leftsubtreeheigh – rightsubtreeheight.