Q:

Program to construct a Binary Search Tree and perform deletion and inorder traversal

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robaa
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2022-11-09
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Explanation

In this program, we need to create a binary search tree, delete a node from the tree, and display the nodes of the tree by traversing the tree using in-order traversal. In in-order traversal, for a given node, first, we traverse the left child then root then right child (Left -> Root -> Right).

In Binary Search Tree, all nodes which are present to the left of root will be less than root node and nodes which are present to the right will be greater than the root node.

Insertion:

  1. If the value of the new node is less than the root node then, it will be inserted to the left subtree.
  2. If the value of the new node is greater than root node then, it will be inserted to the right subtree.

Deletion:

  1. If the node to be deleted is a leaf node then, parent of that node will point to null. For eg. If we delete 90, then parent node 70 will point to null.
  2. If the node to be deleted has one child node, then child node will become a child node of the parent node. For eg. If we delete 30, then node 10 which was left child of 30 will become left child of 50.
  3. If the node to be deleted has two children then, we find the node(minNode) with minimum value from the right subtree of that current node. The current node will be replaced by its successor(minNode).

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 the 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. insert() will insert the new value into a binary search tree:
    1. It checks whether root is null, which means tree is empty. New node will become root node of tree.
    2. If tree is not empty, it will compare value of new node with root node. If value of new node is greater than root, new node will be inserted to right subtree. Else, it will be inserted in left subtree.
  5. deleteNode() will delete a particular node from the tree:
    1. If value of node to be deleted is less than root node, search node in left subtree. Else, search in right subtree.
    2. If node is found and it has no children, then set the node to null.
    3. If node has one child then, child node will take position of node.
    4. If node has two children then, find a minimum value node from its right subtree. This minimum value node will replace the current node.

Input:

Output:

Binary search tree after insertion: 10 30 50 60 70 90
Binary search tree after deleting node 90: 10 30 50 60 70
Binary search tree after deleting node 30: 10 50 60 70
Binary search tree after deleting node 50: 10 60 70
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robaa
2022-11-09
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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 BinarySearchTree:  
    def __init__(self):  
        #Represent the root of binary tree  
        self.root = None;  
          
    #insert() will add new node to the binary search tree  
    def insert(self, data):  
        #Create a new node  
        newNode = Node(data);  
          
        #Check whether tree is empty  
        if(self.root == None):  
            self.root = newNode;  
            return;  
        else:  
            #current node point to root of the tree  
            current = self.root;  
              
            while(True):  
                #parent keep track of the parent node of current node.  
                parent = current;  
                  
                #If data is less than current's data, node will be inserted to the left of tree  
                if(data < current.data):  
                    current = current.left;  
                    if(current == None):  
                        parent.left = newNode;  
                        return;  
                          
                #If data is greater than current's data, node will be inserted to the right of tree  
                else:  
                    current = current.right;  
                    if(current == None):  
                        parent.right = newNode;  
                        return;  
                          
    #minNode() will find out the minimum node  
    def minNode(self, root):  
        if(root.left != None):  
            return self.minNode(root.left);  
        else:  
            return root;  
              
    #deleteNode() will delete the given node from the binary search tree  
    def deleteNode(self, node, value):  
        if(node == None):  
            return None;  
        else:  
            #value is less than node's data then, search the value in left subtree  
            if(value < node.data):  
                node.left = self.deleteNode(node.left, value);  
              
            #value is greater than node's data then, search the value in right subtree  
            elif(value > node.data):  
                node.right = self.deleteNode(node.right, value);  
                  
            #If value is equal to node's data that is, we have found the node to be deleted  
            else:  
                #If node to be deleted has no child then, set the node to None  
                if(node.left == None and node.right == None):  
                    node = None;  
                      
                #If node to be deleted has only one right child  
                elif(node.left == None):  
                    node = node.right;  
                  
                #If node to be deleted has only one left child  
                elif(node.right == None):  
                    node = node.left;  
                      
                #If node to be deleted has two children node  
                else:  
                    #then find the minimum node from right subtree  
                    temp = self.minNode(node.right);  
                    #Exchange the data between node and temp  
                    node.data = temp.data;  
                    #Delete the node duplicate node from right subtree  
                    node.right = self.deleteNode(node.right, temp.data);  
        return node;  
                  
    #inorder() will perform inorder traversal on binary search tree  
    def inorderTraversal(self, node):  
        #Check whether tree is empty  
        if(self.root == None):  
            print("Tree is empty");  
            return;  
        else:  
            if(node.left != None):  
                self.inorderTraversal(node.left);  
            print(node.data, end=" ");  
            if(node.right != None):  
                self.inorderTraversal(node.right);  
                  
bt = BinarySearchTree();  
#Add nodes to the binary tree  
bt.insert(50);  
bt.insert(30);  
bt.insert(70);  
bt.insert(60);  
bt.insert(10);  
bt.insert(90);  
   
print("Binary search tree after insertion:");  
#Displays the binary tree  
bt.inorderTraversal(bt.root);  
   
#Deletes node 90 which has no child  
deletedNode = bt.deleteNode(bt.root, 90);  
print("\nBinary search tree after deleting node 90:");  
bt.inorderTraversal(bt.root);  
   
#Deletes node 30 which has one child  
deletedNode = bt.deleteNode(bt.root, 30);  
print("\nBinary search tree after deleting node 30:");  
bt.inorderTraversal(bt.root);  
   
#Deletes node 50 which has two children  
deletedNode = bt.deleteNode(bt.root, 50);  
print("\nBinary search tree after deleting node 50:");  
bt.inorderTraversal(bt.root);

 

Output:

Binary search tree after insertion:
10 30 50 60 70 90 
Binary search tree after deleting node 90:
10 30 50 60 70 
Binary search tree after deleting node 30:
10 50 60 70 
Binary search tree after deleting node 50:
10 60 70

 

C

#include <stdio.h>  
#include <stdlib.h>  
#include <stdbool.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;  
}  
   
//insert() will add new node to the binary search tree  
void insert(int data) {  
    //Create a new node  
    struct node *newNode = createNode(data);  
      
    //Check whether tree is empty  
    if(root == NULL){  
        root = newNode;  
        return;  
      }  
    else {  
        //current node point to root of the tree  
        struct node *current = root, *parent = NULL;  
          
        while(true) {  
            //parent keep track of the parent node of current node.  
            parent = current;  
   
            //If data is less than current's data, node will be inserted to the left of tree  
            if(data < current->data) {  
                current = current->left;  
                if(current == NULL) {  
                    parent->left = newNode;  
                    return;  
                }  
            }  
            //If data is greater than current's data, node will be inserted to the right of tree  
            else {  
                current = current->right;  
                if(current == NULL) {  
                    parent->right = newNode;  
                    return;  
                }  
            }  
        }  
    }  
}  
   
//minNode() will find out the minimum node  
struct node* minNode(struct node *root) {  
    if (root->left != NULL)  
        return minNode(root->left);  
    else   
        return root;  
}   
   
//deleteNode() will delete the given node from the binary search tree  
struct node* deleteNode(struct node *node, int value) {  
    if(node == NULL){  
          return NULL;  
     }  
    else {  
        //value is less than node's data then, search the value in left subtree  
        if(value < node->data)  
            node->left = deleteNode(node->left, value);  
          
        //value is greater than node's data then, search the value in right subtree  
        else if(value > node->data)  
            node->right = deleteNode(node->right, value);  
          
        //If value is equal to node's data that is, we have found the node to be deleted  
        else {  
            //If node to be deleted has no child then, set the node to NULL  
            if(node->left == NULL && node->right == NULL)  
                node = NULL;  
              
            //If node to be deleted has only one right child  
            else if(node->left == NULL) {  
                node = node->right;  
            }  
              
            //If node to be deleted has only one left child  
            else if(node->right == NULL) {  
                node = node->left;  
            }  
              
            //If node to be deleted has two children node  
            else {  
                //then find the minimum node from right subtree  
                struct node *temp = minNode(node->right);  
                //Exchange the data between node and temp  
                node->data = temp->data;  
                //Delete the node duplicate node from right subtree  
                node->right = deleteNode(node->right, temp->data);  
            }  
        }  
        return node;  
    }  
}  
   
//inorder() will perform inorder traversal on binary search tree  
void inorderTraversal(struct node *node) {  
        
    //Check whether tree is empty  
    if(root == NULL){  
        printf("Tree is empty\n");  
          return;  
     }  
    else {  
            
        if(node->left!= NULL)  
            inorderTraversal(node->left);  
        printf("%d ", node->data);  
        if(node->right!= NULL)  
          inorderTraversal(node->right);  
            
    }        
}  
        
int main()  
{  
    //Add nodes to the binary tree  
    insert(50);  
    insert(30);  
    insert(70);  
    insert(60);  
    insert(10);  
    insert(90);  
      
    printf("Binary search tree after insertion: \n");  
    //Displays the binary tree  
    inorderTraversal(root);  
      
    struct node *deletedNode = NULL;  
    //Deletes node 90 which has no child  
    deletedNode = deleteNode(root, 90);  
    printf("\nBinary search tree after deleting node 90: \n");  
    inorderTraversal(root);  
      
    //Deletes node 30 which has one child  
    deletedNode = deleteNode(root, 30);  
    printf("\nBinary search tree after deleting node 30: \n");  
    inorderTraversal(root);  
      
    //Deletes node 50 which has two children  
    deletedNode = deleteNode(root, 50);  
    printf("\nBinary search tree after deleting node 50: \n");  
    inorderTraversal(root);  
   
    return 0;  
}

 

Output:

Binary search tree after insertion:
10 30 50 60 70 90 
Binary search tree after deleting node 90:
10 30 50 60 70 
Binary search tree after deleting node 30:
10 50 60 70 
Binary search tree after deleting node 50:
10 60 70

 

JAVA

public class BinarySearchTree {  
      
    //Represent a 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 BinarySearchTree(){  
          root = null;  
      }  
        
      //insert() will add new node to the binary search tree  
      public void insert(int data) {  
          //Create a new node  
          Node newNode = new Node(data);  
            
          //Check whether tree is empty  
          if(root == null){  
              root = newNode;  
              return;  
            }  
          else {  
              //current node point to root of the tree  
              Node current = root, parent = null;  
                
              while(true) {  
                  //parent keep track of the parent node of current node.  
                  parent = current;  
   
                  //If data is less than current's data, node will be inserted to the left of tree  
                  if(data < current.data) {  
                      current = current.left;  
                      if(current == null) {  
                          parent.left = newNode;  
                          return;  
                      }  
                  }  
                  //If data is greater than current's data, node will be inserted to the right of tree  
                  else {  
                      current = current.right;  
                      if(current == null) {  
                          parent.right = newNode;  
                          return;  
                      }  
                  }  
              }  
          }  
      }  
        
      //minNode() will find out the minimum node  
      public Node minNode(Node root) {  
          if (root.left != null)  
              return minNode(root.left);  
          else   
              return root;  
      }   
        
      //deleteNode() will delete the given node from the binary search tree  
      public Node deleteNode(Node node, int value) {  
          if(node == null){  
              return null;  
           }  
          else {  
              //value is less than node's data then, search the value in left subtree  
              if(value < node.data)  
                  node.left = deleteNode(node.left, value);  
                
              //value is greater than node's data then, search the value in right subtree  
              else if(value > node.data)  
                  node.right = deleteNode(node.right, value);  
                
              //If value is equal to node's data that is, we have found the node to be deleted  
              else {  
                  //If node to be deleted has no child then, set the node to null  
                  if(node.left == null && node.right == null)  
                      node = null;  
                    
                  //If node to be deleted has only one right child  
                  else if(node.left == null) {  
                      node = node.right;  
                  }  
                    
                  //If node to be deleted has only one left child  
                  else if(node.right == null) {  
                      node = node.left;  
                  }  
                    
                  //If node to be deleted has two children node  
                  else {  
                      //then find the minimum node from right subtree  
                      Node temp = minNode(node.right);  
                      //Exchange the data between node and temp  
                      node.data = temp.data;  
                      //Delete the node duplicate node from right subtree  
                      node.right = deleteNode(node.right, temp.data);  
                  }  
              }  
              return node;  
          }  
      }  
        
      //inorder() will perform inorder traversal on binary search tree  
      public void inorderTraversal(Node node) {  
            
          //Check whether tree is empty  
          if(root == null){  
              System.out.println("Tree is empty");  
              return;  
           }  
          else {  
                
              if(node.left!= null)  
                  inorderTraversal(node.left);  
              System.out.print(node.data + " ");  
              if(node.right!= null)  
                  inorderTraversal(node.right);  
                
          }        
      }  
        
      public static void main(String[] args) {  
            
          BinarySearchTree bt = new BinarySearchTree();  
          //Add nodes to the binary tree  
          bt.insert(50);  
          bt.insert(30);  
          bt.insert(70);  
          bt.insert(60);  
          bt.insert(10);  
          bt.insert(90);  
            
          System.out.println("Binary search tree after insertion:");  
          //Displays the binary tree  
          bt.inorderTraversal(bt.root);  
            
          Node deletedNode = null;  
          //Deletes node 90 which has no child  
          deletedNode = bt.deleteNode(bt.root, 90);  
          System.out.println("\nBinary search tree after deleting node 90:");  
          bt.inorderTraversal(bt.root);  
            
          //Deletes node 30 which has one child  
          deletedNode = bt.deleteNode(bt.root, 30);  
          System.out.println("\nBinary search tree after deleting node 30:");  
          bt.inorderTraversal(bt.root);  
            
          //Deletes node 50 which has two children  
          deletedNode = bt.deleteNode(bt.root, 50);  
          System.out.println("\nBinary search tree after deleting node 50:");  
          bt.inorderTraversal(bt.root);  
      }  
}

 

Output:

Binary search tree after insertion:
10 30 50 60 70 90 
Binary search tree after deleting node 90:
10 30 50 60 70 
Binary search tree after deleting node 30:
10 50 60 70 
Binary search tree after deleting node 50:
10 60 70

 

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 BinarySearchTree<T> where T : IComparable<T>{  
            //Represent the root of binary tree  
            public Node<T> root;  
              
            public BinarySearchTree(){  
                root = null;  
            }  
              
        //insert() will add new node to the binary search tree  
        public void insert(T data) {  
          //Create a new node  
          Node<T> newNode = new Node<T>(data);  
            
          //Check whether tree is empty  
          if(root == null){  
              root = newNode;  
              return;  
            }  
          else {  
              //current node point to root of the tree  
              Node<T> current = root, parent = null;  
                
              while(true) {  
                  //parent keep track of the parent node of current node.  
                  parent = current;  
   
                  //If data is less than current's data, node will be inserted to the left of tree  
                  if(data.CompareTo(current.data) < 0) {  
                      current = current.left;  
                      if(current == null) {  
                          parent.left = newNode;  
                          return;  
                      }  
                  }  
                  //If data is greater than current's data, node will be inserted to the right of tree  
                  else {  
                      current = current.right;  
                      if(current == null) {  
                          parent.right = newNode;  
                          return;  
                      }  
                  }  
              }  
          }  
        }  
        
        //minNode() will find out the minimum node  
        public Node<T> minNode(Node<T> root) {  
          if (root.left != null)  
              return minNode(root.left);  
          else   
              return root;  
        }   
          
        //deleteNode() will delete the given node from the binary search tree  
        public Node<T> deleteNode(Node<T> node, T value) {  
          if(node == null){  
              return null;  
           }  
          else {  
              //value is less than node's data then, search the value in left subtree  
              if(value.CompareTo(node.data) < 0)  
                  node.left = deleteNode(node.left, value);  
                
              //value is greater than node's data then, search the value in right subtree  
              else if(value.CompareTo(node.data) > 0)  
                  node.right = deleteNode(node.right, value);  
                
              //If value is equal to node's data that is, we have found the node to be deleted  
              else {  
                  //If node to be deleted has no child then, set the node to null  
                  if(node.left == null && node.right == null)  
                      node = null;  
                    
                  //If node to be deleted has only one right child  
                  else if(node.left == null) {  
                      node = node.right;  
                  }  
                    
                  //If node to be deleted has only one left child  
                  else if(node.right == null) {  
                      node = node.left;  
                  }  
                    
                  //If node to be deleted has two children node  
                  else {  
                      //then find the minimum node from right subtree  
                      Node<T> temp = minNode(node.right);  
                      //Exchange the data between node and temp  
                      node.data = temp.data;  
                      //Delete the node duplicate node from right subtree  
                      node.right = deleteNode(node.right, temp.data);  
                  }  
              }  
              return node;  
          }  
        }  
          
        //inorder() will perform inorder traversal on binary search tree  
        public void inorderTraversal(Node<T> node) {  
            
          //Check whether tree is empty  
          if(root == null){  
              Console.WriteLine("Tree is empty");  
              return;  
           }  
          else {  
                
              if(node.left!= null)  
                  inorderTraversal(node.left);  
              Console.Write(node.data + " ");  
              if(node.right!= null)  
                  inorderTraversal(node.right);  
                
          }        
        }  
    }  
          
        public static void Main()  
        {  
            BinarySearchTree<int> bt = new BinarySearchTree<int>();  
            //Add nodes to the binary tree  
            bt.insert(50);  
            bt.insert(30);  
            bt.insert(70);  
            bt.insert(60);  
            bt.insert(10);  
            bt.insert(90);  
              
            Console.WriteLine("Binary search tree after insertion:");  
            //Displays the binary tree  
            bt.inorderTraversal(bt.root);  
              
            Node<int> deletedNode = null;  
            //Deletes node 90 which has no child  
            deletedNode = bt.deleteNode(bt.root, 90);  
            Console.WriteLine("\nBinary search tree after deleting node 90:");  
            bt.inorderTraversal(bt.root);  
              
            //Deletes node 30 which has one child  
            deletedNode = bt.deleteNode(bt.root, 30);  
            Console.WriteLine("\nBinary search tree after deleting node 30:");  
            bt.inorderTraversal(bt.root);  
              
            //Deletes node 50 which has two children  
            deletedNode = bt.deleteNode(bt.root, 50);  
            Console.WriteLine("\nBinary search tree after deleting node 50:");  
            bt.inorderTraversal(bt.root);                  
        }      
    }  
}

 

 

Output:

Binary search tree after insertion:
10 30 50 60 70 90 
Binary search tree after deleting node 90:
10 30 50 60 70 
Binary search tree after deleting node 30:
10 50 60 70 
Binary search tree after deleting node 50:
10 60 70

 

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 BinarySearchTree{  
    //Represent the root of binary tree  
    public $root;  
    function __construct(){  
        $this->root = NULL;  
    }  
      
    //insert() will add new node to the binary search tree  
    function insert($data) {  
        //Create a new node  
        $newNode = new Node($data);  
            
        //Check whether tree is empty  
        if($this->root == NULL){  
            $this->root = $newNode;  
            return;  
        }  
        else {  
            //current node point to root of the tree  
            $current = $this->root;  
            $parent = NULL;  
              
            while(true) {  
                //parent keep track of the parent node of current node.  
                $parent = $current;  
   
                  //If data is less than current's data, node will be inserted to the left of tree  
                if($data < $current->data) {  
                    $current = $current->left;  
                    if($current == NULL) {  
                        $parent->left = $newNode;  
                          return;  
                    }  
                }  
                //If data is greater than current's data, node will be inserted to the right of tree  
                else {  
                    $current = $current->right;  
                    if($current == NULL) {  
                        $parent->right = $newNode;  
                        return;  
                    }  
                }  
            }  
        }  
    }  
        
    //minNode() will find out the minimum node  
    function minNode($root) {  
        if ($root->left != NULL)  
            return $this->minNode($root->left);  
        else   
            return $root;  
    }   
      
    //deleteNode() will delete the given node from the binary search tree  
    function deleteNode($node, $value) {  
        if($node == NULL){  
            return NULL;  
        }  
        else {  
            //value is less than node's data then, search the value in left subtree  
            if($value < $node->data)  
                $node->left = $this->deleteNode($node->left, $value);  
                
            //value is greater than node's data then, search the value in right subtree  
            else if($value > $node->data)  
                $node->right = $this->deleteNode($node->right, $value);  
                
            //If value is equal to node's data that is, we have found the node to be deleted  
            else {  
                //If node to be deleted has no child then, set the node to null  
                if($node->left == NULL && $node->right == NULL)  
                    $node = NULL;  
                  
                //If node to be deleted has only one right child  
                else if($node->left == NULL) {  
                    $node = $node->right;  
                }  
                  
                //If node to be deleted has only one left child  
                else if($node->right == NULL) {  
                  $node = $node->left;  
                }  
                  
                //If node to be deleted has two children node  
                else {  
                    //then find the minimum node from right subtree  
                    $temp = $this->minNode($node->right);  
                    //Exchange the data between node and temp  
                    $node->data = $temp->data;  
                    //Delete the node duplicate node from right subtree  
                    $node->right = $this->deleteNode($node->right, $temp->data);  
                }  
            }  
            return $node;  
        }  
    }  
        
    //inorder() will perform inorder traversal on binary search tree  
    function inorderTraversal($node) {  
          
        //Check whether tree is empty  
        if($this->root == NULL){  
            print("Tree is empty <br>");  
            return;  
        }  
        else {  
            
            if($node->left != NULL)  
              $this->inorderTraversal($node->left);  
            print("$node->data  ");  
            if($node->right != NULL)  
              $this->inorderTraversal($node->right);  
            
        }        
    }  
}  
$bt = new BinarySearchTree();  
//Add nodes to the binary tree  
$bt->insert(50);  
$bt->insert(30);  
$bt->insert(70);  
$bt->insert(60);  
$bt->insert(10);  
$bt->insert(90);  
   
print("Binary search tree after insertion: <br>");  
//Displays the binary tree  
$bt->inorderTraversal($bt->root);  
   
//Deletes node 90 which has no child  
$deletedNode = $bt->deleteNode($bt->root, 90);  
print("<br>Binary search tree after deleting node 90: <br>");  
$bt->inorderTraversal($bt->root);  
   
//Deletes node 30 which has one child  
$deletedNode = $bt->deleteNode($bt->root, 30);  
print("<br>Binary search tree after deleting node 30: <br>");  
$bt->inorderTraversal($bt->root);  
   
//Deletes node 50 which has two children  
$deletedNode = $bt->deleteNode($bt->root, 50);  
print("<br>Binary search tree after deleting node 50: <br>");  
$bt->inorderTraversal($bt->root);  
?>  
</body>  
</html>

 

Output:

Binary search tree after insertion:
10 30 50 60 70 90 
Binary search tree after deleting node 90:
10 30 50 60 70 
Binary search tree after deleting node 30:
10 50 60 70 
Binary search tree after deleting node 50:
10 60 70

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