Program to Find the Smallest Element in a Binary Tree

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.

Program to find the smallest element in a Binary Tree

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

So, smallest node in above binary tree is 1.

Algorithm

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.
When a node is created, data will pass to data attribute of node and both left and right will be set to null.
Define another class which has an attribute root.
1. Root represent root node of the tree and initialize it to null.

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.

Solution

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 emptyn”);          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

Next TopicPrograms List

Q. Program to find the smallest element in a Binary Tree.

Explanation

Algorithm

Solution

Python

C

JAVA

C#

PHP

Potential Energy

Program to Find The Transpose of a Given Matrix

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