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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:
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.
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 ...
If we have a pointer to a node x in a Min HBLT, we can delete it as follows: Replace the node x with the result of merging its two subtrees and update the s-values of the nodes on the path from x to the root, swapping the right and left subtrees if necessary to maintain the leftist tree property.
To uninstall the AOL Shield Pro browser: 1. Right click on the AOL Shield Pro desktop icon. 2. Click Open file location.. 3. Double click Uninstall.exe in the AOL Shield Pro folder.
To merge two binomial trees of the same order, first compare the root key. Since 7>3, the black tree on the left (with root node 7) is attached to the grey tree on the right (with root node 3) as a subtree. The result is a tree of order 3. The operation of merging two heaps is used as a subroutine in most other operations. A basic subroutine ...