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  2. Red–black tree - Wikipedia

    en.wikipedia.org/wiki/Redblack_tree

    In computer science, a redblack tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, which help ensure that the tree is always approximately balanced.

  3. WAVL tree - Wikipedia

    en.wikipedia.org/wiki/WAVL_tree

    In AVL trees, each deletion may require a logarithmic number of tree rotation operations, while redblack trees have simpler deletion operations that use only a constant number of tree rotations. WAVL trees, like redblack trees, use only a constant number of tree rotations, and the constant is even better than for redblack trees. [1] [2]

  4. 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).

  5. AVL tree - Wikipedia

    en.wikipedia.org/wiki/AVL_tree

    Both AVL trees and redblack (RB) trees are self-balancing binary search trees and they are related mathematically. Indeed, every AVL tree can be colored redblack, [14] but there are RB trees which are not AVL balanced. For maintaining the AVL (or RB) tree's invariants, rotations play an important role.

  6. 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.

  7. 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 ...

  8. AA tree - Wikipedia

    en.wikipedia.org/wiki/AA_tree

    AA trees are named after their originator, Swedish computer scientist Arne Andersson. [1] AA trees are a variation of the redblack tree, a form of binary search tree which supports efficient addition and deletion of entries. Unlike redblack trees, red nodes on an AA tree can only be added as a right subchild.

  9. Binary search tree - Wikipedia

    en.wikipedia.org/wiki/Binary_search_tree

    Various height-balanced binary search trees were introduced to confine the tree height, such as AVL trees, Treaps, and redblack trees. [5] The AVL tree was invented by Georgy Adelson-Velsky and Evgenii Landis in 1962 for the efficient organization of information. [6] [7] It was the first self-balancing binary search tree to be invented. [8]