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# N ary tree implementation

The N-ary tree is a tree data structure in which each node can have an arbitrary number of children. It's a generalization of the binary tree where each node can have more than two children. This structure finds applications in various fields including computer science, data representation, hierarchical relationships, and more.

## Problem Statement

In this code, an N-ary tree is implemented in Java using a class `TreeNode` to represent nodes and a class `NAryTree` to manage the tree operations. The code also demonstrates how to construct an N-ary tree and perform a preorder traversal on it.

## Idea to Solve the Problem

The idea to solve this problem is to implement an `TreeNode` class that stores the node's key and children. Then, create an `NAryTree` class to manage the tree structure. Using the provided methods, construct the desired N-ary tree and perform a preorder traversal using recursion.

## Pseudocode

Here's the pseudocode for constructing an N-ary tree and performing a preorder traversal:

``````Class TreeNode:
Initialize TreeNode(key):
Set this.key = key
Initialize this.child as an empty vector

Create a new TreeNode t with key

Class NAryTree:
Initialize NAryTree():
Set this.root = null

Function printPreorder(node):
If node is null:
Return
Print node.key
For each child c in node.child:
Recursively call printPreorder(c)

Function main():
Create a new NAryTree called tree
Set tree.root as a new TreeNode with key 10
Add children to tree.root and their children as shown in the example
Call tree.printPreorder(tree.root)``````

## Algorithm Explanation

1. The `TreeNode` class is implemented with a constructor to initialize a node's key and create an empty vector for children. The `addChild` method appends a new child node to the current node's children.

2. The `NAryTree` class is created with a constructor to initialize the root as null. The `printPreorder` method performs a recursive preorder traversal starting from the given node.

3. In the `main` function, an instance of `NAryTree` is created. Nodes are added to the tree following the example provided. The `printPreorder` function is then called on the root node to print the preorder traversal.

## Time Complexity

The time complexity of the provided code is O(n), where n is the number of nodes in the N-ary tree. This is because the `printPreorder` function visits each node exactly once in a recursive manner, and the number of nodes visited is proportional to the number of nodes in the tree.

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