AlgoViz.
Hierarchical Structures Hub

Tree Structures & Hierarchies

Visualize non-overlapping dynamic coordinate node layouts, animated recursive traversals, and self-balancing B-Tree index splits.

Explore Tree VisualizersAll Data Structures

Interactive Tree Visualizers

Select an algorithm to inspect real-time pointer manipulation and coordinate layout.

Binary Search Tree (BST)

Hierarchical

Ordered binary tree where left descendants are strictly less than and right descendants are greater than the node. Features dynamic SVG non-overlapping layout, search, insertion, deletion, and inorder/preorder/postorder/level-order traversals.

Search: O(log n)Insert: O(log n)Delete: O(log n)
Best for: Dynamic sorted sets, range queries, symbol tables, and priority search.

AVL Tree (Self-Balancing BST)

Self-Balancing

Strictly height-balanced BST guaranteeing O(log n) operations. Calculates balance factors and executes single (LL, RR) or double (LR, RL) rotations when imbalance exceeds ±1.

Search: O(log n)Insert: O(log n)Delete: O(log n)
Best for: Read-intensive database in-memory indexes, IP lookup routing tables, and compiler symbol tables.

Red-Black Tree

Self-Balancing

CLRS self-balancing binary search tree using node color bits (red/black), NIL sentinels, recoloring, and rotation fixups guaranteeing O(log n) worst-case height.

Search: O(log n)Insert: O(log n)Delete: O(log n)
Best for: Standard associative maps (C++ std::map, Java TreeMap), Linux kernel Completely Fair Scheduler (CFS).

B-Tree

Multi-Way

Self-balancing multi-way tree data structure with order m. Nodes maintain between ceil(m/2)-1 and m-1 keys, executing proactive node splits to minimize block read operations.

Search: O(log n)Insert: O(log n)Delete: O(log n)
Best for: Database index engines (PostgreSQL, SQLite, MySQL InnoDB) and large disk-backed filesystems.

Tree Traversal Strategies

In-Order TraversalLeft → Root → Right

Visits nodes in strictly ascending numerical order in a BST.

Pre-Order TraversalRoot → Left → Right

Useful for cloning or serializing the exact tree structure.

Post-Order TraversalLeft → Right → Root

Essential for bottom-up deletions, subtree sizing, and expression tree evaluation.

Level-Order Traversal (BFS)Breadth-first top-to-bottom

Visits nodes depth by depth using a FIFO queue.