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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: Both operations can be performed in O(log n) worst case time when a self-balancing tree is used as the base data structure.
Mathematical terminology. Viewed as a whole, a tree data structure is an ordered tree, generally with values attached to each node. Concretely, it is (if required to be non-empty): A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning:
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.
A binary tree may thus be also called a bifurcating arborescence, [3] a term which appears in some early programming books [4] before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than directed graph, in which case a binary tree is an ordered, rooted tree. [5]
A rooted tree T that is a subgraph of some graph G is a normal tree if the ends of every T-path in G are comparable in this tree-order (Diestel 2005, p. 15). Rooted trees, often with an additional structure such as an ordering of the neighbors at each vertex, are a key data structure in computer science; see tree data structure.
Tree traversal. In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
According to Knuth's definition, a B-tree of order m is a tree which satisfies the following properties: [7] Every node has at most m children. Every node, except for the root and the leaves, has at least ⌈m/2⌉ children. The root node has at least two children unless it is a leaf. All leaves appear on the same level.
In computer science, a red–black 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.