Heap (data structure)

In <a href="/facts/Computer_science/lN3pEyPz">computer science</a>, a heap is a <a href="/facts/Tree_(data_structure)/RcXz9noF">tree</a>-based <a href="/facts/Data_structure/yNsNvL1I">data structure</a> that satisfies the heap property: In a max heap, for any given <a href="/facts/Node_(computer_science)/eYlvVE0z">node</a> C, if P is the 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 <a href="/facts/Abstract_data_type/BaVGSHNP">abstract data type</a> called a <a href="/facts/Priority_queue/1uXVo4Uf">priority queue</a>, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority, or when insertions need to be interspersed with removals of the root node.
A common implementation of a heap is the <a href="/facts/Binary_heap/YPJAEN94">binary heap</a>, in which the tree is a <a href="/facts/Binary_tree/TDV7GMpu">complete</a> binary tree (see figure). The heap data structure, specifically the binary heap, was introduced by <a href="/facts/J._W._J._Williams/VIJdvrJ8">J. W. J. Williams</a> in 1964, as a data structure for the <a href="/facts/Heapsort/Cz22lLKq">heapsort</a> sorting algorithm. Heaps are also crucial in several efficient <a href="/facts/Graph_algorithms/g3uenNkc">graph algorithms</a> such as <a href="/facts/Dijkstra%2527s_algorithm/ehun88jl">Dijkstra's algorithm</a>. When a heap is a complete binary tree, it has the smallest possible height—a heap with N nodes and a branches for each node always has loga N height.
Note that, as shown in the graphic, there is no implied ordering between siblings or cousins and no implied sequence for an <a href="/facts/Inorder_traversal/Dkch34pz">in-order traversal</a> (as there would be in, e.g., a <a href="/facts/Binary_search_tree/gWubNt7b">binary search tree</a>). The heap relation mentioned above applies only between nodes and their parents, grandparents. The maximum number of children each node can have depends on the type of heap.
Heaps are typically constructed in-place in the same array where the elements are stored, with their structure being implicit in the access pattern of the operations. Heaps differ in this way from other data structures with similar or in some cases better theoretic bounds such as <a href="/facts/Radix_tree/a1JKJPYc">radix trees</a> in that they require no additional memory beyond that used for storing the keys.

Heap (data structure) open-in-new

Heap (data structure)