In computer science, heapsort is a comparison-based sorting algorithm which can be thought of as "an implementation of selection sort using the right data structure." Like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. Unlike selection sort, heapsort does not waste time with a linear-time scan of the unsorted region; rather, heap sort maintains the unsorted region in a heap data structure to efficiently find the largest element in each step.
In computer science, a heap is a 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 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 is called the root node.
In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure. Each element in a priority queue has an associated priority. In a priority queue, elements with high priority are served before elements with low priority. In some implementations, if two elements have the same priority, they are served in the same order in which they were enqueued. In other implementations, the order of elements with the same priority is undefined.
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort.
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, a binomial heap is a data structure that acts as a priority queue. It is an example of a mergeable heap, as it supports merging two heaps in logarithmic time. It is implemented as a heap similar to a binary heap but using a special tree structure that is different from the complete binary trees used by binary heaps. Binomial heaps were invented in 1978 by Jean Vuillemin.
In computer science, a Fibonacci heap is a data structure for priority queue operations. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap. consisting of a collection of heap-ordered trees. Fibonacci heaps were originally explained to be an extension of binomial heaps. Michael L. Fredman and Robert E. Tarjan developed Fibonacci heaps in 1984 and published them in a scientific journal in 1987. Fibonacci heaps are named after the Fibonacci numbers, which are used in their running time analysis.
In computer science, a soft heap is a variant on the simple heap data structure that has constant amortized time complexity for 5 types of operations. This is achieved by carefully "corrupting" (increasing) the keys of at most a constant number of values in the heap.
In computer science, a selection algorithm is an algorithm for finding the th smallest value in a collection of ordered values, such as numbers. The value that it finds is called the th order statistic. Selection includes as special cases the problems of finding the minimum, median, and maximum element in the collection. Selection algorithms include quickselect, and the median of medians algorithm. When applied to a collection of values, these algorithms take linear time, as expressed using big O notation. For data that is already structured, faster algorithms may be possible; as an extreme case, selection in an already-sorted array takes time .
In 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 Tarjan's 1986 article.
A van Emde Boas tree, also known as a vEB tree or van Emde Boas priority queue, is a tree data structure which implements an associative array with m-bit integer keys. It was invented by a team led by Dutch computer scientist Peter van Emde Boas in 1975. It performs all operations in O(log m) time, or equivalently in time, where is the largest element that can be stored in the tree. The parameter is not to be confused with the actual number of elements stored in the tree, by which the performance of other tree data-structures is often measured.
A B+ tree is an m-ary tree with a variable but often large number of children per node. A B+ tree consists of a root, internal nodes and leaves. The root may be either a leaf or a node with two or more children.
A pairing heap is a type of heap data structure with relatively simple implementation and excellent practical amortized performance, introduced by Michael Fredman, Robert Sedgewick, Daniel Sleator, and Robert Tarjan in 1986. Pairing heaps are heap-ordered multiway tree structures, and can be considered simplified Fibonacci heaps. They are considered a "robust choice" for implementing such algorithms as Prim's MST algorithm, and support the following operations :
In computer science, an implicit data structure or space-efficient data structure is a data structure that stores very little information other than the main or required data: a data structure that requires low overhead. They are called "implicit" because the position of the elements carries meaning and relationship between elements; this is contrasted with the use of pointers to give an explicit relationship between elements. Definitions of "low overhead" vary, but generally means constant overhead; in big O notation, O(1) overhead. A less restrictive definition is a succinct data structure, which allows greater overhead.
A Fenwick tree or binary indexed tree(BIT) is a data structure that can efficiently update values and calculate prefix sums in an array of values.
In computer science, a search data structure is any data structure that allows the efficient retrieval of specific items from a set of items, such as a specific record from a database.
In computer science, a min-max heap is a complete binary tree data structure which combines the usefulness of both a min-heap and a max-heap, that is, it provides constant time retrieval and logarithmic time removal of both the minimum and maximum elements in it. This makes the min-max heap a very useful data structure to implement a double-ended priority queue. Like binary min-heaps and max-heaps, min-max heaps support logarithmic insertion and deletion and can be built in linear time. Min-max heaps are often represented implicitly in an array; hence it's referred to as an implicit data structure.
In computer science, k-way merge algorithms or multiway merges are a specific type of sequence merge algorithms that specialize in taking in k sorted lists and merging them into a single sorted list. These merge algorithms generally refer to merge algorithms that take in a number of sorted lists greater than two. Two-way merges are also referred to as binary merges.The k- way merge is also an external sorting algorithm.
In computer science, a weak heap is a data structure for priority queues, combining features of the binary heap and binomial heap. It can be stored in an array as an implicit binary tree like a binary heap, and has the efficiency guarantees of binomial heaps.
This is a comparison of the performance of notable data structures, as measured by the complexity of their logical operations. For a more comprehensive listing of data structures, see List of data structures.
