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

Program to Construct a Binary Search Tree and Perform Deletion and Inorder Traversal on fibonacci, factorial, prime, armstrong, swap, reverse, search, sort, stack, queue, array, linkedlist, tree, graph etc.

## 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).

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.

### 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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