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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.
This is a list of well-known data structures. For a wider list of terms, see list of terms relating to algorithms and data structures. For a comparison of running times for a subset of this list see comparison of data structures.
Most operations on a binary search tree (BST) take time directly proportional to the height of the tree, so it is desirable to keep the height small. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...
This unsorted tree has non-unique values (e.g., the value 2 existing in different nodes, not in a single node only) and is non-binary (only up to two children nodes per parent node in a binary tree). The root node at the top (with the value 2 here), has no parent as it is the highest in the tree hierarchy.
A Binary Search Tree is a node-based data structure where each node contains a key and two subtrees, the left and right. For all nodes, the left subtree's key must be less than the node's key, and the right subtree's key must be greater than the node's key. These subtrees must all qualify as binary search trees.
A perfect tree is therefore always complete but a complete tree is not always perfect. Some authors use the term complete to refer instead to a perfect binary tree as defined above, in which case they call this type of tree (with a possibly not filled last level) an almost complete binary tree or nearly complete binary tree.
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.