Lecture 269:- n-ary Trees

An n-ary tree is a tree data structure in which each node can have at most n children. An n-ary tree generalizes the concept of a binary tree, where each node has at most two children, to allow nodes with multiple children. In an n-ary tree, the number of children for each node can vary from 0 to n.

Some key characteristics of n-ary trees:

1. Root: The topmost node of the tree is called the root. It is the starting point of the tree and has no parent.
2. Parent: A node is the parent of its children. It is the node from which the child nodes originate.
3. Child: Nodes that are directly connected to a parent node are called its child nodes.
4. Sibling: Nodes that have the same parent node are called siblings. They share the same parent.
5. Leaf: A leaf node is a node that has no children; it is the terminal node in the tree.
6. Height: The height of an n-ary tree is the number of edges in the longest path from the root node to a leaf node. Alternatively, the height of a node is the number of edges in the longest path from that node to a leaf node.
7. Depth: The depth of a node in an n-ary tree is the number of edges from the root node to that node.
8. Level: The level of a node in an n-ary tree is its depth plus one. The root node is at level 1.

N-ary trees are used in various applications, and they offer more flexibility compared to binary trees. Examples of n-ary trees include ternary trees (3-ary trees), quaternary trees (4-ary trees), and so on.

N-ary trees are commonly used in computer science and various algorithms, such as parsing expressions, representing hierarchical data structures, file systems, and organization charts. The structure of n-ary trees allows for efficient representation and manipulation of data with multiple hierarchical relationships.