# Program to Find the Largest Element in a Binary Tree

Program to Find the Largest Element in a Binary Tree on fibonacci, factorial, prime, armstrong, swap, reverse, search, sort, stack, queue, array, linkedlist, tree, graph etc.

## Q. Program to find the largest element in a Binary Tree.

### Explanation

In this program, we will find out the largest node in the given binary tree. We first define variable max that will hold root's data. Then, we traverse through the left sub-tree to find the largest node. Compare it with max and store the maximum of two in a variable max. Then, we traverse through the right subtree to find the largest node and compare it with max. In the end, max will have the largest node.

Above diagram represents a binary tree. Initially, max will hold 15. Recursive through left subtree.

```max = 15, leftMax = 20 => (20 > 15) then max = 20
max = 20, leftMax = 74 => (74 > 20) then max = 74
```

Recursive through right subtree.

```max = 74, rightMax = 35 => (74 > 35) then max = 74
```

Recurse in the left subtree of 35

```max = 74, leftMax = 55 => (74 > 55) then max = 74
```

Recurse in the right subtree of 35

```max = 74, rightMax = 6 => (74 > 6) then max = 74
```

So, the largest node in above binary tree is 74.

### Algorithm

1. Define the class Node 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. Assign the data part of the node with an appropriate value and assign left and right to null.
3. Define another class which has an attribute root.
1. Root represents the root node of the tree which is initialized to null.
2. largestElement() will find out the largest node in the binary tree:
1. It checks whether the root is null, which means the tree is empty.
2. If the tree is not empty, define a variable max that will store temp's data.
3. Find out the maximum node in the left subtree by calling largestElement() recursively. Store that value in leftMax. Compare the value of max with leftMax and store the maximum of two to max.
4. Find out the maximum node in right subtree by calling largestElement() recursively. Store that value in rightMax. Compare the value of max with rightMax and store the maximum of two to max.
5. In the end, max will hold the largest node in the binary tree.

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

#largestElement() will find out the largest node in the binary tree
def largestElement(self, temp):
#Check whether tree is empty
if(self.root == None):
print("Tree is empty");
return 0;

else:
#Variable maximum will store temp's data
maximum = temp.data;

#It will find largest element in left subtree
if(temp.left != None):
leftMax = self.largestElement(temp.left);
#Compare variable maximum with leftMax and store greater value into maximum
maximum = max(maximum, leftMax);

#It will find largest element in right subtree
if(temp.right != None):
rightMax = self.largestElement(temp.right);
#Compare variable maximum with rightMax and store greater value into maximum
maximum = max(maximum, rightMax);

return maximum;

bt = LargestNode();
#Add nodes to the binary tree
bt.root = Node(15);
bt.root.left = Node(20);
bt.root.right = Node(35);
bt.root.left.left = Node(74);
bt.root.right.left = Node(55);
bt.root.right.right = Node(6);

#Display largest node in the binary tree
print("Largest element in the binary tree: " + str(bt.largestElement(bt.root)));
```

Output:

```Largest element in the binary tree: 74
```

### C

```#include <stdio.h>
#include <stdbool.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;
}

//largestElement() will find out the largest node in the binary tree
int largestElement(struct node *temp){
//Check whether tree is empty
if(root == NULL) {
printf("Tree is empty\n");
return 0;
}
else{
int leftMax, rightMax;
//Max will store temp's data
int max = temp->data;
//It will find largest element in left subtree
if(temp->left != NULL){
leftMax = largestElement(temp->left);
//Compare max with leftMax and store greater value into max
max = (max > leftMax) ? max : leftMax;
}

//It will find largest element in right subtree
if(temp->right != NULL){
rightMax = largestElement(temp->right);
//Compare max with rightMax and store greater value into max
max = (max > rightMax) ? max : rightMax;
}
return max;
}
}

int main()
{
//Add nodes to the binary tree
root = createNode(15);
root->left = createNode(20);
root->right = createNode(35);
root->left->left = createNode(74);
root->right->left = createNode(55);
root->right->right = createNode(6);

//Display largest node in the binary tree
printf("Largest element in the binary tree: %d", largestElement(root));
return 0;
}
```

Output:

```Largest element in the binary tree: 74
```

### JAVA

```public class LargestNode {
//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 LargestNode(){
root = null;
}

//largestElement() will find out the largest node in the binary tree
public int largestElement(Node temp){
//Check whether tree is empty
if(root == null) {
System.out.println("Tree is empty");
return 0;
}
else{
int leftMax, rightMax;
//Max will store temp's data
int max = temp.data;

//It will find largest element in left subtree
if(temp.left != null){
leftMax = largestElement(temp.left);
//Compare max with leftMax and store greater value into max
max = Math.max(max, leftMax);
}

//It will find largest element in right subtree
if(temp.right != null){
rightMax = largestElement(temp.right);
//Compare max with rightMax and store greater value into max
max = Math.max(max, rightMax);
}
return max;
}
}

public static void main(String[] args) {

LargestNode bt = new LargestNode();
//Add nodes to the binary tree
bt.root = new Node(15);
bt.root.left = new Node(20);
bt.root.right = new Node(35);
bt.root.left.left = new Node(74);
bt.root.right.left = new Node(55);
bt.root.right.right = new Node(6);

//Display largest node in the binary tree
System.out.println("Largest element in the binary tree: " + bt.largestElement(bt.root));
}
}
```

Output:

```Largest element in the binary tree: 74
```

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

public LargestNode(){
root = null;
}

//largestElement() will find out the largest node in the binary tree
public T largestElement(Node<T> temp){
//Check whether tree is empty
if(root == null) {
Console.WriteLine("Tree is empty");
return default(T);
}
else{
T leftMax, rightMax;
//Max will store temp's data
T max = temp.data;

//It will find largest element in left subtree
if(temp.left != null){
leftMax = largestElement(temp.left);
//Compare max with leftMax and store greater value into max
max = (max.CompareTo(leftMax) < 0) ? leftMax : max;
}

//It will find largest element in right subtree
if(temp.right != null){
rightMax = largestElement(temp.right);
//Compare max with rightMax and store greater value into max
max = (max.CompareTo(rightMax) < 0) ? rightMax : max;
}
return max;
}
}
}

public static void Main()
{
LargestNode<int> bt = new LargestNode<int>();
//Add nodes to the binary tree
bt.root = new Node<int>(15);
bt.root.left = new Node<int>(20);
bt.root.right = new Node<int>(35);
bt.root.left.left = new Node<int>(74);
bt.root.right.left = new Node<int>(55);
bt.root.right.right = new Node<int>(6);

//Display largest node in the binary tree
Console.WriteLine("Largest element in the binary tree: " + bt.largestElement(bt.root));
}
}
}
```

Output:

```Largest element in the binary tree: 74
```

### 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 LargestNode{
//Represent the root of binary tree
public \$root;
function __construct(){
\$this->root = NULL;
}

//largestElement() will find out the largest node in the binary tree
function largestElement(\$temp){
//Check whether tree is empty
if(\$this->root == NULL) {
print "Tree is empty<br>";
return 0;
}
else{
//\$max will store \$temp's data
\$max = \$temp->data;

//It will find largest element in left subtree
if(\$temp->left != NULL){
\$leftMax = \$this->largestElement(\$temp->left);
//Compare \$max with \$leftMax and store greater value into \$max
\$max = max(\$max, \$leftMax);
}

//It will find largest element in right subtree
if(\$temp->right != NULL){
\$rightMax = \$this->largestElement(\$temp->right);
//Compare \$max with \$rightMax and store greater value into \$max
\$max = max(\$max, \$rightMax);
}
return \$max;
}
}
}
\$bt = new LargestNode();
//Add nodes to the binary tree
\$bt->root = new Node(15);
\$bt->root->left = new Node(20);
\$bt->root->right = new Node(35);
\$bt->root->left->left = new Node(74);
\$bt->root->right->left = new Node(55);
\$bt->root->right->right = new Node(6);

//Display largest node in the binary tree
print "Largest element in the binary tree: " . \$bt->largestElement(\$bt->root);
?>
</body>
</html>
```

Output:

```Largest element in the binary tree: 74
```

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