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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.
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 ...
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:
Product type (also called a tuple), a record in which the fields are not named; String, a sequence of characters representing text; Union, a datum which may be one of a set of types; Tagged union (also called a variant, discriminated union or sum type), a union with a tag specifying which type the data is
Such a data structure is known as a treap or a randomized binary search tree. [11] Variants of the treap including the zip tree and zip-zip tree replace the tree rotations by "zipping" operations that split and merge trees, and that limit the number of random bits that need to be generated and stored alongside the keys.
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 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 mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: Types of random trees include: Uniform spanning tree , a spanning tree of a given graph in which each different tree is equally likely to be selected