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

    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

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.

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 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.