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For example, given a binary tree of infinite depth, a depth-first search will go down one side (by convention the left side) of the tree, never visiting the rest, and indeed an in-order or post-order traversal will never visit any nodes, as it has not reached a leaf (and in fact never will). By contrast, a breadth-first (level-order) traversal ...
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.
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 ...
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 ternary search tree is a type of tree that can have 3 nodes: a low child, an equal child, and a high child. Each node stores a single character and the tree itself is ordered the same way a binary search tree is, with the exception of a possible third node.
Henzinger and King [2] suggest to represent a given tree by keeping its Euler tour in a balanced binary search tree, keyed by the index in the tour. So for example, the unbalanced tree in the example above, having 7 nodes, will be represented by a balanced binary tree with 14 nodes, one for each time each node appears on the tour.
In this case, an advantage of using a binary tree is significantly reduced because it is essentially a linked list which time complexity is O(n) (n as the number of nodes) and it has more data space than the linked list due to two pointers per node, while the complexity of O(log 2 n) for data search in a balanced binary tree is normally expected.
The cost of a search is modeled by assuming that the search tree algorithm has a single pointer into a binary search tree, which at the start of each search points to the root of the tree. The algorithm may then perform any sequence of the following operations: Move the pointer to its left child. Move the pointer to its right child.