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AVL Tree Visualizer

Interactive visualization of AVL Tree operations (Self-Balancing Binary Search Tree) with animated rotations.

📚 How AVL Tree Balancing Works

Try this: Insert values 10, 20, 30 and watch the automatic rotation! The tree will rotate to keep balance.

🔄 Four Types of Rotations:

Before (Left-Left Case)
30
/
20
/
10

➜

After (Right Rotation)
  20
/  \
10  30

1 Insert Node: New node is added following BST property (left if smaller, right if larger)
2 Update Heights: All ancestor heights are recalculated from the inserted node upward
3 Check Balance: Balance factor = left height - right height (must be -1, 0, or 1)
4 Apply Rotation: If balance factor is outside [-1, 1], perform appropriate rotation:
- Left-Left: Single Right Rotation
- Right-Right: Single Left Rotation
- Left-Right: Left rotation on left child, then Right rotation on parent
- Right-Left: Right rotation on right child, then Left rotation on parent
5 Watch Animation: Nodes smoothly transition to their new positions with 0.8s animation

✨ Visual Features:

Smooth Animations: Nodes move with cubic-bezier easing for natural motion
Appear Effect: New nodes scale up from zero with fade-in animation
Auto-Center: Tree automatically centers in the container
Balanced Layout: Horizontal spacing adapts to tree depth

About AVL Trees

An AVL tree is a self-balancing binary search tree named after inventors Adelson-Velsky and Landis. 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.

Key Features:

Self-Balancing: Automatically maintains O(log n) height through rotations
Guaranteed Performance: Search, insertion, and deletion all O(log n) time
Balance Factor: Each node stores height information for efficient balancing
Four Rotation Types: Handles all imbalance cases with single or double rotations

Common Use Cases:

Database indexing where balanced search is critical
Memory allocation systems
Priority queues with frequent updates
Applications requiring guaranteed O(log n) operations