## Introduction:

A red-black tree is a form of a self-balancing binary seek tree in which each node has a further bit, and that bit is regularly interpreted because of the coloration (crimson or black). Those colors are used to make sure that the tree remains balanced, all through insertions and deletions. Even though the balance of the tree isn't always the best, it is ideal to reduce the looking time and hold it around o(log n) time, where n is the total quantity of factors in the tree. This tree was invented in 1972 with the aid of Rudolf Bayer. As each node requires the handiest one little bit of area to store the coloration records, these kinds of bushes show an equal reminiscence footprint to the conventional (uncolored) binary seek tree. In this article, We will talk about the Red-Black Tree, we will compare it with the AVL tree, and we will see how various operations work in the Red-Black tree-like searching. Finally, we will discuss the application of the Red-Black Tree.

## What are Red-Black trees?

Red-Black trees are a type of self-balancing binary search tree. They are designed to maintain balance and ensure efficient operations, such as insertion, deletion, and search, even in the worst-case scenarios. Red-Black trees are named after the color of their nodes, which can be either red or black.

When inserting or deleting a node, the tree may become unbalanced, violating one or more of the Red-Black tree properties. To restore the balance, the tree performs rotations and recoloring of nodes. There are two types of rotations:

1. Left Rotation: Performed when the right child of a node is red, and its left child is black.

2. Right Rotation: Performed when the left child of a node is red, and its left child's left child is also red.

Recoloring involves changing the color of nodes to maintain the Red-Black tree properties. It is done in conjunction with rotations to rebalance the tree.

The time complexity of basic operations (insertion, deletion, and search) in a Red-Black tree is O(log n), where n is the number of nodes in the tree. This is because the tree maintains its balance, ensuring that the height of the tree is always logarithmic.

Red-Black trees are widely used in various applications and libraries that require efficient sorting, searching, and maintaining ordered data.

Some common examples are:

1. The Java TreeMap and TreeSet classes

2. The C++ STL map and set associative containers

3. The Linux kernel's Completely Fair Scheduler (CFS)

4. The Nginx HTTP server's timer implementation