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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 a parent node of C, then the key (the value) of P is greater than or equal to the key of C. In a min heap, the key of P is less than or equal to the key of C. [1] The node at the "top" of the heap (with no ...
The decrease key operation replaces the value of a node with a given value with a lower value, and the increase key operation does the same but with a higher value. This involves finding the node with the given value, changing the value, and then down-heapifying or up-heapifying to restore the heap property. Decrease key can be done as follows:
In computer science, heapsort is a comparison-based sorting algorithm which can be thought of as "an implementation of selection sort using the right data structure." [3] Like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region.
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, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of ...
Pairing heap. A pairing heap is a type of heap data structure with relatively simple implementation and excellent practical amortized performance, introduced by Michael Fredman, Robert Sedgewick, Daniel Sleator, and Robert Tarjan in 1986. [1] Pairing heaps are heap-ordered multiway tree structures, and can be considered simplified Fibonacci heaps.
A weak heap is most easily understood as a heap-ordered multi-way tree stored as a binary tree using the "right-child left-sibling" convention. (This is equivalent to, but reversed from, the usual left-child right-sibling binary tree.) In the multi-way tree, and assuming a max-heap, each parent's key is greater than or equal to (≥) all the ...
Adaptive heap sort is a variant of heap sort that seeks optimality (asymptotically optimal) with respect to the lower bound derived with the measure of presortedness by taking advantage of the existing order in the data. In heap sort, for a data , we put all n elements into the heap and then keep extracting the maximum (or minimum) for n times.