What is a binary tree?

A binary tree is a hierarchical data structure where each node has at most two children, referred to as the left child and the right child. Terminology: Root — top node with no parent; Leaf — node with no children; Internal node — node with at least one child; Height — longest path from root to leaf; Depth — length of path from root to a node; Subtree — a node and all its descendants. Types: Full binary tree — every node has 0 or 2 children; Complete binary tree — all levels filled except possibly the last, filled left to right; Perfect binary tree — all internal nodes have 2 children, all leaves at same depth; Balanced binary tree — height is O(log n); Degenerate/skewed tree — every node has only one child (like a linked list, O(n) height). Properties of a perfect binary tree with height h: nodes = 2^(h+1) - 1, leaves = 2^h. Binary trees are the basis for BSTs, heaps, tries, segment trees, and expression trees.