# An introduction to binary search and red-black trees

Because a red-black tree is a binary search tree and operations that don't change the structure of a tree won't affect whether the tree satisfies the red-black tree properties, the lookup and print operations are identical to lookup and print for binary search trees. This step is O 1 since it just requires setting the value of one node's color field. Once a restructuring is done, the double-red situation has been an introduction to binary search and red-black trees and there's nothing more to do you should convince yourself, by looking at the diagrams above, that restructuring will not result in a violation of the black property.

Red-black trees are binary search trees that store one additional piece of information in each node the node's color and satisfy three properties. If we were to use external nodes in a binary search an introduction to binary search and red-black trees, then the children of a leaf node would be external nodes and not nullthat is:. While the lookup method is identical for binary search trees and red-black trees, the insert and delete methods are more complicated for red-black trees.

Changing the colors of nodes during recoloring is O 1. P 's sibling S is red. Recall that the BST insert algorithm always adds a leaf node.

If T is empty, replace it with a single black node with black external nodes containing K. In fixing a red property violation, we will need to make sure that we don't end up with a tree that violates the root or black properties. Once a restructuring is done, the insert algorithm is done, so at most 1 restructuring is done in step 3.

The important idea behind all of these trees is that the insert and delete operations may restructure the tree to keep it balanced. While the lookup method is identical for binary search trees and red-black trees, the insert and delete methods are more complicated for red-black trees. The insert method initially performs the same insert algorithm as is done in binary search trees and an introduction to binary search and red-black trees must perform steps to restore the red-black tree properties through restructuring and recoloring.