What is the primary purpose of performing rotations in an AVL tree?a)To create new child nodesb)To maintain or restore balancec)To delete nodes with duplicate valuesd)To increase the height of the tree
Question
What is the primary purpose of performing rotations in an AVL tree?a)To create new child nodesb)To maintain or restore balancec)To delete nodes with duplicate valuesd)To increase the height of the tree
Solution
The primary purpose of performing rotations in an AVL tree is b) To maintain or restore balance.
Here's why:
An AVL (Adelson-Velsky and Landis) tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one. If at any time they differ by more than one, rebalancing is done to restore this property. This rebalancing is achieved through tree rotations.
So, when we insert or delete nodes, the tree might become unbalanced. To bring the tree back to its balanced state, we perform rotations. There are four types of rotations: left, right, left-right, and right-left.
Therefore, the primary purpose of performing rotations in an AVL tree is to maintain or restore balance, not to create new child nodes, delete nodes with duplicate values, or increase the height of the tree.
Similar Questions
Which rotations in AVL trees are known as single rotations?
Consider the following scenario:In a weight-balanced tree, a new node with a large weight is inserted as the right child of a node with a small weight.How might the tree adapt to maintain balance, and what rotation operation is likely to be involved?a)The left subtree's weight increases; left rotation is performed.b)No action is needed.c)The left subtree's weight decreases; double rotation is performed.d)The right subtree's weight increases; right rotation is performed.
Consider the below left-left rotation pseudo code where the node contains value pointers to left, right child nodes and a height value and Height() function returns height value stored at a particular node.avltree leftrotation(avltreenode z): avltreenode w =x-left x-left=w-right w-right=x x-height=max(Height(x-left),Height(x-right))+1 w-height=max(missing)+1 return w*2 pointsHeight(w-left), x-heightHeight(w-right), x-heightHeight(w-left), xHeight(w-left)
In AVL Tree Balancing is done if the Balance Factor of a node is
Which operation is not a valid balancing operation in a height-balanced tree?a)Right rotationb)Left rotationc)Swap operationd)Left-right rotation (LR Rotation)
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