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Depending on the problem at hand, pre-order, post-order, and especially one of the number of subtrees − 1 in-order operations may be optional. Also, in practice more than one of pre-order, post-order, and in-order operations may be required. For example, when inserting into a ternary tree, a pre-order operation is performed by comparing items.
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.
In pre-order, we always visit the current node; next, we recursively traverse the current node's left subtree, and then we recursively traverse the current node's right subtree. The pre-order traversal is a topologically sorted one, because a parent node is processed before any of its child nodes is done.
left-child right-sibling binary tree also termed first-child next-sibling binary tree, doubly chained tree, or filial-heir chain; Lempel–Ziv–Welch (LZW) level-order traversal; Levenshtein distance; lexicographical order; linear; linear congruential generator; linear hash; linear insertion sort; linear order; linear probing; linear probing ...
The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree. The ETT allows for efficient, parallel computation of solutions to common problems in algorithmic graph theory ...
An example of conversion of a m-ary tree to a binary tree.m=6. Using an array for representing a m-ary tree is inefficient, because most of the nodes in practical applications contain less than m children. As a result, this fact leads to a sparse array with large unused space in the memory.
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. For example, leaf nodes by definition have no descendants ...
A binary tree may be transformed into a stack-sortable permutation by numbering its nodes in left-to-right order, and then listing these numbers in the order they would be visited by a preorder traversal of the tree: the root first, then the left subtree, then the right subtree, continuing recursively within each subtree.