←Back to Tutorials
Trees: Fundamentals & Advanced
Master tree data structures from basics to advanced: binary trees, BSTs, balanced trees, heaps, tries, and when to use each—with code, pros/cons, and use cases.
75 minutes
11Detailed Sections
Senior Level
A tree is a hierarchical data structure of nodes connected by edges. Unlike arrays or linked lists, it has a single root and no cycles: every node (except the root) has exactly one parent.
- Key terms: The root is the top node. A child has one parent; nodes with the same parent are siblings. A leaf has no children; an internal node has at least one. Depth is the number of edges from root to a node; height is the maximum depth in the tree (or in a subtree).
Trees model real-world hierarchies (file systems, org charts), expressions (parse trees), and ordered data (BST). In code, recursion is natural: do something at this node, then recurse on children.
Key Takeaways
1
Tree: Hierarchical, acyclic; one root, each node has one parent2
Root: Top node; leaf: no children; internal: has children3
Depth: Edges root → node; height: max depth in subtree4
Recursion: Base case = null or leaf; recurse on children5
Use cases: File systems, DOM, org charts, parse trees6
Common pitfall: Forgetting null checks on children7
Senior takeaway: Most tree problems are "visit + recurse"Visual Diagram
┌─────────────────────────────────────────────────────────┐ │ Tree Terminology │ ├─────────────────────────────────────────────────────────┤ │ (root) depth 0 │ │ / \ │ │ (node) (node) depth 1 siblings │ │ / \ \ │ │ (node) (leaf) (leaf) depth 2 │ │ | │ │ (leaf) depth 3 height of root = 3 │ │ │ │ Path: root → ... → node (unique, no cycles) │ │ Subtree: node + all descendants │ └─────────────────────────────────────────────────────────┘