# Left Leaning Red Black Tree

## Definition

A BST such that:

* No node has two red links connected to it.
* Every path from root to null link has the same number of black links.
* Red links lean left.

![](/files/jyzV0BE442PvisZ5k0MM)

![](/files/jGeyLUXa6cPHFoNuFuQM)

{% hint style="success" %}

#### Properties

* Height of tree is ≤ 2 lg N in the worst case.
* Every path from root to null link has same number of black links.
* Never two red links in-a-row.
  {% endhint %}

## **Sample Red Black Tree with 255 Random Nodes**

![](/files/FM2qWZVrekNDpdMadQTl)

## **Balancing Red Black Tree**

![](/files/N6aID2kVit4EN6JultvU)

## **Complexity Analysis with other Data Structures**

![](/files/7IIf2gSTVoPHqQSmXnUF)


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