Program to Convert Binary Tree to Binary Search Tree

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.

Program to convert Binary Tree to Binary Search Tree

Algorithm

Define Node class which has three attributes namely: data left and right. Here, left represents the left child of the node and right represents the right child of the node.
When a node is created, data will pass to data attribute of the node and both left and right will be set to null.
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.
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().
calculateSize() will count the number of nodes present in the tree.
convertBTtoArray() will convert binary tree to its array representation by traversing the tree and adding elements to treeArray.
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.
Inorder() will display the nodes of the tree in inorder fashion, i.e., left child followed by root node followed by the right child.

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 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 emptyn”);              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 emptyn”);              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 emptyn”);          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 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      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

Next TopicPrograms List

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

Explanation

Algorithm

Solution

Python

C

JAVA

C#

PHP

Potential Energy

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