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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.
In computer science, a double-ended priority queue (DEPQ) [1] or double-ended heap [2] 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.
Merge sort. In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order.The most frequently used orders are numerical order and lexicographical order, and either ascending or descending.
For Haskell there is the Data.Heap module. The Java platform (since version 1.5) provides a binary heap implementation with the class java.util.PriorityQueue in the Java Collections Framework. This class implements by default a min-heap; to implement a max-heap, programmer should write a custom comparator.
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.
and we want to add the number 15 to the heap. We first place the 15 in the position marked by the X. However, the heap property is violated since 15 > 8, so we need to swap the 15 and the 8. So, we have the heap looking as follows after the first swap: However the heap property is still violated since 15 > 11, so we need to swap again:
For instance, using a binary heap as a priority queue in selection sort leads to the heap sort algorithm, a comparison sorting algorithm that takes O(n log n) time. Instead, using selection sort with a bucket queue gives a form of pigeonhole sort , and using van Emde Boas trees or other integer priority queues leads to other fast integer ...
Introsort or introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance. It begins with quicksort, it switches to heapsort when the recursion depth exceeds a level based on (the logarithm of) the number of elements being sorted and it switches to insertion sort when the number of elements is below some threshold.