N ary tree implementation
The Nary 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 Nary 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 Nary 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 Nary tree and perform a preorder traversal using recursion.
Pseudocode
Here's the pseudocode for constructing an Nary tree and performing a preorder traversal:
Class TreeNode:
Initialize TreeNode(key):
Set this.key = key
Initialize this.child as an empty vector
Function addChild(key):
Create a new TreeNode t with key
Add t to this.child
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

The
TreeNode
class is implemented with a constructor to initialize a node's key and create an empty vector for children. TheaddChild
method appends a new child node to the current node's children. 
The
NAryTree
class is created with a constructor to initialize the root as null. TheprintPreorder
method performs a recursive preorder traversal starting from the given node. 
In the
main
function, an instance ofNAryTree
is created. Nodes are added to the tree following the example provided. TheprintPreorder
function is then called on the root node to print the preorder traversal.
Code Solution

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Time Complexity
The time complexity of the provided code is O(n), where n is the number of nodes in the Nary 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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