Binary tree

Definition and Recursive Definition of Binary Trees - A binary tree is a tree data structure in which each node has at most two children. - It can be defined as a -ary tree with = 2. - Binary trees can be interpreted as arborescences in graph theory. - The recursive definition of a binary tree allows for the distinction between left and right children. Types of Binary Trees - Rooted binary tree: has a root node and every node has at most two children. - Full binary tree: every node has either 0 or 2 children. - Perfect binary tree: all interior nodes have two children. - Complete binary tree: every level, except possibly the last, is completely filled. - Balanced binary tree: the left and right subtrees of every node differ in height by no more than 1. Properties and Storage of Binary Trees - The number of nodes in a full binary tree is at least 2h+1 and at most 2^(h+1)-1. - Binary trees can be used for efficient searching and sorting. - Binary trees can be stored using nodes and references. - Special null values or sentinel nodes can be used for nodes with fewer than two children. - Another storage method is using bits to represent the structure of the tree. Encoding and Common Operations on Binary Trees - There is a one-to-one correspondence between ordered trees and binary trees. - Various operations can be performed on binary trees, such as insertion and deletion. - Tree rotations are common internal operations on self-balancing binary trees. - Traversal methods include pre-order, in-order, and post-order. - Deletion operations help in maintaining the integrity of the binary tree. Introduction, Types, Operations, and Applications of Binary Trees - Binary trees are a type of data structure used in computer science. - Types of binary trees include binary search trees, AVL trees, red-black trees, heap trees, and binary expression trees. - Operations on binary trees include traversing, searching, inserting, deleting, and balancing. - Binary trees are used in applications such as file systems, database indexing, expression evaluation, Huffman coding, and dictionary implementations. Note: The resources and references section is excluded from the groups as it does not contain concepts or detailed points.