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A binary heap is defined as a binary tree with two additional constraints: [3] Shape property: a binary heap is a complete binary tree; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right.
The heap data structure, specifically the binary heap, was introduced by J. W. J. Williams in 1964, as a data structure for the heapsort sorting algorithm. [3] Heaps are also crucial in several efficient graph algorithms such as Dijkstra's algorithm. When a heap is a complete binary tree, it has the smallest possible height—a heap with N ...
A typical Floyd's build-heap algorithm [6] goes as follows: function FLOYD-BUILD-HEAP(h): for each index i from ⌊ / ⌋ down to 1 do: push-down(h, i) return h In this function, h is the initial array, whose elements may not be ordered according to the min-max heap property.
Dijkstra's algorithm is usually the working principle behind link-state routing protocols. OSPF and IS-IS are the most common. Unlike Dijkstra's algorithm, the Bellman–Ford algorithm can be used on graphs with negative edge weights, as long as the graph contains no negative cycle reachable from the source vertex s. The presence of such cycles ...
The heapsort algorithm can be divided into two phases: heap construction, and heap extraction. The heap is an implicit data structure which takes no space beyond the array of objects to be sorted; the array is interpreted as a complete binary tree where each array element is a node and each node's parent and child links are defined by simple arithmetic on the array indexes.
A pairing heap is either an empty heap, or a pairing tree consisting of a root element and a possibly empty list of pairing trees. The heap ordering property requires that parent of any node is no greater than the node itself. The following description assumes a purely functional heap that does not support the decrease-key operation.
A medial- or length-oriented tree is similar to an augmented tree, but symmetrical, with the binary search tree ordered by the medial points of the intervals. There is a maximum-oriented binary heap in every node, ordered by the length of the interval (or half of the length). Also we store the minimum and maximum possible value of the subtree ...
A demo for Prim's algorithm based on Euclidean distance. In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. The ...