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LLRB is a Left-Leaning Red-Black (LLRB) implementation of 2–3 balanced binary search trees in Python. This is a straightforward port of the code presented by Robert Sedgewick in his paper.


A balanced binary search tree (BBST) maintains elements in sorted order under dynamic updates (inserts and deletes) and can support various order-specific queries.

Red-black trees are the de facto standard BBST algorithms, and are the underlying data structure for symbol-table implementations within C++, Java, Python, BSD Unix, Linux and many other modern systems.

All red–black trees are based on implementing 2-3 or 2-3-4 trees within a binary tree, using red links to bind together internal nodes into 3-nodes or 4-nodes. Search, insert and delete operations are O(log n) and space requirements are O(n).

However, many traditional implementations have lots of repetitive code on the symmetric branches of rotation and deletion operations. So they are not easy to reason about and augment with other properties, which is what BBST's are often used for: They are used to implement other common data structures like Priority Queues and Interval Trees.

The LLRB method of implementing 2-3 trees is a recent improvement over the traditional implementation — it maintains an additional invariant that all red links must lean left except during inserts and deletes. Because of this, they can be implemented by adding just a few lines of code to standard BST algorithms.

The LLRB tree is based on combining three ideas:

  • Use a recursive implementation.
  • Require that all 3-nodes lean left.
  • Perform rotations on the way up the tree (after the recursive calls).

The LLRB approach was discovered relatively recently (in 2008) by Robert Sedgewick of Princeton University. For original code and more information read the paper "Left-leaning Red-Black Trees" at


From Python package index:

pip install leftrb

or from Github source:

git clone
cd leftrb 
python install


Leftrb/LLRB was written by Peter Hillerström.

Follow me on Twitter @peterhil!

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