Balanced Binary Trees: Why Balance Is Needed and A Simple Explanation of Rotation Operations

Binary Search Trees (BST) may degenerate into linked lists due to extreme insertions, causing operation complexity to rise to O(n). Balanced binary trees control balance through the **balance factor** (the height difference between the left and right subtrees of a node), requiring a balance factor of -1, 0, or 1. When unbalanced, **rotation operations** (LL right rotation, RR left rotation, LR left rotation followed by right rotation, RL right rotation followed by left rotation) are used to adjust the structure, keeping the tree height at a logarithmic level (log n) and ensuring that operations such as search, insertion, and deletion maintain a stable complexity of O(log n). Rotations essentially adjust the pivot point to restore the balanced structure of the tree.