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  2. Red–black tree - Wikipedia

    en.wikipedia.org/wiki/Redblack_tree

    The persistent version of redblack trees requires (⁡) space for each insertion or deletion, in addition to time. For every 2–3–4 tree, there are corresponding redblack trees with data elements in the same order. The insertion and deletion operations on 2–3–4 trees are also equivalent to color-flipping and rotations in red ...

  3. Tree rotation - Wikipedia

    en.wikipedia.org/wiki/Tree_rotation

    A double left rotation at X can be defined to be a right rotation at the right child of X followed by a left rotation at X; similarly, a double right rotation at X can be defined to be a left rotation at the left child of X followed by a right rotation at X. Tree rotations are used in a number of tree data structures such as AVL trees, red ...

  4. Self-balancing binary search tree - Wikipedia

    en.wikipedia.org/wiki/Self-balancing_binary...

    Self-balancing binary trees solve this problem by performing transformations on the tree (such as tree rotations) at key insertion times, in order to keep the height proportional to log 2 (n). Although a certain overhead is involved, it is not bigger than the always necessary lookup cost and may be justified by ensuring fast execution of all ...

  5. AVL tree - Wikipedia

    en.wikipedia.org/wiki/AVL_tree

    It is the first self-balancing binary search tree data structure to be invented. [3] AVL trees are often compared with redblack trees because both support the same set of operations and take (⁡) time for the basic operations.

  6. Left-leaning red–black tree - Wikipedia

    en.wikipedia.org/wiki/Left-leaning_redblack_tree

    A left-leaning red-black tree satisfies all the properties of a red-black tree: Every node is either red or black. A NIL node is considered black. A red node does not have a red child. Every path from a given node to any of its descendant NIL nodes goes through the same number of black nodes. The root is black (by convention).

  7. Rotation distance - Wikipedia

    en.wikipedia.org/wiki/Rotation_distance

    The rotation distance between the two trees is the number of rotations in the shortest possible sequence of rotations that performs this transformation. It can also be described as the shortest path distance in a rotation graph , a graph that has a vertex for each binary tree on a given left-to-right sequence of nodes and an edge for each ...

  8. Left rotation - Wikipedia

    en.wikipedia.org/wiki/Left_rotation

    AVL trees and redblack trees are two examples of binary search trees that use the left rotation. A single left rotation is done in O(1) time but is often integrated within the node insertion and deletion of binary search trees. The rotations are done to keep the cost of other methods and tree height at a minimum.

  9. Binary search tree - Wikipedia

    en.wikipedia.org/wiki/Binary_search_tree

    Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.