What is a red-black tree?

A red-black tree is a self-balancing binary search tree that maintains balance by using a set of rules and properties. It is named after the color assigned to each node in the tree, which can be either red or black.

The main properties of a red-black tree are as follows:

1. Every node is either red or black.
2. The root node is always black.
3. Every leaf (null node) is considered black.
4. If a node is red, both its children are black.
5. Every path from a node to its descendant leaves contains an equal number of black nodes. This property is known as the black height.

These properties ensure that the longest path from the root to any leaf is no more than twice the length of the shortest path, which helps maintain a balanced tree structure.

Red-black trees support efficient insertion, deletion, and search operations with a worst-case time complexity of O(log n), where n is the number of nodes in the tree. The self-balancing nature of red-black trees makes them suitable for applications where frequent modifications to the tree structure are expected.

Overall, red-black trees provide a balanced and efficient data structure for storing and retrieving data in a sorted manner.