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The Build-Max-Heap function that follows, converts an array A which stores a complete binary tree with n nodes to a max-heap by repeatedly using Max-Heapify (down-heapify for a max-heap) in a bottom-up manner.
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.
The reason given is: This list is based on the NIST "Dictionary of Algorithms and Data Structures," which was published online in 1998. Please help update this article to reflect recent events or newly available information. (September 2018)
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.
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. [2]
Remove the last element from the heap and put it at the end of the list. Adjust the heap so that the first element ends up at the right place in the heap. Repeat Step 2 and 3 until the heap has only one element. Put this last element at the end of the list and output the list. The data in the list will be sorted.
The strange thing about the above implementation is that it uses heapify-down operations to achieve what we really want to achieve using heapify-up operations. Imagine building the heap. As we add new elements, we want them to crawl up the heap. For the actual sorting, however, the standard implementation jibes with intuition.
The d-ary heap consists of an array of n items, each of which has a priority associated with it. These items may be viewed as the nodes in a complete d-ary tree, listed in breadth first traversal order: the item at position 0 of the array (using zero-based numbering) forms the root of the tree, the items at positions 1 through d are its children, the next d 2 items are its grandchildren, etc.