# Program to Find the Maximum Depth or Height of a Tree

Program to Find the Maximum Depth or Height of a Tree on fibonacci, factorial, prime, armstrong, swap, reverse, search, sort, stack, queue, array, linkedlist, tree, graph etc.

## Q. Program to find the maximum depth or height of a tree

### Explanation

In this program, we need to find out the maximum height of the binary tree. The height of the binary tree can be defined as the number of nodes between root and a leaf. Maximum height will be the number of levels between root and deepest leaf. To solve this problem, we traverse through the left subtree and calculate the height of the left subtree. Again, calculate the height of the right subtree by traversing through it. Maximum height will be maximum of the height of the left subtree and right subtree.

In the above binary tree,

Height of left subtree is 2.
Height of right subtree is 4.
MaxHeight = Max(leftHeight, rightHeight) + 1; Here, 1 Represents root node's height

The maximum height of the given binary tree is (4 + 1) = 5 denoted by white dotted line.

### Algorithm

1. Define Node class which has three attributes namely: data left and right. Here, left represents the left child of the node and right represents the right child of the node.
2. When a node is created, data will pass to data attribute of the node and both left and right will be set to null.
3. Define another class which has an attribute root.
1. Root represents the root node of the tree and initializes it to null.
4. findHeight() will determine the maximum height of the binary tree:
1. It checks whether the root is null, which means the tree is empty.
2. If the tree is not empty, traverse through left subtree to determine the height of the left subtree and store the value in leftHeight.
3. Similarly, determine the height of the right subtree and store the value in rightHeight.
4. Maximum will determine the maximum of leftHeight and rightHeight then, add 1 for root's height.

### Python

```#Represent a node of binary tree
class Node:
def __init__(self,data):
#Assign data to the new node, set left and right children to None
self.data = data;
self.left = None;
self.right = None;

class BinaryTree:
def __init__(self):
#Represent the root of binary tree
self.root = None;

#findHeight() will determine the maximum height of the binary tree
def findHeight(self, temp):
#Check whether tree is empty
if(self.root == None):
print("Tree is empty");
return 0;
else:
leftHeight = 0;
rightHeight = 0;

#Calculate the height of left subtree
if(temp.left != None):
leftHeight = self.findHeight(temp.left);

#Calculate the height of right subtree
if(temp.right != None):
rightHeight = self.findHeight(temp.right);

#Compare height of left subtree and right subtree
#and store maximum of two in variable max
maximum = leftHeight if (leftHeight > rightHeight) else rightHeight;

#Calculate the total height of the tree by adding the height of the root
return (maximum + 1);

bt = BinaryTree();
#Add nodes to the binary tree
bt.root = Node(1);
bt.root.left = Node(2);
bt.root.right = Node(3);
bt.root.left.left = Node(4);
bt.root.right.left = Node(5);
bt.root.right.right = Node(6);
bt.root.right.right.right= Node(7);
bt.root.right.right.right.right = Node(8);

#Display the maximum height of the given binary tree
print("Maximum height of given binary tree: " + str(bt.findHeight(bt.root)));
```

Output:

```Maximum height of given binary tree: 5
```

### C

```#include <stdio.h>
#include <stdlib.h>

//Represent a node of binary tree
struct node{
int data;
struct node *left;
struct node *right;
};

//Represent the root of binary tree
struct node *root = NULL;

//createNode() will create a new node
struct node* createNode(int data){
//Create a new node
struct node *newNode = (struct node*)malloc(sizeof(struct node));
//Assign data to newNode, set left and right children to NULL
newNode->data = data;
newNode->left = NULL;
newNode->right = NULL;

return newNode;
}

//findHeight() will determine the maximum height of the binary tree
int findHeight(struct node *temp){
//Check whether tree is empty
if(root == NULL) {
printf("Tree is empty\n");
return 0;
}
else {
int leftHeight = 0, rightHeight = 0;

//Calculate the height of left subtree
if(temp->left != NULL)
leftHeight = findHeight(temp->left);

//Calculate the height of right subtree
if(temp->right != NULL)
rightHeight = findHeight(temp->right);

//Compare height of left subtree and right subtree
//and store maximum of two in variable max
int max = (leftHeight > rightHeight) ? leftHeight : rightHeight;

//Calculate the total height of tree by adding height of root
return (max + 1);
}
}

int main()
{
//Add nodes to the binary tree
root = createNode(1);
root->left = createNode(2);
root->right = createNode(3);
root->left->left = createNode(4);
root->right->left = createNode(5);
root->right->right = createNode(6);
root->right->right->right= createNode(7);
root->right->right->right->right = createNode(8);

//Display the maximum height of the given binary tree
printf("Maximum height of given binary tree: %d", findHeight(root));
return 0;
}
```

Output:

```Maximum height of given binary tree: 5
```

### JAVA

```public class BinaryTree {

//Represent the node of binary tree
public static class Node{
int data;
Node left;
Node right;

public Node(int data){
//Assign data to the new node, set left and right children to null
this.data = data;
this.left = null;
this.right = null;
}
}

//Represent the root of binary tree
public Node root;
public BinaryTree(){
root = null;
}

//findHeight() will determine the maximum height of the binary tree
public int findHeight(Node temp){
//Check whether tree is empty
if(root == null) {
System.out.println("Tree is empty");
return 0;
}
else {
int leftHeight = 0, rightHeight = 0;

//Calculate the height of left subtree
if(temp.left != null)
leftHeight = findHeight(temp.left);

//Calculate the height of right subtree
if(temp.right != null)
rightHeight = findHeight(temp.right);

//Compare height of left subtree and right subtree
//and store maximum of two in variable max
int max = (leftHeight > rightHeight) ? leftHeight : rightHeight;

//Calculate the total height of tree by adding height of root
return (max + 1);
}
}

public static void main(String[] args) {

BinaryTree bt = new BinaryTree();
//Add nodes to the binary tree
bt.root = new Node(1);
bt.root.left = new Node(2);
bt.root.right = new Node(3);
bt.root.left.left = new Node(4);
bt.root.right.left = new Node(5);
bt.root.right.right = new Node(6);
bt.root.right.right.right= new Node(7);
bt.root.right.right.right.right = new Node(8);

//Display the maximum height of the given binary tree
System.out.println("Maximum height of given binary tree: " + bt.findHeight(bt.root));
}
}
```

Output:

```Maximum height of given binary tree: 5
```

### C#

```using System;
namespace Tree
{
public class Program
{
//Represent a node of binary tree
public class Node<T>{
public T data;
public Node<T> left;
public Node<T> right;

public Node(T data) {
//Assign data to the new node, set left and right children to null
this.data = data;
this.left = null;
this.right = null;
}
}

public class BinaryTree<T> where T : IComparable<T>{
//Represent the root of binary tree
public Node<T> root;

public static Boolean flag = false;

public BinaryTree(){
root = null;
}

//findHeight() will determine the maximum height of the binary tree
public int findHeight(Node<T> temp){
//Check whether tree is empty
if(root == null) {
Console.WriteLine("Tree is empty");
return 0;
}
else {
int leftHeight = 0, rightHeight = 0;

//Calculate the height of left subtree
if(temp.left != null)
leftHeight = findHeight(temp.left);

//Calculate the height of right subtree
if(temp.right != null)
rightHeight = findHeight(temp.right);

//Compare height of left subtree and right subtree
//and store maximum of two in variable max
int max = (leftHeight > rightHeight) ? leftHeight : rightHeight;

//Calculate the total height of tree by adding height of root
return (max + 1);
}
}
}
public static void Main()
{
BinaryTree<int> bt = new BinaryTree<int>();
//Add nodes to the binary tree
bt.root = new Node<int>(1);
bt.root.left = new Node<int>(2);
bt.root.right = new Node<int>(3);
bt.root.left.left = new Node<int>(4);
bt.root.right.left = new Node<int>(5);
bt.root.right.right = new Node<int>(6);
bt.root.right.right.right= new Node<int>(7);
bt.root.right.right.right.right = new Node<int>(8);

//Display the maximum height of the given binary tree
Console.WriteLine("Maximum height of given binary tree: " + bt.findHeight(bt.root));
}
}
}
```

Output:

```Maximum height of given binary tree: 5
```

### PHP

```<!DOCTYPE html>
<html>
<body>
<?php
//Represent a node of binary tree
class Node{
public \$data;
public \$left;
public \$right;

function __construct(\$data){
//Assign data to the new node, set left and right children to NULL
\$this->data = \$data;
\$this->left = NULL;
\$this->right = NULL;
}
}
class BinaryTree{
//Represent the root of binary tree
public \$root;
function __construct(){
\$this->root = NULL;
}

//findHeight() will determine the maximum height of the binary tree
function findHeight(\$temp){
//Check whether tree is empty
if(\$this->root == null) {
print "Tree is empty <br>";
return 0;
}
else {
\$leftHeight = 0;
\$rightHeight = 0;
//Calculate the height of left subtree
if(\$temp->left != NULL)
\$leftHeight = \$this->findHeight(\$temp->left);

//Calculate the height of right subtree
if(\$temp->right != NULL)
\$rightHeight = \$this->findHeight(\$temp->right);

//Compare height of left subtree and right subtree
//and store maximum of two in variable max
\$max = (\$leftHeight > \$rightHeight) ? \$leftHeight : \$rightHeight;

//Calculate the total height of tree by adding height of root
return (\$max + 1);
}
}
}
\$bt = new BinaryTree();
//Add nodes to the binary tree
\$bt->root = new Node(1);
\$bt->root->left = new Node(2);
\$bt->root->right = new Node(3);
\$bt->root->left->left = new Node(4);
\$bt->root->right->left = new Node(5);
\$bt->root->right->right = new Node(6);
\$bt->root->right->right->right= new Node(7);
\$bt->root->right->right->right->right = new Node(8);

//Display the maximum height of the given binary tree
print "Maximum height of given binary tree: " . \$bt->findHeight(\$bt->root);
?>
</body>
</html>
```

Output:

```Maximum height of given binary tree: 5
```

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