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Depth of an N-Ary tree

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  • Difficulty Level : Easy
  • Last Updated : 28 Jun, 2021

Given an N-Ary tree, find depth of the tree. An N-Ary tree is a tree in which nodes can have at most N children.
Examples: 
Example 1: 
 

narry1

Example 2: 
 

nary2

 

N-Ary tree can be traversed just like a normal tree. We just have to consider all childs of a given node and recursively call that function on every node. 
 

C++




// C++ program to find the height of
// an N-ary tree
#include <bits/stdc++.h>
using namespace std;
 
// Structure of a node of an n-ary tree
struct Node
{
   char key;
   vector<Node *> child;
};
 
// Utility function to create a new tree node
Node *newNode(int key)
{
   Node *temp = new Node;
   temp->key = key;
   return temp;
}
 
// Function that will return the depth
// of the tree
int depthOfTree(struct Node *ptr)
{
    // Base case
    if (!ptr)
        return 0;
 
    // Check for all children and find
    // the maximum depth
    int maxdepth = 0;
    for (vector<Node*>::iterator it = ptr->child.begin();
                              it != ptr->child.end(); it++)
        maxdepth = max(maxdepth, depthOfTree(*it));
 
    return maxdepth + 1 ;
}
 
// Driver program
int main()
{
   /*   Let us create below tree
   *             A
   *         / /  \  \
   *       B  F   D  E
   *      / \    |  /|\
   *     K  J    G  C H I
   *      /\            \
   *    N   M            L
   */
 
   Node *root = newNode('A');
   (root->child).push_back(newNode('B'));
   (root->child).push_back(newNode('F'));
   (root->child).push_back(newNode('D'));
   (root->child).push_back(newNode('E'));
   (root->child[0]->child).push_back(newNode('K'));
   (root->child[0]->child).push_back(newNode('J'));
   (root->child[2]->child).push_back(newNode('G'));
   (root->child[3]->child).push_back(newNode('C'));
   (root->child[3]->child).push_back(newNode('H'));
   (root->child[3]->child).push_back(newNode('I'));
   (root->child[0]->child[0]->child).push_back(newNode('N'));
   (root->child[0]->child[0]->child).push_back(newNode('M'));
   (root->child[3]->child[2]->child).push_back(newNode('L'));
 
   cout << depthOfTree(root) << endl;
 
   return 0;
}

Java




// Java program to find the height of
// an N-ary tree
import java.util.*;
 
class GFG
{
 
// Structure of a node of an n-ary tree
static class Node
{
    char key;
    Vector<Node > child;
};
 
// Utility function to create a new tree node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = (char) key;
    temp.child = new Vector<Node>();
    return temp;
}
 
// Function that will return the depth
// of the tree
static int depthOfTree(Node ptr)
{
    // Base case
    if (ptr == null)
        return 0;
 
    // Check for all children and find
    // the maximum depth
    int maxdepth = 0;
    for (Node it : ptr.child)
        maxdepth = Math.max(maxdepth,
                            depthOfTree(it));
 
    return maxdepth + 1 ;
}
 
// Driver Code
public static void main(String[] args)
{
    /* Let us create below tree
    *             A
    *         / / \ \
    *     B F D E
    *     / \ | /|\
    *     K J G C H I
    *     /\         \
    * N M         L
    */
     
    Node root = newNode('A');
    (root.child).add(newNode('B'));
    (root.child).add(newNode('F'));
    (root.child).add(newNode('D'));
    (root.child).add(newNode('E'));
    (root.child.get(0).child).add(newNode('K'));
    (root.child.get(0).child).add(newNode('J'));
    (root.child.get(2).child).add(newNode('G'));
    (root.child.get(3).child).add(newNode('C'));
    (root.child.get(3).child).add(newNode('H'));
    (root.child.get(3).child).add(newNode('I'));
    (root.child.get(0).child.get(0).child).add(newNode('N'));
    (root.child.get(0).child.get(0).child).add(newNode('M'));
    (root.child.get(3).child.get(2).child).add(newNode('L'));
     
    System.out.print(depthOfTree(root) + "\n");
}
}
 
// This code is contributed by Rajput-Ji

C#




// C# program to find the height of
// an N-ary tree
using System;
using System.Collections.Generic;
 
class GFG
{
 
// Structure of a node of an n-ary tree
public class Node
{
    public char key;
    public List<Node > child;
};
 
// Utility function to create a new tree node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = (char) key;
    temp.child = new List<Node>();
    return temp;
}
 
// Function that will return the depth
// of the tree
static int depthOfTree(Node ptr)
{
    // Base case
    if (ptr == null)
        return 0;
 
    // Check for all children and find
    // the maximum depth
    int maxdepth = 0;
    foreach (Node it in ptr.child)
        maxdepth = Math.Max(maxdepth,
                            depthOfTree(it));
 
    return maxdepth + 1 ;
}
 
// Driver Code
public static void Main(String[] args)
{
     
    /* Let us create below tree
    *             A
    *         / / \ \
    *     B F D E
    *     / \ | /|\
    *     K J G C H I
    *     /\         \
    * N M         L
    */
    Node root = newNode('A');
    (root.child).Add(newNode('B'));
    (root.child).Add(newNode('F'));
    (root.child).Add(newNode('D'));
    (root.child).Add(newNode('E'));
    (root.child[0].child).Add(newNode('K'));
    (root.child[0].child).Add(newNode('J'));
    (root.child[2].child).Add(newNode('G'));
    (root.child[3].child).Add(newNode('C'));
    (root.child[3].child).Add(newNode('H'));
    (root.child[3].child).Add(newNode('I'));
    (root.child[0].child[0].child).Add(newNode('N'));
    (root.child[0].child[0].child).Add(newNode('M'));
    (root.child[3].child[2].child).Add(newNode('L'));
     
    Console.Write(depthOfTree(root) + "\n");
}
}
 
// This code is contributed by Rajput-Ji

Javascript




<script>
 
// JavaScript program to find the height of
// an N-ary tree
 
// Structure of a node of an n-ary tree
class Node
{
    constructor()
    {
        this.key = 0;
        this.child = [];
    }
};
 
// Utility function to create a new tree node
function newNode(key)
{
    var temp = new Node();
    temp.key =  key;
    temp.child = [];
    return temp;
}
 
// Function that will return the depth
// of the tree
function depthOfTree(ptr)
{
    // Base case
    if (ptr == null)
        return 0;
 
    // Check for all children and find
    // the maximum depth
    var maxdepth = 0;
    for(var it of ptr.child)
        maxdepth = Math.max(maxdepth,
                            depthOfTree(it));
 
    return maxdepth + 1 ;
}
 
// Driver Code
 
/* Let us create below tree
*             A
*         / / \ \
*     B F D E
*     / \ | /|\
*     K J G C H I
*     /\         \
* N M         L
*/
var root = newNode('A');
(root.child).push(newNode('B'));
(root.child).push(newNode('F'));
(root.child).push(newNode('D'));
(root.child).push(newNode('E'));
(root.child[0].child).push(newNode('K'));
(root.child[0].child).push(newNode('J'));
(root.child[2].child).push(newNode('G'));
(root.child[3].child).push(newNode('C'));
(root.child[3].child).push(newNode('H'));
(root.child[3].child).push(newNode('I'));
(root.child[0].child[0].child).push(newNode('N'));
(root.child[0].child[0].child).push(newNode('M'));
(root.child[3].child[2].child).push(newNode('L'));
document.write(depthOfTree(root) + "<br>");
 
 
</script>

Output:  

4

 

This article is contributed by Shubham Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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