Search results
Results from the WOW.Com Content Network
Construction of a binary (or d-ary) heap out of a given array of elements may be performed in linear time using the classic Floyd algorithm, with the worst-case number of comparisons equal to 2N − 2s 2 (N) − e 2 (N) (for a binary heap), where s 2 (N) is the sum of all digits of the binary representation of N and e 2 (N) is the exponent of 2 ...
A heap on n elements can be merged with a heap on k elements using O(log n log k) key comparisons, or, in case of a pointer-based implementation, in O(log n log k) time. [14] An algorithm for splitting a heap on n elements into two heaps on k and n-k elements, respectively, based on a new view of heaps as an ordered collections of subheaps was ...
Theorem: A semiheap with a biunitary element e may be considered an involuted semigroup with operation given by ab = [a, e, b] and involution by a –1 = [e, a, e]. [1]: 76 When the above construction is applied to a heap, the result is in fact a group. [1]: 143 Note that the identity e of the group can be chosen to be any element of the heap.
We assume in the next points that the root element is at the first level, i.e., 0. 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.
The d-ary heap or d-heap is a priority queue data structure, a generalization of the binary heap in which the nodes have d children instead of 2. [1] [2] [3] Thus, a binary heap is a 2-heap, and a ternary heap is a 3-heap. According to Tarjan [2] and Jensen et al., [4] d-ary heaps were invented by Donald B. Johnson in 1975. [1]
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.
To delete the minimum element from the heap, first find this element, remove it from the root of its binomial tree, and obtain a list of its child subtrees (which are each themselves binomial trees, of distinct orders). Transform this list of subtrees into a separate binomial heap by reordering them from smallest to largest order.
Sifting down in a weak heap can be done in h = ⌈log 2 n⌉ comparisons, as opposed to 2 log 2 n for a binary heap, or 1.5 log 2 n for the "bottom-up heapsort" variant. This is done by "merging up": after swapping the root with the last element of the heap, find the last (height 1) child of the root.