Explain Left Leaning Red Black Trees. What are their advantages and disadvantages?

What is a Left-Leaning Red–Black Tree?

A Left-Leaning Red–Black Tree (LLRB) is a simplified form of a Red–Black Tree that enforces an additional rule:
all red links must lean left.

LLRB trees were introduced to make red–black trees easier to implement and reason about, while still maintaining balanced binary search tree properties.

Conceptually, an LLRB tree represents a 2–3 tree using a binary tree structure.

Basic Idea

• Red links represent the connection between two keys in a 3-node of a 2–3 tree.
• Black links represent normal parent–child links.
• Red links are allowed only as left child links, never as right child links.

Properties of LLRB Trees

1. Each node is either red or black
2. Root is always black
3. No node has two red links connected to it – No red node can have a red child
4. Red links lean left  – Right-leaning red links are not allowed
5. Every path from root to a NULL link has the same number of black links – Ensures tree balance

Operations in LLRB Trees

To maintain the properties, LLRB trees use:

1. Left Rotation – Fixes right-leaning red links

2. Right Rotation – Fixes two consecutive left-leaning red links

3. Color Flipping – Splits temporary 4-nodes

These operations are applied during insertion and deletion.

Why “Left-Leaning”?

In standard Red–Black Trees: Red links can lean left or right

In LLRB Trees:

• Only left-leaning red links are allowed
• This restriction simplifies balancing logic

Advantages of LLRB Trees

1. Simpler implementation
   • Fewer cases compared to classical red–black trees
   • Easier to code correctly
2. Guaranteed balance
   • Height ≤ 2 × log₂(n)
   • Ensures O(log n) search, insert, delete
3. Direct correspondence with 2–3 trees – Easier theoretical understanding
4. Good practical performance – Comparable to standard red–black trees

Disadvantages of LLRB Trees

1. More restrictive – Right-leaning red links disallowed even if they could be valid
2. Slightly more rotations – Enforcing left-leaning rule may cause extra rotations
3. Less flexible than standard Red–Black Trees – Classical RB trees allow both left and right red links
4. Not ideal for some specialized optimizations – Fewer balancing choices compared to general RB trees