Red-Black Trees

Question

I\'ve seen binary trees and binary searching mentioned in several books I\'ve read lately, but as I\'m still at the beginning of my studies in Computer Science, I\'ve yet to

Answer 1

Since you ask which tree people use, you need to know that a Red Black tree is fundamentally a 2-3-4 B-tree (i.e a B-tree of order 4). A B-tree is not equivalent to a binary tree(as asked in your question).

Here's an excellent resource describing the initial abstraction known as the symmetric binary B-tree that later evolved into the RBTree. You would need a good grasp on B-trees before it makes sense. To summarize: a 'red' link on a Red Black tree is a way to represent nodes that are part of a B-tree node (values within a key range), whereas 'black' links are nodes that are connected vertically in a B-tree.

So, here's what you get when you translate the rules of a Red Black tree in terms of a B-tree (I'm using the format Red Black tree rule => B Tree equivalent):

1) A node is either red or black. => A node in a b-tree can either be part of a node, or as a node in a new level.

2) The root is black. (This rule is sometimes omitted, since it doesn't affect analysis) => The root node can be thought of either as a part of an internal root node as a child of an imaginary parent node.

3) All leaves (NIL) are black. (All leaves are same color as the root.) => Since one way of representing a RB tree is by omitting the leaves, we can rule this out.

4)Both children of every red node are black. => The children of an internal node in a B-tree always lie on another level.

5)Every simple path from a given node to any of its descendant leaves contains the same number of black nodes. => A B-tree is kept balanced as it requires that all leaf nodes are at the same depth (Hence the height of a B-tree node is represented by the number of black links from the root to the leaf of a Red Black tree)

Also, there's a simpler 'non-standard' implementation by Robert Sedgewick here: (He's the author of the book Algorithms along with Wayne)