Can you explain what a red-black tree is and how it works in the context of data balancing?

Red-Black Tree is a self-balancing binary search tree that ensures approximately uniform distribution of subtree heights, guaranteeing search, insertion, and deletion operations in O(log n) time.

Main properties of a red-black tree:

• Each node is colored either red or black.
• The root is always black.
• All leaves (NULL nodes) are considered black.
• If a node is red, then both its children are black (no two reds in a row).
• For each node, all paths to the leaves contain the same number of black nodes.

These rules ensure the tree remains balanced, preventing overly deep branches. During insertion or deletion of nodes, recoloring and rotations are performed to maintain the tree's properties.

Example of usage: In Java, the TreeMap class implements a red-black tree for storing key-value pairs with ordered access and efficient search.