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  2. Tree rotation - Wikipedia

    en.wikipedia.org/wiki/Tree_rotation

    The tree rotation renders the inorder traversal of the binary tree invariant. This implies the order of the elements is not affected when a rotation is performed in any part of the tree. Here are the inorder traversals of the trees shown above: Left tree: ((A, P, B), Q, C) Right tree: (A, P, (B, Q, C))

  3. AVL tree - Wikipedia

    en.wikipedia.org/wiki/AVL_tree

    Both AVL trees and red–black (RB) trees are self-balancing binary search trees and they are related mathematically. Indeed, every AVL tree can be colored red–black, [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.

  4. Left rotation - Wikipedia

    en.wikipedia.org/wiki/Left_rotation

    AVL trees and red–black 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.

  5. Right rotation - Wikipedia

    en.wikipedia.org/wiki/Right_rotation

    AVL trees and red–black trees are two examples of binary search trees that use a right rotation. A single right 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.

  6. Day–Stout–Warren algorithm - Wikipedia

    en.wikipedia.org/wiki/Day–Stout–Warren_algorithm

    First, the tree is turned into a linked list by means of an in-order traversal, reusing the pointers in the tree's nodes. A series of left-rotations forms the second phase. [ 3 ] The Stout–Warren modification generates a complete binary tree, namely one in which the bottom-most level is filled strictly from left to right.

  7. Join-based tree algorithms - Wikipedia

    en.wikipedia.org/wiki/Join-based_tree_algorithms

    At this point a new node with left child c, root k and right child t 2 is created to replace c. The new node may invalidate the balancing invariant. This can be fixed with rotations. The following is the join algorithms on different balancing schemes. The join algorithm for AVL trees:

  8. Self-balancing binary search tree - Wikipedia

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

    Most operations on a binary search tree (BST) take time directly proportional to the height of the tree, so it is desirable to keep the height small. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:

  9. Tree (abstract data type) - Wikipedia

    en.wikipedia.org/wiki/Tree_(abstract_data_type)

    Trees can be used to represent and manipulate various mathematical structures, such as: Paths through an arbitrary node-and-edge graph (including multigraphs), by making multiple nodes in the tree for each graph node used in multiple paths; Any mathematical hierarchy; Tree structures are often used for mapping the relationships between things ...