Search results
Results from the WOW.Com Content Network
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 common implementation of a heap is the binary heap, in which the tree is a complete [2] binary tree (see figure). 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]
Basis: Heap's Algorithm trivially permutes an array A of size 1 as outputting A is the one and only permutation of A. Induction: Assume Heap's Algorithm permutes an array of size i . Using the results from the previous proof, every element of A will be in the "buffer" once when the first i elements are permuted.
A kind of opposite of a sorting algorithm is a shuffling algorithm. These are fundamentally different because they require a source of random numbers. Shuffling can also be implemented by a sorting algorithm, namely by a random sort: assigning a random number to each element of the list and then sorting based on the random numbers.
Binary heaps are also commonly employed in the heapsort sorting algorithm, which is an in-place algorithm because binary heaps can be implemented as an implicit data structure, storing keys in an array and using their relative positions within that array to represent child–parent relationships.
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.
Weak heaps may be used to sort an array, in essentially the same way as a conventional heapsort. [3] First, a weak heap is built out of all of the elements of the array, and then the root is repeatedly exchanged with the last element, which is sifted down to its proper place. A weak heap of n elements can be formed in n − 1 merges. It can be ...
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 ...