What are the properties of a red-black tree?

What are the properties of a red-black tree?

A red-black tree is a balanced binary search tree with specific properties: 1) Each node is either red or black. 2) The root is always black. 3) All leaves (NIL nodes) are black. 4) If a red node has children, they must be black. 5) Every path from a node to its descendant leaves has the same number of black nodes.

Why is it important for a tree to be balanced?

Balancing a tree ensures that operations like insertion, deletion, and lookup can be performed in logarithmic time, which is efficient. An unbalanced tree can degrade to a linked list, leading to O(n) time complexity.

Can you explain how insertion works in a red-black tree?

Sure! Insertion in a red-black tree involves adding a new node like in a regular binary search tree, then coloring it red. After that, we may need to perform rotations and recoloring to maintain the red-black properties.

What are the advantages of using a red-black tree over other types of trees?

Red-black trees provide good performance for dynamic sets and associative arrays. They guarantee O(log n) time for insertion, deletion, and lookup, making them efficient for many applications.