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  2. Tree traversal - Wikipedia

    en.wikipedia.org/wiki/Tree_traversal

    Note that the function does not use keys, which means that the sequential structure is completely recorded by the binary search tree’s edges. For traversals without change of direction, the ( amortised ) average complexity is O ( 1 ) , {\displaystyle {\mathcal {O}}(1),} because a full traversal takes 2 n − 2 {\displaystyle 2n-2} steps for a ...

  3. Tree sort - Wikipedia

    en.wikipedia.org/wiki/Tree_sort

    Adding one item to a binary search tree is on average an O(log n) process (in big O notation). Adding n items is an O ( n log n ) process, making tree sorting a 'fast sort' process. Adding an item to an unbalanced binary tree requires O ( n ) time in the worst-case: When the tree resembles a linked list ( degenerate tree ).

  4. Binary search - Wikipedia

    en.wikipedia.org/wiki/Binary_search

    Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...

  5. 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.

  6. Geometry of binary search trees - Wikipedia

    en.wikipedia.org/wiki/Geometry_of_binary_search...

    The cost of a search is modeled by assuming that the search tree algorithm has a single pointer into a binary search tree, which at the start of each search points to the root of the tree. The algorithm may then perform any sequence of the following operations: Move the pointer to its left child. Move the pointer to its right child.

  7. Order statistic tree - Wikipedia

    en.wikipedia.org/wiki/Order_statistic_tree

    In computer science, an order statistic tree is a variant of the binary search tree (or more generally, a B-tree [1]) that supports two additional operations beyond insertion, lookup and deletion: Select( i ) – find the i -th smallest element stored in the tree

  8. B-tree - Wikipedia

    en.wikipedia.org/wiki/B-tree

    Searching is similar to searching a binary search tree. Starting at the root, the tree is recursively traversed from top to bottom. At each level, the search reduces its field of view to the child pointer (subtree) whose range includes the search value. A subtree's range is defined by the values, or keys, contained in its parent node.

  9. Optimal binary search tree - Wikipedia

    en.wikipedia.org/wiki/Optimal_binary_search_tree

    In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, [1] is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities). Optimal BSTs are generally divided into two types: static and dynamic.