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# Depth of an N-Ary tree

• Difficulty Level : Easy
• Last Updated : 29 Mar, 2023

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 ` `using` `namespace` `std;`   `// Structure of a node of an n-ary tree` `struct` `Node` `{` `   ``char` `key;` `   ``vector 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::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 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();` `    ``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 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();` `    ``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

 ``

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.

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