Depth of an N-Ary tree

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.

Algorithm

Here is the algorithm for finding the depth of an N-Ary tree:

1)Define a struct for the nodes of the N-ary tree with a key and a vector of pointers to its child nodes.
2)Create a utility function to create a new node with the given key.
3)Define a function depthOfTree that takes in a pointer to a Node and returns the depth of the tree.
4)If the pointer to the Node is null, return 0.
5)Initialize a variable maxdepth to 0.
6)Iterate through the vector of child nodes of the current Node and for each child node, recursively call depthOfTree function on the child and find the maximum depth.
7)Update the maxdepth variable to be the maximum of the current maxdepth and the depth of the child node.
8)Return the maxdepth plus 1 as the depth of the tree.
9)In the main function, create an N-ary tree and call depthOfTree function on the root node of the tree to get the depth.
10)Print the depth of the tree.

Examples:

• Example 1: 
  

• Example 2: 
  

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. 

Implementation:

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

Python3

# Python program to find the height of
# an N-ary tree

# Structure of a node of an n-ary tree
class Node:
    def __init__(self, key):
        self.key = key
        self.child = []

# Utility function to create a new tree node
def new_node(key):
    temp = Node(key)
    return temp

# Function that will return the depth
# of the tree
def depth_of_tree(ptr):
    # Base case
    if ptr is None:
        return 0

    # Check for all children and find
    # the maximum depth
    maxdepth = 0
    for child in ptr.child:
        maxdepth = max(maxdepth, depth_of_tree(child))

    return maxdepth + 1

# Driver program
if __name__ == '__main__':
    """ Let us create below tree
            A
        / / \ \
        B F D E
        / \ | /|\
        K J G C H I
        /\         \
        N M         L
    """

    root = new_node('A')
    root.child.extend([new_node('B'), new_node('F'), new_node('D'), new_node('E')])
    root.child[0].child.extend([new_node('K'), new_node('J')])
    root.child[2].child.append(new_node('G'))
    root.child[3].child.extend([new_node('C'), new_node('H'), new_node('I')])
    root.child[0].child[0].child.extend([new_node('N'), new_node('M')])
    root.child[3].child[2].child.append(new_node('L'))

    print(depth_of_tree(root))

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

Time complexity: O(n)
Auxiliary Space: O(n)

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