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A pairing heap is either an empty heap, or a pairing tree consisting of a root element and a possibly empty list of pairing trees. The heap ordering property requires that parent of any node is no greater than the node itself. The following description assumes a purely functional heap that does not support the decrease-key operation.
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:
The decrease-key operation requires a reference to the node we wish to decrease the key of. However, the decrease-key operation itself sometimes swaps the key of a node and the key root. Assume that the insert operation returns some opaque reference that we can call decrease-key on, as part of the public API.
A node is marked if at least one of its children was cut, since this node was made a child of another node (all roots are unmarked). The amortized time for an operation is given by the sum of the actual time and c {\displaystyle c} times the difference in potential, where c is a constant (chosen to match the constant factors in the big O ...
In computer programming, create, read, update, and delete (CRUD) are the four basic operations (actions) of persistent storage. [1] CRUD is also sometimes used to describe user interface conventions that facilitate viewing, searching, and changing information using computer-based forms and reports .
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.
This is, however, not necessary: the algorithm can start with a priority queue that contains only one item, and insert new items as they are discovered (instead of doing a decrease-key, check whether the key is in the queue; if it is, decrease its key, otherwise insert it). [7]: 198 This variant has the same worst-case bounds as the common ...
The running time of the increase key procedure is bounded by O(log k). As there are n elements, the total running time is O(n log k). Note that the operation of replacing the key and iteratively doing decrease-key or sift-down are not supported by many Priority Queue libraries such as C++ stl and Java.