# Encode N ary Tree to Binary Tree

This page explains Java solution to problem `Encode N ary Tree to Binary Tree` using `Tree` data structure.

## Problem Statement

Design an algorithm to encode an `N-ary` tree into a binary tree and decode the binary tree to get the original `N-ary` tree.

An `N-ary` tree is a rooted tree in which each node has no more than `N` children. Similarly, a binary tree is a rooted tree in which each node has no more than `2` children.

There is no restriction on how your encode/decode algorithm should work.

Example 1: ## Solution

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``````
package com.vc.hard;

import java.util.ArrayList;

/**
// Definition for a Node.
class Node {
public int val;
public List<Node> children;

public Node() {}

public Node(int _val) {
val = _val;
}

public Node(int _val, List<Node> _children) {
val = _val;
children = _children;
}
};
*/

/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/

class EncodeNAryTreeToBinaryTree {

// Encodes an n-ary tree to a binary tree.
public TreeNode encode(Node root) {
if(root == null) return null;
else {
TreeNode tree = new TreeNode(root.val);
if(root.children != null && root.children.size() > 0) {
tree.left = encode(root.children.get(0));
TreeNode current = tree.left;
for(int i = 1; i < root.children.size(); i++) {
current.right = encode(root.children.get(i));
current = current.right;
}
}
return tree;
}
}

// Decodes your binary tree to an n-ary tree.
public Node decode(TreeNode root) {
if(root == null) return null;
else {
Node node = new Node(root.val, new ArrayList<>());
TreeNode current = root.left;
while(current != null) {
current = current.right;
}
return node;
}
}
}
``````

## Time Complexity

O(N) Where
N is total number of elements in an input tree

O(1)