How do red-black trees work and what are their operations?

Can you explain how red-black trees work?

Sure! Red-black trees are a type of self-balancing binary search tree. Each node has a color (red or black) and they maintain balance through specific properties.

What are the properties that define a red-black tree?

The properties include: 1) Each node is either red or black, 2) The root is always black, 3) Red nodes cannot have red children, 4) Every path from a node to its descendant leaves has the same number of black nodes.

Can you show me how to perform insertion in a red-black tree?

Absolutely! When inserting, you first add the node like in a regular binary search tree, then you fix any violations of the red-black properties through rotations and recoloring.

What about deletion? How does that work?

Deletion is a bit more complex. You remove the node like in a binary search tree, then you may need to perform rotations and recoloring to maintain the red-black properties.