In computer science, an AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations.
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. The time complexity of operations on the binary search tree is directly proportional to the height of the tree.
In computer science, a binary tree is a k-ary tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well.
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and file systems.
In computer science, a red–black tree is a specialised binary search tree data structure noted for fast storage and retrieval of ordered information, and a guarantee that operations will complete within a known time. Compared to other self-balancing binary search trees, the nodes in a red-black tree hold an extra bit called "color" representing "red" and "black" which is used when re-organising the tree to ensure that it is always approximately balanced.
In computer science, a trie, also called digital tree or prefix tree, is a type of k-ary search tree, a tree data structure used for locating specific keys from within a set. These keys are most often strings, with links between nodes defined not by the entire key, but by individual characters. In order to access a key, the trie is traversed depth-first, following the links between nodes, which represent each character in the key.
In computer science, the treap and the randomized binary search tree are two closely related forms of binary search tree data structures that maintain a dynamic set of ordered keys and allow binary searches among the keys. After any sequence of insertions and deletions of keys, the shape of the tree is a random variable with the same probability distribution as a random binary tree; in particular, with high probability its height is proportional to the logarithm of the number of keys, so that each search, insertion, or deletion operation takes logarithmic time to perform.
In computer science, tree traversal is a form of graph traversal and refers to the process of visiting each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well.
In computer science, a suffix tree is a compressed trie containing all the suffixes of the given text as their keys and positions in the text as their values. Suffix trees allow particularly fast implementations of many important string operations.
In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets, and finding a representative member of a set. The last operation makes it possible to find out efficiently if any two elements are in the same or different sets.
In computer science, a scapegoat tree is a self-balancing binary search tree, invented by Arne Andersson in 1989 and again by Igal Galperin and Ronald L. Rivest in 1993. It provides worst-case lookup time and amortized insertion and deletion time.
In computer science, an interval tree is a tree data structure to hold intervals. Specifically, it allows one to efficiently find all intervals that overlap with any given interval or point. It is often used for windowing queries, for instance, to find all roads on a computerized map inside a rectangular viewport, or to find all visible elements inside a three-dimensional scene. A similar data structure is the segment tree.
An AA tree in computer science is a form of balanced tree used for storing and retrieving ordered data efficiently. AA trees are named after their originator, Swedish computer scientist Arne Andersson.
In computer science, a k-d tree is a space-partitioning data structure for organizing points in a k-dimensional space. k-d trees are a useful data structure for several applications, such as searches involving a multidimensional search key and creating point clouds. k-d trees are a special case of binary space partitioning trees.
In computer science, weight-balanced binary trees (WBTs) are a type of self-balancing binary search trees that can be used to implement dynamic sets, dictionaries (maps) and sequences. These trees were introduced by Nievergelt and Reingold in the 1970s as trees of bounded balance, or BB[α] trees. Their more common name is due to Knuth.
A tango tree is a type of binary search tree proposed by Erik D. Demaine, Dion Harmon, John Iacono, and Mihai Pătrașcu in 2004. It is named after Buenos Aires, of which the tango is emblematic.
A Fenwick tree or binary indexed tree(BIT) is a clever implementation of a datastructure called bionomal tree. It can update values and solve range queries [l,r] with operations that is; commulative, associative and has an inverse for this type of element. It can also solve inmutable range queries [0,r] (min/max), when operations only are associative over this type of element. Some of these restrictions can be removed, by storing redunant information; like in max/min range queries.
In computer science, an x-fast trie is a data structure for storing integers from a bounded domain. It supports exact and predecessor or successor queries in time O(log log M), using O(n log M) space, where n is the number of stored values and M is the maximum value in the domain. The structure was proposed by Dan Willard in 1982, along with the more complicated y-fast trie, as a way to improve the space usage of van Emde Boas trees, while retaining the O(log log M) query time.
In computer science, a ball tree, balltree or metric tree, is a space partitioning data structure for organizing points in a multi-dimensional space. A ball tree partitions data points into a nested set of balls. The resulting data structure has characteristics that make it useful for a number of applications, most notably nearest neighbor search.
In computer science, the list-labeling problem involves maintaining a totally ordered set S supporting the following operations:
