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  2. AVL tree - Wikipedia

    en.wikipedia.org/wiki/AVL_tree

    To split an AVL tree into two smaller trees, those smaller than key k, and those greater than key k, first draw a path from the root by inserting k into the AVL. After this insertion, all values less than k will be found on the left of the path, and all values greater than k will be found on the right.

  3. Join-based tree algorithms - Wikipedia

    en.wikipedia.org/wiki/Join-based_tree_algorithms

    Join follows the right spine of t 1 until a node c which is balanced with t 2. 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 ...

  4. List of data structures - Wikipedia

    en.wikipedia.org/wiki/List_of_data_structures

    AA tree; AVL tree; Binary search tree; Binary tree; Cartesian tree; Conc-tree list; Left-child right-sibling binary tree; Order statistic tree; Pagoda; Randomized binary search tree; Red–black tree; Rope; Scapegoat tree; Self-balancing binary search tree; Splay tree; T-tree; Tango tree; Threaded binary tree; Top tree; Treap; WAVL tree; Weight ...

  5. WAVL tree - Wikipedia

    en.wikipedia.org/wiki/WAVL_tree

    The weak AVL tree is defined by the weak AVL rule: Weak AVL rule: all rank differences are 1 or 2, and all leaf nodes have rank 0. Note that weak AVL tree generalizes the AVL tree by allowing for 2,2 type node. A simple proof shows that a weak AVL tree can be colored in a way that represents a red-black tree.

  6. List of graph theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_graph_theory_topics

    Abstract syntax tree; B-tree; Binary tree. Binary search tree. Self-balancing binary search tree. AVL tree; Red–black tree; Splay tree; T-tree; Binary space partitioning

  7. 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 ...

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  9. Weight-balanced tree - Wikipedia

    en.wikipedia.org/wiki/Weight-balanced_tree

    A weight-balanced tree is a binary search tree that stores the sizes of subtrees in the nodes. That is, a node has fields key, of any ordered type; value (optional, only for mappings) left, right, pointer to node; size, of type integer. By definition, the size of a leaf (typically represented by a nil pointer) is zero.