Search results
Results from the WOW.Com Content Network
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 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.
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:
Figure 4. Fibonacci heap from Figure 1 after decreasing key of node 9 to 0. If decreasing the key of a node causes it to become smaller than its parent, then it is cut from its parent, becoming a new unmarked root. If it is also less than the minimum key, then the minimum pointer is updated.
insert: adding a new key to the heap (a.k.a., push [4]) extract-max (or extract-min): returns the node of maximum value from a max heap [or minimum value from a min heap] after removing it from the heap (a.k.a., pop [5]) delete-max (or delete-min): removing the root node of a max heap (or min heap), respectively; replace: pop root and push a ...
The AOL.com video experience serves up the best video content from AOL and around the web, curating informative and entertaining snackable videos.
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.
Min-reduce the local solutions to find the vertex v having the minimum possible value of C[v] (global solution). Broadcast the selected node to every processor. Add v to F and, if E[v] is not the special flag value, also add E[v] to F. On every processor: update and as in the sequential algorithm.