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A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a node). [18] A perfect binary tree is a full binary tree.
Degree of tree The degree of a tree is the maximum degree of a node in the tree. Distance The number of edges along the shortest path between two nodes. Level The level of a node is the number of edges along the unique path between it and the root node. [4] This is the same as depth. Width The number of nodes in a level. Breadth The number of ...
In depth-first search (DFS), the search tree is deepened as much as possible before going to the next sibling. To traverse binary trees with depth-first search, perform the following operations at each node: [3] [4] If the current node is empty then return. Execute the following three operations in a certain order: [5] N: Visit the current node.
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.
For an m-ary tree with height h, the upper bound for the maximum number of leaves is . The height h of an m-ary tree does not include the root node, with a tree containing only a root node having a height of 0. The height of a tree is equal to the maximum depth D of any node in the tree.
Conventionally, an empty tree (a tree with no vertices, if such are allowed) has depth and height −1. A k-ary tree (for nonnegative integers k) is a rooted tree in which each vertex has at most k children. [25] 2-ary trees are often called binary trees, while 3-ary trees are sometimes called ternary trees.
A B-tree of depth n+1 can hold about U times as many items as a B-tree of depth n ... where m is the order of the tree as maximum number of ... "Binary B-Trees for ...
Binary trees may also be studied with all nodes unlabeled, or with labels that are not given in sorted order. For instance, the Cartesian tree data structure uses labeled binary trees that are not necessarily binary search trees. [4] A random binary tree is a random tree drawn from a certain probability distribution on binary trees. In many ...