AVL Tree Balance Explorer

CSC-211 · Semester III · Data Structures and Algorithms

advanced30 minAvailable

AVL treeOrdered structure · balanced by design

Nodes

Height

3levels

Active

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Lab brief

Objective

Study height-balanced trees, observe the balance factor of every node, and see how rotations restore balance after insertions.

Theory & concepts

An AVL tree is a binary search tree that stays balanced: for every node, the heights of its two subtrees differ by at most one. This balance factor keeps height at O(log n), guaranteeing O(log n) search, insert and delete. When an insertion violates the balance, rotations (left, right, left-right, right-left) restructure the tree to restore it.

Rendering diagram…

AVL rebalancing rotations

Balance factor = height(left) − height(right) ∈ {−1, 0, +1}
Insert in the left-left case  → single right rotation
Insert in the right-right case → single left rotation
Left-right and right-left cases → double rotations
Guaranteed height h ≤ 1.44 · log₂(n+2) − 1.328

Why balance matters

Inserting 1, 2, 3, ... into a plain BST produces a degenerate chain of height n — search becomes O(n). AVL rotations keep the tree compact so search stays logarithmic.

Prerequisites

Lab: Binary Tree and Traversals
BST insertion

Instructions

1Insert values and read the balance factor shown on each node.
2Watch nodes whose factor leaves {−1, 0, +1} get flagged.
3Observe the rotation that rebalances the offending subtree.
4Compare the final tree height with a naive insertion order.

Tasks

Balance factors
After inserting the sample set, verify every node's factor is within range.
Identify an imbalance
Insert a key that forces a rotation and identify the unbalanced node.
Rotation direction
Describe the single rotation needed for a right-right case.

Self-check

Every node's balance factor stays within {−1, 0, +1}.
The student identifies which rotations restore balance.
The height/logarithmic guarantee is stated.

Environment

balance factorsheight labelsrotation highlightinserttraversals