# Program to Convert Binary Tree to Binary Search Tree

Program to Convert Binary Tree to Binary Search Tree on fibonacci, factorial, prime, armstrong, swap, reverse, search, sort, stack, queue, array, linkedlist, tree, graph etc.

## Q. Program to convert Binary Tree to Binary Search Tree.

### Explanation

In this program, we need to convert given binary tree to a corresponding binary search tree. A tree is said to be the binary tree if each of the nodes has at most two children. Whereas, the binary search tree is the special case of the binary tree in which all the nodes to the left of root node should be less than root node and nodes to the right should be greater than root node.

This problem can be resolved by converting given binary tree to its corresponding array representation. Sort the array. Calculate the middle node from array elements as it will become the root node of the corresponding binary search tree.

### Algorithm

1. Define Node class which has three attributes namely: data left and right. Here, left represents the left child of the node and right represents the right child of the node.
2. When a node is created, data will pass to data attribute of the node and both left and right will be set to null.
3. Define another class which has two attribute root and treeArray.
1. Root represents the root node of the tree and initializes it to null.
2. treeArray will store the array representation of the binary tree.
4. convertBTBST() will convert binary tree to the corresponding binary search tree:
1. It will convert the binary tree to corresponding array by calling convertBTtoArray().
2. Sort the resultant array from step 1 in ascending order.
3. Convert the array to the binary search tree by calling createBST().
5. calculateSize() will count the number of nodes present in the tree.
6. convertBTtoArray() will convert binary tree to its array representation by traversing the tree and adding elements to treeArray.
7. createBST() will create a corresponding binary search tree by selecting a middle node of sorted treeArray as it the root node. treeArray will be divided into two parts i.e [0, mid-1] and [mid+1, end]. Recursively find middle node from each array to create left subtree and right subtree respectively.
8. Inorder() will display the nodes of the tree in inorder fashion, i.e., left child followed by root node followed by the right child.

### 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 ConvertBTtoBST:
def __init__(self):
#Represent the root of binary tree
self.root = None;
self.treeArray = [];

#convertBTBST() will convert a binary tree to the binary search tree
def convertBTBST(self, node):

#Converts binary tree to array
self.convertBTtoArray(node);

#Sort treeArray
self.treeArray.sort();

#Converts array to binary search tree
d = self.createBST(0, len(self.treeArray) -1);
return d;

#convertBTtoArray() will convert the given binary tree to its corresponding array representation
def convertBTtoArray(self, node):

#Check whether tree is empty
if(self.root == None):
print("Tree is empty\n");
return;
else:
if(node.left!= None):
self.convertBTtoArray(node.left);
#Adds nodes of binary tree to treeArray
self.treeArray.append(node.data);

if(node.right!= None):
self.convertBTtoArray(node.right);

#createBST() will convert array to binary search tree
def createBST(self, start, end):

#It will avoid overflow
if(start > end):
return None;

#Variable will store middle element of array and make it root of binary search tree
mid = (start + end) // 2;
node = Node(self.treeArray[mid]);

#Construct left subtree
node.left = self.createBST(start, mid - 1);

#Construct right subtree
node.right = self.createBST(mid + 1, end);

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\n");
return;
else:
if(node.left != None):
self.inorderTraversal(node.left);
print(node.data),
if(node.right!= None):
self.inorderTraversal(node.right);

bt = ConvertBTtoBST();
#Add nodes to the binary tree
bt.root = Node(1);
bt.root.left = Node(2);
bt.root.right = Node(3);
bt.root.left.left = Node(4);
bt.root.left.right = Node(5);
bt.root.right.left = Node(6);
bt.root.right.right = Node(7);

#Display given binary tree
print("Inorder representation of binary tree: ");
bt.inorderTraversal(bt.root);

#Converts binary tree to corresponding binary search tree
bst = bt.convertBTBST(bt.root);

#Display corresponding binary search tree
print("\nInorder representation of resulting binary search tree: ");
bt.inorderTraversal(bst);
```

Output:

```Inorder representation of binary tree:
4 2 5 1 6 3 7
Inorder representation of resulting binary search tree:
1 2 3 4 5 6 7
```

### C

```#include <stdio.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;

int treeArray[100];
int ind = 0;

//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;
}

//calculateSize() will calculate size of tree
int calculateSize(struct node *node)
{
int size = 0;
if (node == NULL)
return 0;
else {
size = calculateSize (node->left) + calculateSize (node->right) + 1;
return size;
}
}

//convertBTtoArray() will convert the given binary tree to its corresponding array representation
void convertBTtoArray(struct node *node) {
//Check whether tree is empty
if(root == NULL){
printf("Tree is empty\n");
return;
}
else {
if(node->left != NULL)
convertBTtoArray(node->left);
//Adds nodes of binary tree to treeArray
treeArray[ind] = node->data;
ind++;
if(node->right!= NULL)
convertBTtoArray(node->right);
}
}

//createBST() will convert array to binary search tree
struct node* createBST(int start, int end) {

//It will avoid overflow
if (start > end) {
return NULL;
}

//Variable will store middle element of array and make it root of binary search tree
int mid = (start + end) / 2;
struct node *temp = createNode(treeArray[mid]);

//Construct left subtree
temp->left = createBST(start, mid - 1);

//Construct right subtree
temp->right = createBST(mid + 1, end);

return temp;
}

//convertBTBST() will convert a binary tree to binary search tree
struct node* convertBTBST(struct node *node) {

//Variable treeSize will hold size of tree
int treeSize = calculateSize(node);

//Converts binary tree to array
convertBTtoArray(node);

//Sort treeArray
int compare (const void * a, const void * b) {
return ( *(int*)a - *(int*)b );
}
qsort(treeArray, treeSize, sizeof(int), compare);

//Converts array to binary search tree
struct node *d = createBST(0, treeSize - 1);
return d;
}

//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
root = createNode(1);
root->left = createNode(2);
root->right = createNode(3);
root->left->left = createNode(4);
root->left->right = createNode(5);
root->right->left = createNode(6);
root->right->right = createNode(7);

//Display given binary tree
printf("Inorder representation of binary tree: \n");
inorderTraversal(root);

//Converts binary tree to corresponding binary search tree
struct node *bst = convertBTBST(root);

//Display corresponding binary search tree
printf("\nInorder representation of resulting binary search tree: \n");
inorderTraversal(bst);

return 0;
}
```

Output:

```Inorder representation of binary tree:
4 2 5 1 6 3 7
Inorder representation of resulting binary search tree:
1 2 3 4 5 6 7
```

### JAVA

```import java.util.Arrays;

public class ConvertBTtoBST {

//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;

int[] treeArray;
int index = 0;

public ConvertBTtoBST(){
root = null;
}

//convertBTBST() will convert a binary tree to binary search tree
public Node convertBTBST(Node node) {

//Variable treeSize will hold size of tree
int treeSize = calculateSize(node);
treeArray = new int[treeSize];

//Converts binary tree to array
convertBTtoArray(node);

//Sort treeArray
Arrays.sort(treeArray);

//Converts array to binary search tree
Node d = createBST(0, treeArray.length -1);
return d;
}

//calculateSize() will calculate size of tree
public int calculateSize(Node node)
{
int size = 0;
if (node == null)
return 0;
else {
size = calculateSize (node.left) + calculateSize (node.right) + 1;
return size;
}
}

//convertBTtoArray() will convert the given binary tree to its corresponding array representation
public void convertBTtoArray(Node node) {
//Check whether tree is empty
if(root == null){
System.out.println("Tree is empty");
return;
}
else {
if(node.left != null)
convertBTtoArray(node.left);
//Adds nodes of binary tree to treeArray
treeArray[index] = node.data;
index++;
if(node.right != null)
convertBTtoArray(node.right);
}
}

//createBST() will convert array to binary search tree
public Node createBST(int start, int end) {

//It will avoid overflow
if (start > end) {
return null;
}

//Variable will store middle element of array and make it root of binary search tree
int mid = (start + end) / 2;
Node node = new Node(treeArray[mid]);

//Construct left subtree
node.left = createBST(start, mid - 1);

//Construct right subtree
node.right = createBST(mid + 1, end);

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) {

ConvertBTtoBST bt = new ConvertBTtoBST();
//Add nodes to the binary tree
bt.root = new Node(1);
bt.root.left = new Node(2);
bt.root.right = new Node(3);
bt.root.left.left = new Node(4);
bt.root.left.right = new Node(5);
bt.root.right.left = new Node(6);
bt.root.right.right = new Node(7);

//Display given binary tree
System.out.println("Inorder representation of binary tree: ");
bt.inorderTraversal(bt.root);

//Converts binary tree to corresponding binary search tree
Node bst = bt.convertBTBST(bt.root);

//Display corresponding binary search tree
System.out.println("\nInorder representation of resulting binary search tree: ");
bt.inorderTraversal(bst);
}
}
```

Output:

```Inorder representation of binary tree:
4 2 5 1 6 3 7
Inorder representation of resulting binary search tree:
1 2 3 4 5 6 7
```

### 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 ConvertBTtoBST<T>{
//Represent the root of binary tree
public Node<T> root;

T[] treeArray;
int index = 0;

public ConvertBTtoBST(){
root = null;
}

//convertBTBST() will convert a binary tree to binary search tree
public Node<T> convertBTBST(Node<T> node) {

//Variable treeSize will hold size of tree
int treeSize = calculateSize(node);
treeArray = new T[treeSize];

//Converts binary tree to array
convertBTtoArray(node);

//Sort treeArray
Array.Sort(treeArray);

//Converts array to binary search tree
Node<T> d = createBST(0, treeArray.Length -1);
return d;
}

//calculateSize() will calculate size of tree
int calculateSize(Node<T> node)
{
int size = 0;
if (node == null)
return 0;
else {
size = calculateSize (node.left) + calculateSize (node.right) + 1;
return size;
}
}

//convertBTtoArray() will convert the given binary tree to its corresponding array representation
public void convertBTtoArray(Node<T> node) {
//Check whether tree is empty
if(root == null){
Console.WriteLine("Tree is empty");
return;
}
else {
if(node.left != null)
convertBTtoArray(node.left);
//Adds nodes of binary tree to treeArray
treeArray[index] = node.data;
index++;
if(node.right != null)
convertBTtoArray(node.right);
}
}

//createBST() will convert array to binary search tree
public Node<T> createBST(int start, int end) {

//It will avoid overflow
if (start > end) {
return null;
}

//Variable will store middle element of array and make it root of binary search tree
int mid = (start + end) / 2;
Node<T> node = new Node<T>(treeArray[mid]);

//Construct left subtree
node.left = createBST(start, mid - 1);

//Construct right subtree
node.right = createBST(mid + 1, end);

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()
{
ConvertBTtoBST<int> bt = new ConvertBTtoBST<int>();

//Add nodes to the binary tree
bt.root = new Node<int>(1);
bt.root.left = new Node<int>(2);
bt.root.right = new Node<int>(3);
bt.root.left.left = new Node<int>(4);
bt.root.left.right = new Node<int>(5);
bt.root.right.left = new Node<int>(6);
bt.root.right.right = new Node<int>(7);

//Display given binary tree
Console.WriteLine("Inorder representation of binary tree: ");
bt.inorderTraversal(bt.root);

//Converts binary tree to corresponding binary search tree
Node<int> bst = bt.convertBTBST(bt.root);

//Display corresponding binary search tree
Console.WriteLine("\nInorder representation of resulting binary search tree: ");
bt.inorderTraversal(bst);
}
}
}
```

Output:

```Inorder representation of binary tree:
4 2 5 1 6 3 7
Inorder representation of resulting binary search tree:
1 2 3 4 5 6 7
```

### 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 ConvertBTtoBST{
//Represent the root of binary tree
public \$root;
public \$treeArray;
public \$index;
function __construct(){
\$this->root = NULL;
\$this->treeArray = array();
\$this->index = 0;
}

//convertBTBST() will convert a binary tree to binary search tree
function convertBTBST(\$node) {

//Converts binary tree to array
\$this->convertBTtoArray(\$node);

//Sort treeArray
sort(\$this->treeArray);

//Converts array to binary search tree
\$d = \$this->createBST(0, count(\$this->treeArray) -1);
return \$d;
}

//convertBTtoArray() will convert the given binary tree to its corresponding array representation
function convertBTtoArray(\$node) {
//Check whether tree is empty
if(\$this->root == null){
print("Tree is empty <br>");
return;
}
else {
if(\$node->left != NULL)
\$this->convertBTtoArray(\$node->left);
//Adds nodes of binary tree to treeArray
\$this->treeArray[\$this->index] = \$node->data;
\$this->index++;
if(\$node->right != NULL)
\$this->convertBTtoArray(\$node->right);
}
}

//createBST() will convert array to binary search tree
function createBST(\$start, \$end) {

//It will avoid overflow
if (\$start > \$end) {
return NULL;
}

//Variable will store middle element of array and make it root of binary search tree
\$mid = (\$start + \$end) / 2;
\$node = new Node(\$this->treeArray[\$mid]);

//Construct left subtree
\$node->left = \$this->createBST(\$start, \$mid - 1);

//Construct right subtree
\$node->right = \$this->createBST(\$mid + 1, \$end);

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 ConvertBTtoBST();
//Add nodes to the binary tree
\$bt->root = new Node(1);
\$bt->root->left = new Node(2);
\$bt->root->right = new Node(3);
\$bt->root->left->left = new Node(4);
\$bt->root->left->right = new Node(5);
\$bt->root->right->left = new Node(6);
\$bt->root->right->right = new Node(7);

//Display given binary tree
print("Inorder representation of binary tree: <br>");
\$bt->inorderTraversal(\$bt->root);

//Converts binary tree to corresponding binary search tree
\$bst = \$bt->convertBTBST(\$bt->root);

//Display corresponding binary search tree
print("<br> Inorder representation of resulting binary search tree: <br>");
\$bt->inorderTraversal(\$bst);
?>
</body>
</html>
```

Output:

```Inorder representation of binary tree:
4 2 5 1 6 3 7
Inorder representation of resulting binary search tree:
1 2 3 4 5 6 7
```

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