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  2. Scapegoat tree - Wikipedia

    en.wikipedia.org/wiki/Scapegoat_tree

    In computer science, a scapegoat tree is a self-balancing binary search tree, invented by Arne Andersson [2] in 1989 and again by Igal Galperin and Ronald L. Rivest in 1993. [1] It provides worst-case O ( log ⁡ n ) {\displaystyle {\color {Blue}O(\log n)}} lookup time (with n {\displaystyle n} as the number of entries) and O ( log ⁡ n ...

  3. Self-balancing binary search tree - Wikipedia

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

    Binary tree sort, in particular, is likely to be slower than merge sort, quicksort, or heapsort, because of the tree-balancing overhead as well as cache access patterns.) Self-balancing BSTs are flexible data structures, in that it's easy to extend them to efficiently record additional information or perform new operations.

  4. AVL tree - Wikipedia

    en.wikipedia.org/wiki/AVL_tree

    This traversal is guided by the comparison function. In this case, the node always replaces a NULL reference (left or right) of an external node in the tree i.e., the node is either made a left-child or a right-child of the external node. After this insertion, if a tree becomes unbalanced, only ancestors of the newly inserted node are unbalanced.

  5. File:An example of an unrooted binary tree with four leaves.pdf

    en.wikipedia.org/wiki/File:An_example_of_an_un...

    Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

  6. Binary tree - Wikipedia

    en.wikipedia.org/wiki/Binary_tree

    A tree whose root node has two subtrees, both of which are full binary trees. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a node). [18] A perfect binary tree is a full ...

  7. Tree sort - Wikipedia

    en.wikipedia.org/wiki/Tree_sort

    A tree sort is a sort algorithm that builds a binary search tree from the elements to be sorted, and then traverses the tree so that the elements come out in sorted order. [1] Its typical use is sorting elements online : after each insertion, the set of elements seen so far is available in sorted order.

  8. Red–black tree - Wikipedia

    en.wikipedia.org/wiki/Red–black_tree

    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. [1] When the tree is modified, the new tree is rearranged and "repainted" to restore the coloring properties that constrain how unbalanced the tree can become in the worst case.

  9. Euler tour technique - Wikipedia

    en.wikipedia.org/wiki/Euler_tour_technique

    Henzinger and King [2] suggest to represent a given tree by keeping its Euler tour in a balanced binary search tree, keyed by the index in the tour. So for example, the unbalanced tree in the example above, having 7 nodes, will be represented by a balanced binary tree with 14 nodes, one for each time each node appears on the tour.