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A labeled binary tree of size 9 (the number of nodes in the tree) and height 3 (the height of a tree defined as the number of edges or links from the top-most or root node to the farthest leaf node), with a root node whose value is 1. The above tree is unbalanced and not sorted.
Complex, representation of complex numbers; Composite types or non-primitive type Array, a sequence ... Binary search tree; Binary tree; Cartesian tree; Conc-tree list;
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.
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.
Let n ≥ 0 be the number of entries in the tree. Let m be the maximum number of children a node can have. Each node can have at most m−1 keys. It can be shown (by induction for example) that a B-tree of height h with all its nodes completely filled has n = m h+1 –1 entries. Hence, the best case height (i.e. the minimum height) of a B-tree is:
Random binary tree, binary trees with various random distributions, including trees formed by random insertion orders, and trees that are uniformly distributed with a given number of nodes; Random recursive tree, increasingly labelled trees, which can be generated using a simple stochastic growth rule. Treap or randomized binary search tree, a ...
In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a binary search tree.
The number of binary rooted trees (every node has out-degree 0 or 2) with n endpoints (and 2n − 1 nodes in all). A001190: Gould's sequence: