Depth of an N-Ary tree

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:

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