# Program to Find the Smallest Element in a Binary Tree

Program to Find the Smallest 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 smallest element in a Binary Tree.

### Explanation

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

Above diagram represents a binary tree. Initially, min will hold 4. Recursive through left subtree.

```min = 4, leftMin = 2    =>  (2 < 4) then min = 2
min = 2, leftMin = 1    =>  (1 < 2) then min = 1
```

Recursive through right subtree.

```min = 1, rightMin = 3  =>  (1 < 3) then min = 1
Recurse in left subtree of 5
min = 1, leftMin = 5    =>  (1 < 5) then min = 1
```

Recurse in right subtree of 3

```min = 1, rightMin = 6  =>  (1 < 6) then min = 1
```

So, smallest node in above binary tree is 1.

### 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 node and both left and right will be set to null.
3. Define another class which has an attribute root.
1. Root represent root node of the tree and initialize it to null.
1. smallestElement() will find out the smallest node in binary tree:
1. It checks whether root is null, which means tree is empty.
2. If tree is not empty, define a variable min that will store temp's data.
3. Find out the minimum node in left subtree by calling smallestElement() recursively. Store that value in leftMin. Compare the value of min with leftMin and store the minimum of two to min.
4. Find out the minimum node in right subtree by calling smallestElement() recursively. Store that value in rightMin. Compare the value of min with rightMin and store the maximum of two to min.
5. At the end, min will hold the smallest 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 SmallestNode:
def __init__(self):
#Represent the root of binary tree
self.root = None;

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

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

#It will find smallest element in left subtree
if(temp.left != None):
leftMin = self.smallestElement(temp.left);
#If value of minimum is greater than leftMin then store the value of leftMin into minimum
minimum = min(minimum, leftMin);

#It will find smallest element in right subtree
if(temp.right != None):
rightMin = self.smallestElement(temp.right);
#If value of minimum is greater than rightMin then store the value of rightMin into minimum
minimum = min(minimum, rightMin);

return minimum;

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

#Display smallest node in the binary tree
print("Smallest element in the binary tree: " + str(bt.smallestElement(bt.root)));
```

Output:

```Smallest element in the binary tree: 1
```

### 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;
}

//smallestElement() will find out the smallest node in the binary tree
int smallestElement(struct node *temp){
//Check whether tree is empty
if(root == NULL) {
printf("Tree is empty\n");
return 0;
}
else{
int leftMin, rightMin;
//Min will store temp's data
int min = temp->data;

//It will find smallest element in left subtree
if(temp->left != NULL){
leftMin = smallestElement(temp->left);
//If min is greater than leftMin then store the value of leftMin into min
min = (min > leftMin) ? leftMin : min;
}

//It will find smallest element in right subtree
if(temp->right != NULL){
rightMin = smallestElement(temp->right);
//If min is greater than rightMin then store the value of rightMin into min
min = (min > rightMin) ? rightMin : min;
}
return min;
}
}

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

//Display smallest node in the binary tree
printf("Smallest element in the binary tree: %d", smallestElement(root));
return 0;
}
```

Output:

```Smallest element in the binary tree: 1
```

### JAVA

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

//smallestElement() will find out the smallest node in the binary tree
public int smallestElement(Node temp){
//Check whether tree is empty
if(root == null) {
System.out.println("Tree is empty");
return 0;
}
else {
int leftMin, rightMin;
//Min will store temp's data
int min = temp.data;

//It will find smallest element in left subtree
if(temp.left != null){
leftMin = smallestElement(temp.left);
//If min is greater than leftMin then store the value of leftMin into min
min = Math.min(min, leftMin);
}

//It will find smallest element in right subtree
if(temp.right != null){
rightMin = smallestElement(temp.right);
//If min is greater than rightMin then store the value of rightMin into min
min = Math.min(min, rightMin);
}
return min;
}
}

public static void main(String[] args) {

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

//Display smallest node in the binary tree
System.out.println("Smallest element in the binary tree: " + bt.smallestElement(bt.root));
}
}
```

Output:

```Smallest element in the binary tree: 1
```

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

public SmallestNode(){
root = null;
}

//smallestElement() will find out the smallest node in the binary tree
public T smallestElement(Node<T> temp){
//Check whether tree is empty
if(root == null) {
Console.WriteLine("Tree is empty");
return default(T);
}
T leftMin, rightMin;
//Min will store temp's data
T min = temp.data;

//It will find smallest element in left subtree
if(temp.left != null){
leftMin = smallestElement(temp.left);
//If min is greater than leftMin then store the value of leftMin into min
min = (min.CompareTo(leftMin) > 0) ? leftMin : min;
}

//It will find smallest element in right subtree
if(temp.right != null){
rightMin = smallestElement(temp.right);
//If min is greater than rightMin then store the value of rightMin into min
min = (min.CompareTo(rightMin) > 0) ? rightMin : min;
}
return min;
}
}

public static void Main()
{
SmallestNode<int> bt = new SmallestNode<int>();
//Add nodes to the binary tree
bt.root = new Node<int>(4);
bt.root.left = new Node<int>(2);
bt.root.right = new Node<int>(3);
bt.root.left.left = new Node<int>(1);
bt.root.right.left = new Node<int>(5);
bt.root.right.right = new Node<int>(6);

//Display smallest node in the binary tree
Console.WriteLine("Smallest element in the binary tree: " + bt.smallestElement(bt.root));
}
}
}
```

Output:

```Smallest element in the binary tree: 1
```

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

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

//It will find smallest element in left subtree
if(\$temp->left != NULL){
\$leftMin = \$this->smallestElement(\$temp->left);
//If \$min is greater than \$leftMin then store the value of \$leftMin into \$min
\$min = min(\$min, \$leftMin);
}

//It will find smallest element in right subtree
if(\$temp->right != NULL){
\$rightMin = \$this->smallestElement(\$temp->right);
//If \$min is greater than \$rightMin then store the value of \$rightMin into \$min
\$min = min(\$min, \$rightMin);
}
return \$min;
}
}
}
\$bt = new SmallestNode();
//Add nodes to the binary tree
\$bt->root = new Node(4);
\$bt->root->left = new Node(2);
\$bt->root->right = new Node(3);
\$bt->root->left->left = new Node(1);
\$bt->root->right->left = new Node(5);
\$bt->root->right->right = new Node(6);

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

Output:

```Smallest element in the binary tree: 1
```

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