 | This article relies largely or entirely on a single source .(May 2024) |
In computer science, a mergeable heap (also called a meldable heap) is an abstract data type, which is a heap supporting a merge operation.
| | This article relies largely or entirely on a single source .(May 2024) |
In computer science, a mergeable heap (also called a meldable heap) is an abstract data type, which is a heap supporting a merge operation.
A mergeable heap supports the usual heap operations: [1]
Make-Heap(), create an empty heap.Insert(H,x), insert an element x into the heap H.Min(H), return the minimum element, or Nil if no such element exists.Extract-Min(H), extract and return the minimum element, or Nil if no such element exists.And one more that distinguishes it: [1]
Merge(H1,H2), combine the elements of H1 and H2 into a single heap.It is straightforward to implement a mergeable heap given a simple heap:
Merge(H1,H2):
x ← Extract-Min(H2)while x ≠ NilInsert(H1, x)x ← Extract-Min(H2)This can however be wasteful as each Extract-Min(H) and Insert(H,x) typically have to maintain the heap property.
Examples of mergeable heap data structures include:
A more complete list with performance comparisons can be found at Heap (data structure) § Comparison of theoretic bounds for variants.
In most mergeable heap structures, merging is the fundamental operation on which others are based. Insertion is implemented by merging a new single-element heap with the existing heap. Deletion is implemented by merging the children of the deleted node.
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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.
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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.
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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 :
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In computer science, a double-ended priority queue (DEPQ) or double-ended heap is a data structure similar to a priority queue or heap, but allows for efficient removal of both the maximum and minimum, according to some ordering on the keys (items) stored in the structure. Every element in a DEPQ has a priority or value. In a DEPQ, it is possible to remove the elements in both ascending as well as descending order.
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In computer science, a skew binomial heap is a variant of the binomial heap that supports constant-time insertion operations in the worst case, rather than the logarithmic worst case and constant amortized time of ordinary binomial heaps.
In computer science, a queap is a priority queue data structure. The data structure allows insertions and deletions of arbitrary elements, as well as retrieval of the highest-priority element. Each deletion takes amortized time logarithmic in the number of items that have been in the structure for a longer time than the removed item. Insertions take constant amortized time.
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In computer science, an addressable heap is an abstract data type. Specifically, it is a mergeable heap supporting access to the elements of the heap via handles. It allows the key of the element referenced by a particular handle to be removed or decreased.
In computer science, a shadow heap is a mergeable heap data structure which supports efficient heap merging in the amortized sense. More specifically, shadow heaps make use of the shadow merge algorithm to achieve insertion in O(f(n)) amortized time and deletion in O((log n log log n)/f(n)) amortized time, for any choice of 1 ≤ f(n) ≤ log log n.
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.
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