Program to Construct a Binary Search Tree and Perform Deletion and Inorder Traversal

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

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).

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

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:

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

Deletion:

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.
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.
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

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 the data attribute of the node and both left and right will be set to null.
Define another class which has an attribute root.
1. Root represents the root node of the tree and initializes it to null.
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.
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.

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 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 emptyn”);            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

Next TopicPrograms List

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

Explanation

Insertion:

Deletion:

Algorithm

Solution

Python

C

JAVA

C#

PHP

Potential Energy

Program to Find The Transpose of a Given Matrix

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