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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.
Adding one item to a binary search tree is on average an O(log n) process (in big O notation). Adding n items is an O(n log n) process, making tree sorting a 'fast sort' process. Adding an item to an unbalanced binary tree requires O(n) time in the worst-case: When the tree resembles a linked list (degenerate tree).
A walk in which each parent node is traversed before its children is called a pre-order walk; a walk in which the children are traversed before their respective parents are traversed is called a post-order walk; a walk in which a node's left subtree, then the node itself, and finally its right subtree are traversed is called an in-order traversal.
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
The algorithm operates by building this tree one vertex at a time, from an arbitrary starting vertex, at each step adding the cheapest possible connection from the tree to another vertex. The algorithm was developed in 1930 by Czech mathematician Vojtěch Jarník [ 1 ] and later rediscovered and republished by computer scientists Robert C. Prim ...
If <, then set T to p, which by definition is a 2–3 tree, and go back to step 2. If >, then set T to q and go back to step 2. Suppose t is a 3-node with left child p, middle child q, and right child r. Let a and b be the two data elements of t, where <. There are four cases:
Split the remaining 3-node up into a pair of 2-nodes (the now missing middle value is handled in the next step). If this is the root node (which thus has no parent): the middle value becomes the new root 2-node and the tree height increases by 1. Ascend into the root. Otherwise, push the middle value up into the parent node.
In computing, a threaded binary tree is a binary tree variant that facilitates traversal in a particular order. An entire binary search tree can be easily traversed in order of the main key, but given only a pointer to a node , finding the node which comes next may be slow or impossible.