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In a doubly linked list, one can insert or delete a node in a constant number of operations given only that node's address. To do the same in a singly linked list, one must have the address of the pointer to that node, which is either the handle for the whole list (in case of the first node) or the link field in the previous node. Some ...
Insert: insert a key/value pair with an m-bit key; Delete: remove the key/value pair with a given key; Lookup: find the value associated with a given key; FindNext: find the key/value pair with the smallest key which is greater than a given k; FindPrevious: find the key/value pair with the largest key which is smaller than a given k
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 purpose of the delete algorithm is to remove the desired entry node from the tree structure. We recursively call the delete algorithm on the appropriate node until no node is found. For each function call, we traverse along, using the index to navigate until we find the node, remove it, and then work back up to the root.
To ensure a key is always stays with the same reference, it is necessary to 'box' the key. Each heap node now contains a pointer to a box containing a key, and the box also has a pointer to the heap node. When inserting an item, we create a box to store the key in, link the heap node to the box both ways, and return the box object. [5]
Traversing a tree involves iterating over all nodes in some manner. Because from a given node there is more than one possible next node (it is not a linear data structure), then, assuming sequential computation (not parallel), some nodes must be deferred—stored in some way for later visiting. This is often done via a stack (LIFO) or queue (FIFO).
This may be done by comparing the keys at the roots of the two trees (the smallest keys in both trees). The root node with the larger key is made into a child of the root node with the smaller key, increasing its order by one: [1] [3] function mergeTree(p, q) if p.root.key <= q.root.key return p.addSubTree(q) else return q.addSubTree(p)
remove a (,) pair from the collection, unmapping a given key from its value. The argument to this operation is the key. Lookup, find, or get find the value (if any) that is bound to a given key. The argument to this operation is the key, and the value is returned from the operation.