AVL treeIn computer science, an AVL tree (named after inventors Adelson-Velsky and Landis) 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.
Binary treeIn 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 and the . 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. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences.
Self-balancing binary search treeIn computer science, a self-balancing binary search tree (BST) is any node-based binary search tree that automatically keeps its height (maximal number of levels below the root) small in the face of arbitrary item insertions and deletions. These operations when designed for a self-balancing binary search tree, contain precautionary measures against boundlessly increasing tree height, so that these abstract data structures receive the attribute "self-balancing".
Red–black treeIn 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.
Tree rotationIn discrete mathematics, tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements. A tree rotation moves one node up in the tree and one node down. It is used to change the shape of the tree, and in particular to decrease its height by moving smaller subtrees down and larger subtrees up, resulting in improved performance of many tree operations. There exists an inconsistency in different descriptions as to the definition of the direction of rotations.
Linked listIn computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes which together represent a sequence. In its most basic form, each node contains data, and a reference (in other words, a link) to the next node in the sequence. This structure allows for efficient insertion or removal of elements from any position in the sequence during iteration.
Splay treeA splay tree is a binary search tree with the additional property that recently accessed elements are quick to access again. Like self-balancing binary search trees, a splay tree performs basic operations such as insertion, look-up and removal in O(log n) amortized time. For random access patterns drawn from a non-uniform random distribution, their amortized time can be faster than logarithmic, proportional to the entropy of the access pattern.
Time complexityIn computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.
Heap (data structure)In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: In a max heap, for any given node C, if P is a parent node of C, then the key (the value) of P is greater than or equal to the key of C. In a min heap, the key of P is less than or equal to the key of C. The node at the "top" of the heap (with no parents) is called the root node. The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented.
Set (abstract data type)In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed.
Tree (data structure)In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal.
Binary search algorithmIn computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found.
B-treeIn 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 s. B-trees were invented by Rudolf Bayer and Edward M.
Persistent data structureIn computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjans' 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified.
T-treeIn computer science a T-tree is a type of binary tree data structure that is used by main-memory databases, such as Datablitz, eXtremeDB, MySQL Cluster, Oracle TimesTen and MobileLite. A T-tree is a balanced index tree data structure optimized for cases where both the index and the actual data are fully kept in memory, just as a B-tree is an index structure optimized for storage on block oriented secondary storage devices like hard disks.
Best, worst and average caseIn computer science, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n.
Tree (graph theory)In graph theory, a tree is an undirected graph in which any two vertices are connected by path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree.
Join-based tree algorithmsIn computer science, join-based tree algorithms are a class of algorithms for self-balancing binary search trees. This framework aims at designing highly-parallelized algorithms for various balanced binary search trees. The algorithmic framework is based on a single operation join. Under this framework, the join operation captures all balancing criteria of different balancing schemes, and all other functions join have generic implementation across different balancing schemes.
Associative arrayIn computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. It supports 'lookup', 'remove', and 'insert' operations. The dictionary problem is the classic problem of designing efficient data structures that implement associative arrays.
Sorting algorithmIn computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.
