Posted on by Kalkicode
Code Tree

# Find height of n-ary tree

Delve into the world of N-ary trees as this article takes you on a journey to uncover the height of these intricate data structures. With a comprehensive breakdown of the problem, solution strategy, and practical Java code implementation, readers will gain a profound understanding of how to determine the height of N-ary trees.

## Problem Statement

Given an N-ary tree, the task is to find and display its height.

## Example

Consider the following N-ary tree:

``````
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
``````

The output is:

``Height: 6``

## Solution Strategy

1. Create a class `TreeNode` to represent nodes in the N-ary tree. This class should include a value and a vector of children.
2. Implement the `NAryTree` class, responsible for building the N-ary tree, computing its height, and displaying the result.
3. Utilize a recursive approach to traverse the tree and find the maximum height of subtrees.

## Code Solution

``````import java.util.Vector;
import java.util.ArrayList;
// Java program for
// Find height of n-ary tree
class TreeNode
{
public int key;
public Vector < TreeNode > child;
public TreeNode(int key)
{
this.key = key;
this.child = new Vector < TreeNode > ();
}
public void addChild(int key)
{
TreeNode t = new TreeNode(key);
}
}
public class NAryTree
{
public TreeNode root;
public NAryTree()
{
// Set initial tree root to null
this.root = null;
}
// Returns a maximum value of two numbers
public int max(int a, int b)
{
if(a > b)
{
return a;
}
else
{
return b;
}
}
public int findHeight(TreeNode node)
{
if (node == null)
{
return 0;
}

int i = 0;
int height = 0;

// iterating the child of given node
while (i < node.child.size())
{
// Recursively visit child node
height = max(findHeight(node.child.get(i)),height);
i++;
}
// return new height
return height+1;
}
public static void main(String[] args)
{
NAryTree tree = new NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
tree.root = new TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)

// Add child node [20] in node (2)
// Add child node [-6] in node (20)
tree.root.child.get(1).child.get(3).child.get(0)

// Get tree height
int height = tree.findHeight(tree.root);

// Display the calculated height
System.out.print(" Height : "+height);
}
}``````

#### input

`` Height : 6``
``````// Include header file
#include <iostream>
#include <vector>
using namespace std;

// C++ program for
// Find height of n-ary tree

class TreeNode
{
public: int key;
vector < TreeNode *> child;
TreeNode(int key)
{
this->key = key;
}
{
TreeNode *t = new TreeNode(key);
this->child.push_back(t);
}
};
class NAryTree
{
public: TreeNode *root;
NAryTree()
{
this->root = NULL;
}
// Returns a maximum value of two numbers
int max(int a, int b)
{
if (a > b)
{
return a;
}
else
{
return b;
}
}
int findHeight(TreeNode *node)
{
if (node == NULL)
{
return 0;
}
int i = 0;
int height = 0;
// iterating the child of given node
while (i < node->child.size())
{
// Recursively visit child node
height = this->max(this->findHeight(node->child.at(i)), height);
i++;
}
// return new height
return height + 1;
}
};
int main()
{
NAryTree *tree = new NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
tree->root = new TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)
// Add child node [20] in node (2)
// Add child node [-6] in node (20)
tree->root->child.at(1)->child.at(3)->child.at(0)
// Get tree height
int height = tree->findHeight(tree->root);
// Display the calculated height
cout << " Height : " << height;
return 0;
}``````

#### input

`` Height : 6``
``````// Include namespace system
using System;
using System.Collections.Generic;
// Csharp program for
// Find height of n-ary tree
public class TreeNode
{
public int key;
public List < TreeNode > child;
public TreeNode(int key)
{
this.key = key;
this.child = new List < TreeNode > ();
}
public void addChild(int key)
{
TreeNode t = new TreeNode(key);
}
}
public class NAryTree
{
public TreeNode root;
public NAryTree()
{
// Set initial tree root to null
this.root = null;
}
// Returns a maximum value of two numbers
public int max(int a, int b)
{
if (a > b)
{
return a;
}
else
{
return b;
}
}
public int findHeight(TreeNode node)
{
if (node == null)
{
return 0;
}
int i = 0;
int height = 0;
// iterating the child of given node
while (i < node.child.Count)
{
// Recursively visit child node
height = this.max(this.findHeight(node.child[i]), height);
i++;
}
// return new height
return height + 1;
}
public static void Main(String[] args)
{
NAryTree tree = new NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
tree.root = new TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)
// Add child node [20] in node (2)
// Add child node [-6] in node (20)
// Get tree height
int height = tree.findHeight(tree.root);
// Display the calculated height
Console.Write(" Height : " + height);
}
}``````

#### input

`` Height : 6``
``````<?php
// Php program for
// Find height of n-ary tree
class TreeNode
{
public \$key;
public \$child;
public	function __construct(\$key)
{
\$this->key = \$key;
\$this->child = array();
}
{
\$t = new TreeNode(\$key);
\$this->child[] = \$t;
}
}
class NAryTree
{
public \$root;
public	function __construct()
{
\$this->root = NULL;
}
// Returns a maximum value of two numbers
public	function max(\$a, \$b)
{
if (\$a > \$b)
{
return \$a;
}
else
{
return \$b;
}
}
public	function findHeight(\$node)
{
if (\$node == NULL)
{
return 0;
}
\$i = 0;
\$height = 0;
// iterating the child of given node
while (\$i < count(\$node->child))
{
// Recursively visit child node
\$height = \$this->max(\$this->findHeight(\$node->child[\$i]), \$height);
\$i++;
}
// return new height
return \$height + 1;
}
}

function main()
{
\$tree = new NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
\$tree->root = new TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)
// Add child node [20] in node (2)
// Add child node [-6] in node (20)
// Get tree height
\$height = \$tree->findHeight(\$tree->root);
// Display the calculated height
echo(" Height : ".\$height);
}
main();``````

#### input

`` Height : 6``
``````// Node JS program for
// Find height of n-ary tree
class TreeNode
{
constructor(key)
{
this.key = key;
this.child = [];
}
{
var t = new TreeNode(key);
this.child.push(t);
}
}
class NAryTree
{
constructor()
{
this.root = null;
}
// Returns a maximum value of two numbers
max(a, b)
{
if (a > b)
{
return a;
}
else
{
return b;
}
}
findHeight(node)
{
if (node == null)
{
return 0;
}
var i = 0;
var height = 0;
// iterating the child of given node
while (i < node.child.length)
{
// Recursively visit child node
height = this.max(this.findHeight(node.child[i]), height);
i++;
}
// return new height
return height + 1;
}
}

function main()
{
var tree = new NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
tree.root = new TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)
// Add child node [20] in node (2)
// Add child node [-6] in node (20)
// Get tree height
var height = tree.findHeight(tree.root);
// Display the calculated height
process.stdout.write(" Height : " + height);
}
main();``````

#### input

`` Height : 6``
``````#  Python 3 program for
#  Find height of n-ary tree
class TreeNode :
def __init__(self, key) :
self.key = key
self.child = []

def addChild(self, key) :
t = TreeNode(key)
self.child.append(t)

class NAryTree :
def __init__(self) :
self.root = None

#  Returns a maximum value of two numbers
def max(self, a, b) :
if (a > b) :
return a
else :
return b

def findHeight(self, node) :
if (node == None) :
return 0

i = 0
height = 0
#  iterating the child of given node
while (i < len(node.child)) :
#  Recursively visit child node
height = self.max(self.findHeight(node.child[i]), height)
i += 1

#  return new height
return height + 1

def main() :
tree = NAryTree()
#           10
#          /   \
#         /     \
#        /       \
#       8         5
#      /|\      /|\ \
#     / | \    / | \ \
#    -2 1  6  7 18 3  4
#      / \           /| \
#     9  11         2 1  3
#       /  \        |
#      17   12      20
#                   |
#                  -6
#    -----------------------
#    Constructing N-Arr tree
#  First element of tree
tree.root = TreeNode(10)
#  Add child node [-2,1,5] in node (8)
#  Add child node [9,11] in node (1)
#  Add child node [17  12] in node (11)
#  Add child node [7 18 3  4] in node (5)
#  Add child node [2,1,3] in node (4)
#  Add child node [20] in node (2)
#  Add child node [-6] in node (20)
#  Get tree height
height = tree.findHeight(tree.root)
#  Display the calculated height
print(" Height : ", height, end = "")

if __name__ == "__main__": main()``````

#### input

`` Height :  6``
``````#  Ruby program for
#  Find height of n-ary tree
class TreeNode
# Define the accessor and reader of class TreeNode
attr_accessor :key, :child
def initialize(key)
self.key = key
self.child = []
end

t = TreeNode.new(key)
self.child.push(t)
end

end

class NAryTree
# Define the accessor and reader of class NAryTree
attr_accessor :root
def initialize()
self.root = nil
end

#  Returns a maximum value of two numbers
def max(a, b)
if (a > b)
return a
else

return b
end

end

def findHeight(node)
if (node == nil)
return 0
end

i = 0
height = 0
#  iterating the child of given node
while (i < node.child.length)
#  Recursively visit child node
height = self.max(self.findHeight(node.child[i]), height)
i += 1
end

#  return new height
return height + 1
end

end

def main()
tree = NAryTree.new()
#           10
#          /   \
#         /     \
#        /       \
#       8         5
#      /|\      /|\ \
#     / | \    / | \ \
#    -2 1  6  7 18 3  4
#      / \           /| \
#     9  11         2 1  3
#       /  \        |
#      17   12      20
#                   |
#                  -6
#    -----------------------
#    Constructing N-Arr tree
#  First element of tree
tree.root = TreeNode.new(10)
#  Add child node [-2,1,5] in node (8)
#  Add child node [9,11] in node (1)
#  Add child node [17  12] in node (11)
#  Add child node [7 18 3  4] in node (5)
#  Add child node [2,1,3] in node (4)
#  Add child node [20] in node (2)
#  Add child node [-6] in node (20)
#  Get tree height
height = tree.findHeight(tree.root)
#  Display the calculated height
print(" Height : ", height)
end

main()``````

#### input

`` Height : 6``
``````import scala.collection.mutable._;
// Scala program for
// Find height of n-ary tree
class TreeNode(var key: Int,
var child: ArrayBuffer[TreeNode])
{
def this(key: Int)
{
this(key, new ArrayBuffer[TreeNode]());
}
def addChild(key: Int): Unit = {
var t: TreeNode = new TreeNode(key);
this.child += t;
}
}
class NAryTree(var root: TreeNode)
{
def this()
{
this(null);
}
// Returns a maximum value of two numbers
def max(a: Int, b: Int): Int = {
if (a > b)
{
return a;
}
else
{
return b;
}
}
def findHeight(node: TreeNode): Int = {
if (node == null)
{
return 0;
}
var i: Int = 0;
var height: Int = 0;
// iterating the child of given node
while (i < node.child.size)
{
// Recursively visit child node
height = max(findHeight(node.child(i)), height);
i += 1;
}
// return new height
return height + 1;
}
}
object Main
{
def main(args: Array[String]): Unit = {
var tree: NAryTree = new NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
tree.root = new TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)
// Add child node [20] in node (2)
// Add child node [-6] in node (20)
// Get tree height
var height: Int = tree.findHeight(tree.root);
// Display the calculated height
print(" Height : " + height);
}
}``````

#### input

`` Height : 6``
``````import Foundation;
// Swift 4 program for
// Find height of n-ary tree
class TreeNode
{
var key: Int;
var child: [TreeNode?] ;
init(_ key: Int)
{
self.key = key;
self.child = [TreeNode]();
}
func addChild(_ key: Int)
{
let t: TreeNode = TreeNode(key);
self.child.append(t);
}
}
class NAryTree
{
var root: TreeNode? ;
init()
{
self.root = nil;
}
// Returns a maximum value of two numbers
func max(_ a: Int, _ b: Int) -> Int
{
if (a > b)
{
return a;
}
else
{
return b;
}
}
func findHeight(_ node: TreeNode? ) -> Int
{
if (node == nil)
{
return 0;
}
var i = 0;
var height = 0;
// iterating the child of given node
while (i < node!.child.count)
{
// Recursively visit child node
height = self.max(self.findHeight(node!.child[i]), height);
i += 1;
}
// return new height
return height + 1;
}
}
func main()
{
let tree = NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
tree.root = TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)
// Add child node [20] in node (2)
// Add child node [-6] in node (20)
// Get tree height
let height = tree.findHeight(tree.root);
// Display the calculated height
print(" Height : ", height, terminator: "");
}
main();``````

#### input

`` Height :  6``
``````// Kotlin program for
// Find height of n-ary tree
class TreeNode
{
var key: Int;
var child: MutableList<TreeNode> ;
constructor(key: Int)
{
this.key = key;
this.child = mutableListOf<TreeNode>();
}
fun addChild(key: Int): Unit
{
val t: TreeNode = TreeNode(key);
}
}
class NAryTree
{
var root: TreeNode ? ;
constructor()
{
this.root = null;
}
// Returns a maximum value of two numbers
fun max(a: Int, b: Int): Int
{
if (a > b)
{
return a;
}
else
{
return b;
}
}
fun findHeight(node: TreeNode ? ): Int
{
if (node == null)
{
return 0;
}
var i: Int = 0;
var height: Int = 0;
// iterating the child of given node
while (i < node.child.size)
{
// Recursively visit child node
height = this.max(this.findHeight(node.child[i]), height);
i += 1;
}
// return new height
return height + 1;
}
}
fun main(args: Array < String > ): Unit
{
val tree: NAryTree = NAryTree();
/*
10
/   \
/     \
/       \
8         5
/|\      /|\ \
/ | \    / | \ \
-2 1  6  7 18 3  4
/ \           /| \
9  11         2 1  3
/  \        |
17   12      20
|
-6
-----------------------
Constructing N-Arr tree
*/
// First element of tree
tree.root = TreeNode(10);
// Add child node [-2,1,5] in node (8)
// Add child node [9,11] in node (1)
// Add child node [17  12] in node (11)
// Add child node [7 18 3  4] in node (5)
// Add child node [2,1,3] in node (4)
// Add child node [20] in node (2)
// Add child node [-6] in node (20)
// Get tree height
var height: Int = tree.findHeight(tree.root);
// Display the calculated height
print(" Height : " + height);
}``````

#### input

`` Height : 6``

## Time Complexity Analysis

In the worst case, the traversal of the N-ary tree requires visiting each node once. Since the tree's depth is limited, the time complexity is O(n), where n is the number of nodes in the tree.

## Comment

Please share your knowledge to improve code and content standard. Also submit your doubts, and test case. We improve by your feedback. We will try to resolve your query as soon as possible.

Categories
Relative Post