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In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
The simple Sethi–Ullman algorithm works as follows (for a load/store architecture): . Traverse the abstract syntax tree in pre- or postorder . For every leaf node, if it is a non-constant left-child, assign a 1 (i.e. 1 register is needed to hold the variable/field/etc.), otherwise assign a 0 (it is a non-constant right child or constant leaf node (RHS of an operation – literals, values)).
To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
A tree sort is a sort algorithm that builds a binary search tree from the elements to be sorted, and then traverses the tree so that the elements come out in sorted order. [1] Its typical use is sorting elements online : after each insertion, the set of elements seen so far is available in sorted order.
"A binary tree is threaded by making all right child pointers that would normally be null point to the in-order successor of the node (if it exists), and all left child pointers that would normally be null point to the in-order predecessor of the node." [1] This assumes the traversal order is the same as in-order traversal of the tree. However ...
An augmented tree can be built from a simple ordered tree, for example a binary search tree or self-balancing binary search tree, ordered by the 'low' values of the intervals. An extra annotation is then added to every node, recording the maximum upper value among all the intervals from this node down.
Below are two versions of a subroutine (implemented in the C programming language) for looking up a given search key in a singly linked list.The first one uses the sentinel value NULL, and the second one a (pointer to the) sentinel node Sentinel, as the end-of-list indicator.
Let Y 1 be a minimum spanning tree of graph P. If Y 1 =Y then Y is a minimum spanning tree. Otherwise, let e be the first edge added during the construction of tree Y that is not in tree Y 1, and V be the set of vertices connected by the edges added before edge e. Then one endpoint of edge e is in set V and the other is not.