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BINARY TREES – BASIC CONCEPTS AND TYPES

Binary trees are trees where every node has a maximum of two children. You may have one child or no child at all. An empty tree is also a valid binary tree.

TYPES OF BINARY TREES

Strict (or proper) Binary Trees

Each node has exactly two children or no children.

Complete Binary Tree

A complete binary tree is a binary tree where

• all levels except possibly the last are completely filled, and
• the last level has all its nodes to the left side (without any missing ones in between).

Note: There can be cases where a binary tree is

• strict and complete
• strict but not complete
• complete but not strict
• Not strict and not complete

Full (or Perfect) Binary Tree

Full binary tree is a binary tree where

• all leaves are at bottom of the tree and
• all non-leaf nodes has exactly two children.

Binary Search Tree (BST)

A Binary Search Tree (BST) is a binary tree where all nodes in the left sub tree of a node are less than (or equal to) the node and all nodes in the right sub tree of a node are greater than the node.

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