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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.
One example application of the double-ended priority queue is external sorting. In an external sort, there are more elements than can be held in the computer's memory. The elements to be sorted are initially on a disk and the sorted sequence is to be left on the disk. The external quick sort is implemented using the DEPQ as follows:
Example of a binary max-heap with node keys being integers between 1 and 100. 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 the parent node of C, then the key (the value) of P is greater than or equal to the key of C.
Example of a complete binary max-heap Example of a complete binary min heap. 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. [1]: 162–163 The binary heap was introduced by J. W. J. Williams in 1964 as a data structure for implementing heapsort. [2]
Example of Min-max heap. Each node in a min-max heap has a data member (usually called key) whose value is used to determine the order of the node in the min-max heap. The root element is the smallest element in the min-max heap. One of the two elements in the second level, which is a max (or odd) level, is the greatest element in the min-max heap
In computer science, smoothsort is a comparison-based sorting algorithm.A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981. [1] Like heapsort, smoothsort is an in-place algorithm with an upper bound of O(n log n) operations (see big O notation), [2] but it is not a stable sort.
In computer science, adaptive heap sort is a comparison-based sorting algorithm of the adaptive sort family. It is a variant of heap sort that performs better when the data contains existing order. Published by Christos Levcopoulos and Ola Petersson in 1992, the algorithm utilizes a new measure of presortedness, Osc, as the number of ...
heap.addTree(tree) heap.next(); p.next(); q.next() Because each binomial tree in a binomial heap corresponds to a bit in the binary representation of its size, there is an analogy between the merging of two heaps and the binary addition of the sizes of the two heaps, from right-to-left. Whenever a carry occurs during addition, this corresponds ...