What Is N-Ary Tree in Data Structure?


Angela Bailey

What Is N-Ary Tree in Data Structure?

An N-ary tree, also known as a k-ary tree, is a data structure that represents hierarchical relationships between elements. It is similar to a binary tree, but instead of having two children for each node, an N-ary tree can have up to N children, where N is a positive integer.

Structure of an N-Ary Tree

An N-ary tree consists of nodes connected by edges. Each node can have up to N child nodes, and the topmost node is called the root. The children of a node are usually unordered, meaning there is no particular order in which they are arranged.

Each node in an N-ary tree contains two main components:

  • Value/Key: Represents the data stored in the node.
  • Child Pointers: Pointers to the child nodes of the current node.

Applications of N-Ary Trees

N-Ary trees are used in various real-world applications due to their ability to represent hierarchical relationships efficiently. Some common applications include:

  • File Systems: N-Ary trees can be used to represent file systems where directories can contain subdirectories and files.
  • Parsing and Syntax Trees: In computer science and linguistics, N-Ary trees are used to represent the syntax structure of sentences or programming languages.
  • Organizational Hierarchies: Many organizations use N-Ary trees to represent organizational hierarchies such as departments, teams, and employees.

N-Ary Tree Traversals

Traversing an N-Ary tree means visiting each node in a specific order. There are several ways to traverse an N-Ary tree:

1. Depth-First Traversal

In depth-first traversal, we start at the root and visit each node along the path from the root to the deepest node before backtracking. There are three common methods for depth-first traversal:

  • Preorder Traversal: Visit the current node, then recursively visit each child from left to right.
  • Inorder Traversal: Recursively visit each child from left to right, and then visit the current node.
  • Postorder Traversal: Recursively visit each child from left to right, and then visit the current node.

2. Breadth-First Traversal

In breadth-first traversal, we start at the root and visit all nodes at the same level before moving on to the next level. This is done by visiting nodes in a level-by-level manner from left to right.


N-Ary trees are a powerful data structure for representing hierarchical relationships with up to N children for each node. They find applications in various domains such as file systems, parsing, organizational hierarchies, and more. Understanding how N-Ary trees work and how to traverse them is crucial for efficient manipulation of hierarchical data structures.

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