Red-Black Trees: A Type of Balanced Binary Tree, Understanding Its Rules Simply
A red-black tree is a self-balancing binary search tree that ensures balance through color marking and five rules, resulting in stable insertion, deletion, and search complexities of O(log n). The core rules are: nodes are either red or black; the root is black; empty leaves (NIL) are black; red nodes must have black children (to avoid consecutive red nodes); and the number of black nodes on any path from a node to its descendant NIL leaves (black height) is consistent. Rule 4 prevents consecutive red nodes, while Rule 5 ensures equal black heights, together limiting the tree height to O(log n). Newly inserted nodes are red, and adjustments (color changes or rotations) are performed if the parent is red. Widely used in Java TreeMap and Redis sorted sets, it enables efficient ordered operations through its balanced structure.
Read MoreBalanced 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.
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