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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.
"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 ...
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.
Search trees store data in a way that makes an efficient search algorithm possible via tree traversal. A binary search tree is a type of binary tree; Representing sorted lists of data; Computer-generated imagery: Space partitioning, including binary space partitioning; Digital compositing; Storing Barnes–Hut trees used to simulate galaxies ...
(The Haskell code given in the reference uses generic programming to generate a traversal function for any data structure, but this is optional – any suitable traversal function can be used.) However, the generic zipper involves inversion of control , so some uses of it require a state machine (or equivalent) to keep track of what to do next.
As with any binary search tree, the inorder traversal order of the nodes is the same as the sorted order of the keys. The structure of the tree is determined by the requirement that it be heap-ordered: that is, the priority number for any non-leaf node must be greater than or equal to the priority of its children.
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
The tree rotation renders the inorder traversal of the binary tree invariant. This implies the order of the elements is not affected when a rotation is performed in any part of the tree. Here are the inorder traversals of the trees shown above: Left tree: ((A, P, B), Q, C) Right tree: (A, P, (B, Q, C))