How many rotations are needed in the worst case to balance an AVL tree after an
Practice Questions
Q1
How many rotations are needed in the worst case to balance an AVL tree after an insertion?
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Questions & Step-by-Step Solutions
How many rotations are needed in the worst case to balance an AVL tree after an insertion?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance by ensuring the heights of the two child subtrees of any node differ by no more than one.
Step 2: Know that after inserting a new node into an AVL tree, the tree may become unbalanced.
Step 3: Identify the possible cases of imbalance. There are four cases: Left-Left, Left-Right, Right-Right, and Right-Left.
Step 4: For each case, determine how many rotations are needed to restore balance.
Step 5: Realize that in the worst-case scenario, you may need two rotations to balance the tree. This can happen in cases like Left-Right or Right-Left.
Step 6: Conclude that the maximum number of rotations needed to balance an AVL tree after an insertion is 2.
AVL Tree Balancing – AVL trees are self-balancing binary search trees where the difference in heights between the left and right subtrees (balance factor) is at most 1. After an insertion, the tree may become unbalanced, requiring rotations to restore balance.
Rotations in AVL Trees – There are four types of rotations (single and double) used to balance an AVL tree: left rotation, right rotation, left-right rotation, and right-left rotation. In the worst case, two rotations may be necessary.
