FAANG Interview Binary Tree
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What is a Binary Tree?
Introduction
A binary tree is a hierarchical data structure in which each node has at most two children — commonly called the left and the right child. It's used widely for efficient search, insert, delete and traversal operations in algorithms and interviews.
Key Characteristics of a Binary Tree
- Node: Element with value and up to two children.
- Root: Top node and entry point.
- Children: Left and right nodes connected to parent.
- Leaf: Node without children.
- Subtree: Any node plus its descendants.
Types of Binary Trees
- Full Binary Tree: Each node has 0 or 2 children.
- Perfect Binary Tree: All leaves have same depth; all internal nodes have two children.
- Complete Binary Tree: All levels filled except possibly last (left-packed).
- Balanced Binary Tree: Heights of subtrees differ by ≤ 1 for every node.
- Binary Search Tree (BST): Left < node < right ordering property.
Operations on a Binary Tree
- Insertion: Place nodes per tree rules (BST differs).
- Deletion: Remove node and re-link tree.
- Traversal: In-order, Pre-order, Post-order (DFS variants), Level-order (BFS).
Applications
Binary trees underpin many data structures & algorithms — BSTs for searching, heaps for priority queues, syntax trees for compilers, and tries (prefix trees) for text processing.
Master traversal techniques (recursive & iterative), understand tree shapes and invariants (BST, balanced conditions) and practice common interview problems.
DFS vs BFS — quick intuition
DFS (pre/in/post order) explores depth first — recursion or stack. BFS (level-order) uses a queue and processes nodes by level. In interviews, choose method based on required ordering and constraints.
Level-Order Traversal (Iterative / Queue) — Intuition
- Use a queue of TreeNode: push root initially.
- While queue not empty: get size of level, iterate that many nodes, pop and push children; process nodes in that loop to get per-level results.
Common Problems to Practice
- BST search / insert / delete — use BST property to optimize.
- Path sum / root-to-leaf — recursion and backtracking practice.
- Lowest Common Ancestor — iterative and recursive patterns.
- View & level problems — right/left side view, vertical order.