# Binary Tree to Binary Search Tree Conversion

• Difficulty Level : Medium
• Last Updated : 12 Jan, 2022

Given a Binary Tree, convert it to a Binary Search Tree. The conversion must be done in such a way that keeps the original structure of Binary Tree.

Examples

```Example 1
Input:
10
/  \
2    7
/ \
8   4
Output:
8
/  \
4    10
/ \
2   7

Example 2
Input:
10
/  \
30   15
/      \
20       5
Output:
15
/  \
10    20
/      \
5        30```

Solution

Following is a 3 step solution for converting Binary tree to Binary Search Tree.

1) Create a temp array arr[] that stores inorder traversal of the tree. This step takes O(n) time.

2) Sort the temp array arr[]. Time complexity of this step depends upon the sorting algorithm. In the following implementation, Quick Sort is used which takes (n^2) time. This can be done in O(nLogn) time using Heap Sort or Merge Sort.

3) Again do inorder traversal of tree and copy array elements to tree nodes one by one. This step takes O(n) time.

Following is C implementation of the above approach. The main function to convert is highlighted in the following code.

## C++

 `/* A program to convert Binary Tree to Binary Search Tree */``#include ``using` `namespace` `std;` `/* A binary tree node structure */``struct` `node {``    ``int` `data;``    ``struct` `node* left;``    ``struct` `node* right;``};` `/* A helper function that stores inorder traversal of a tree rooted``with node */``void` `storeInorder(``struct` `node* node, ``int` `inorder[], ``int``* index_ptr)``{``    ``// Base Case``    ``if` `(node == NULL)``        ``return``;` `    ``/* first store the left subtree */``    ``storeInorder(node->left, inorder, index_ptr);` `    ``/* Copy the root's data */``    ``inorder[*index_ptr] = node->data;``    ``(*index_ptr)++; ``// increase index for next entry` `    ``/* finally store the right subtree */``    ``storeInorder(node->right, inorder, index_ptr);``}` `/* A helper function to count nodes in a Binary Tree */``int` `countNodes(``struct` `node* root)``{``    ``if` `(root == NULL)``        ``return` `0;``    ``return` `countNodes(root->left) + countNodes(root->right) + 1;``}` `// Following function is needed for library function qsort()``int` `compare(``const` `void``* a, ``const` `void``* b)``{``    ``return` `(*(``int``*)a - *(``int``*)b);``}` `/* A helper function that copies contents of arr[] to Binary Tree.``This function basically does Inorder traversal of Binary Tree and``one by one copy arr[] elements to Binary Tree nodes */``void` `arrayToBST(``int``* arr, ``struct` `node* root, ``int``* index_ptr)``{``    ``// Base Case``    ``if` `(root == NULL)``        ``return``;` `    ``/* first update the left subtree */``    ``arrayToBST(arr, root->left, index_ptr);` `    ``/* Now update root's data and increment index */``    ``root->data = arr[*index_ptr];``    ``(*index_ptr)++;` `    ``/* finally update the right subtree */``    ``arrayToBST(arr, root->right, index_ptr);``}` `// This function converts a given Binary Tree to BST``void` `binaryTreeToBST(``struct` `node* root)``{``    ``// base case: tree is empty``    ``if` `(root == NULL)``        ``return``;` `    ``/* Count the number of nodes in Binary Tree so that``    ``we know the size of temporary array to be created */``    ``int` `n = countNodes(root);` `    ``// Create a temp array arr[] and store inorder traversal of tree in arr[]``    ``int``* arr = ``new` `int``[n];``    ``int` `i = 0;``    ``storeInorder(root, arr, &i);` `    ``// Sort the array using library function for quick sort``    ``qsort``(arr, n, ``sizeof``(arr), compare);` `    ``// Copy array elements back to Binary Tree``    ``i = 0;``    ``arrayToBST(arr, root, &i);` `    ``// delete dynamically allocated memory to avoid memory leak``    ``delete``[] arr;``}` `/* Utility function to create a new Binary Tree node */``struct` `node* newNode(``int` `data)``{``    ``struct` `node* temp = ``new` `struct` `node;``    ``temp->data = data;``    ``temp->left = NULL;``    ``temp->right = NULL;``    ``return` `temp;``}` `/* Utility function to print inorder traversal of Binary Tree */``void` `printInorder(``struct` `node* node)``{``    ``if` `(node == NULL)``        ``return``;` `    ``/* first recur on left child */``    ``printInorder(node->left);` `    ``/* then print the data of node */``    ``cout <<``" "``<< node->data;` `    ``/* now recur on right child */``    ``printInorder(node->right);``}` `/* Driver function to test above functions */``int` `main()``{``    ``struct` `node* root = NULL;` `    ``/* Constructing tree given in the above figure``        ``10``        ``/ \``        ``30 15``    ``/     \``    ``20     5 */``    ``root = newNode(10);``    ``root->left = newNode(30);``    ``root->right = newNode(15);``    ``root->left->left = newNode(20);``    ``root->right->right = newNode(5);` `    ``// convert Binary Tree to BST``    ``binaryTreeToBST(root);` `    ``cout <<``"Following is Inorder Traversal of the converted BST:"` `<< endl ;``    ``printInorder(root);` `    ``return` `0;``}`` ` `// This code is contributed by shivanisinghss2110`

## C

 `/* A program to convert Binary Tree to Binary Search Tree */``#include ``#include ` `/* A binary tree node structure */``struct` `node {``    ``int` `data;``    ``struct` `node* left;``    ``struct` `node* right;``};` `/* A helper function that stores inorder traversal of a tree rooted``with node */``void` `storeInorder(``struct` `node* node, ``int` `inorder[], ``int``* index_ptr)``{``    ``// Base Case``    ``if` `(node == NULL)``        ``return``;` `    ``/* first store the left subtree */``    ``storeInorder(node->left, inorder, index_ptr);` `    ``/* Copy the root's data */``    ``inorder[*index_ptr] = node->data;``    ``(*index_ptr)++; ``// increase index for next entry` `    ``/* finally store the right subtree */``    ``storeInorder(node->right, inorder, index_ptr);``}` `/* A helper function to count nodes in a Binary Tree */``int` `countNodes(``struct` `node* root)``{``    ``if` `(root == NULL)``        ``return` `0;``    ``return` `countNodes(root->left) + countNodes(root->right) + 1;``}` `// Following function is needed for library function qsort()``int` `compare(``const` `void``* a, ``const` `void``* b)``{``    ``return` `(*(``int``*)a - *(``int``*)b);``}` `/* A helper function that copies contents of arr[] to Binary Tree.``This function basically does Inorder traversal of Binary Tree and``one by one copy arr[] elements to Binary Tree nodes */``void` `arrayToBST(``int``* arr, ``struct` `node* root, ``int``* index_ptr)``{``    ``// Base Case``    ``if` `(root == NULL)``        ``return``;` `    ``/* first update the left subtree */``    ``arrayToBST(arr, root->left, index_ptr);` `    ``/* Now update root's data and increment index */``    ``root->data = arr[*index_ptr];``    ``(*index_ptr)++;` `    ``/* finally update the right subtree */``    ``arrayToBST(arr, root->right, index_ptr);``}` `// This function converts a given Binary Tree to BST``void` `binaryTreeToBST(``struct` `node* root)``{``    ``// base case: tree is empty``    ``if` `(root == NULL)``        ``return``;` `    ``/* Count the number of nodes in Binary Tree so that``    ``we know the size of temporary array to be created */``    ``int` `n = countNodes(root);` `    ``// Create a temp array arr[] and store inorder traversal of tree in arr[]``    ``int``* arr = ``new` `int``[n];``    ``int` `i = 0;``    ``storeInorder(root, arr, &i);` `    ``// Sort the array using library function for quick sort``    ``qsort``(arr, n, ``sizeof``(arr), compare);` `    ``// Copy array elements back to Binary Tree``    ``i = 0;``    ``arrayToBST(arr, root, &i);` `    ``// delete dynamically allocated memory to avoid memory leak``    ``delete``[] arr;``}` `/* Utility function to create a new Binary Tree node */``struct` `node* newNode(``int` `data)``{``    ``struct` `node* temp = ``new` `struct` `node;``    ``temp->data = data;``    ``temp->left = NULL;``    ``temp->right = NULL;``    ``return` `temp;``}` `/* Utility function to print inorder traversal of Binary Tree */``void` `printInorder(``struct` `node* node)``{``    ``if` `(node == NULL)``        ``return``;` `    ``/* first recur on left child */``    ``printInorder(node->left);` `    ``/* then print the data of node */``    ``printf``(``"%d "``, node->data);` `    ``/* now recur on right child */``    ``printInorder(node->right);``}` `/* Driver function to test above functions */``int` `main()``{``    ``struct` `node* root = NULL;` `    ``/* Constructing tree given in the above figure``        ``10``        ``/ \``        ``30 15``    ``/     \``    ``20     5 */``    ``root = newNode(10);``    ``root->left = newNode(30);``    ``root->right = newNode(15);``    ``root->left->left = newNode(20);``    ``root->right->right = newNode(5);` `    ``// convert Binary Tree to BST``    ``binaryTreeToBST(root);` `    ``printf``(``"Following is Inorder Traversal of the converted BST: \n"``);``    ``printInorder(root);` `    ``return` `0;``}`

## Java

 `/* A program to convert Binary Tree to Binary Search Tree */``import` `java.util.*;` `public` `class` `GFG{``    ` `    ``/* A binary tree node structure */``    ``static` `class` `Node {``        ``int` `data;``        ``Node left;``        ``Node right;``    ``};` `    ``// index pointer to pointer to the array index``    ``static` `int` `index;`  `    ``/* A helper function that stores inorder traversal of a tree rooted``    ``with node */``    ``static` `void` `storeInorder(Node node, ``int` `inorder[])``    ``{``        ``// Base Case``        ``if` `(node == ``null``)``            ``return``;` `        ``/* first store the left subtree */``        ``storeInorder(node.left, inorder);` `        ``/* Copy the root's data */``        ``inorder[index] = node.data;``        ``index++; ``// increase index for next entry` `        ``/* finally store the right subtree */``        ``storeInorder(node.right, inorder);``    ``}` `    ``/* A helper function to count nodes in a Binary Tree */``    ``static` `int` `countNodes(Node root)``    ``{``        ``if` `(root == ``null``)``            ``return` `0``;``        ``return` `countNodes(root.left) + countNodes(root.right) + ``1``;``    ``}` `    ``/* A helper function that copies contents of arr[] to Binary Tree.``    ``This function basically does Inorder traversal of Binary Tree and``    ``one by one copy arr[] elements to Binary Tree nodes */``    ``static` `void` `arrayToBST(``int``[] arr, Node root)``    ``{``        ``// Base Case``        ``if` `(root == ``null``)``            ``return``;` `        ``/* first update the left subtree */``        ``arrayToBST(arr, root.left);` `        ``/* Now update root's data and increment index */``        ``root.data = arr[index];``        ``index++;` `        ``/* finally update the right subtree */``        ``arrayToBST(arr, root.right);``    ``}` `    ``// This function converts a given Binary Tree to BST``    ``static` `void` `binaryTreeToBST(Node root)``    ``{``        ``// base case: tree is empty``        ``if` `(root == ``null``)``            ``return``;` `        ``/* Count the number of nodes in Binary Tree so that``        ``we know the size of temporary array to be created */``        ``int` `n = countNodes(root);` `        ``// Create a temp array arr[] and store inorder traversal of tree in arr[]``        ``int` `arr[] = ``new` `int``[n];` `        ``storeInorder(root, arr);` `        ``// Sort the array using library function for quick sort``        ``Arrays.sort(arr);``        ` `        ` `        ``// Copy array elements back to Binary Tree``        ``index = ``0``;``        ``arrayToBST(arr, root);``    ``}` `    ``/* Utility function to create a new Binary Tree node */``    ``static` `Node newNode(``int` `data)``    ``{``        ``Node temp = ``new` `Node();``        ``temp.data = data;``        ``temp.left = ``null``;``        ``temp.right = ``null``;``        ``return` `temp;``    ``}` `    ``/* Utility function to print inorder traversal of Binary Tree */``    ``static` `void` `printInorder(Node node)``    ``{``        ``if` `(node == ``null``)``            ``return``;` `        ``/* first recur on left child */``        ``printInorder(node.left);` `        ``/* then print the data of node */``        ``System.out.print(node.data + ``" "``);` `        ``/* now recur on right child */``        ``printInorder(node.right);``    ``}` `    ``/* Driver function to test above functions */``    ``public` `static` `void` `main(String args[])``    ``{``        ``Node root = ``null``;` `        ``/* Constructing tree given in the above figure``            ``10``            ``/ \``            ``30 15``        ``/     \``        ``20     5 */``        ``root = newNode(``10``);``        ``root.left = newNode(``30``);``        ``root.right = newNode(``15``);``        ``root.left.left = newNode(``20``);``        ``root.right.right = newNode(``5``);` `        ``// convert Binary Tree to BST``        ``binaryTreeToBST(root);` `        ``System.out.println(``"Following is Inorder Traversal of the converted BST: "``);``        ``printInorder(root);` `    ``}``}` `// This code is contributed by adityapande88.`

## Python3

 `# Program to convert binary tree to BST` `# A binary tree node``class` `Node:``    ` `    ``# Constructor to create a new node``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# Helper function to store the inorder traversal of a tree``def` `storeInorder(root, inorder):``    ` `    ``# Base Case``    ``if` `root ``is` `None``:``        ``return``    ` `    ``# First store the left subtree``    ``storeInorder(root.left, inorder)``    ` `    ``# Copy the root's data``    ``inorder.append(root.data)` `    ``# Finally store the right subtree``    ``storeInorder(root.right, inorder)` `# A helper function to count nodes in a binary tree``def` `countNodes(root):``    ``if` `root ``is` `None``:``        ``return` `0` `    ``return` `countNodes(root.left) ``+` `countNodes(root.right) ``+` `1` `# Helper function that copies contents of sorted array``# to Binary tree``def` `arrayToBST(arr, root):` `    ``# Base Case``    ``if` `root ``is` `None``:``        ``return``    ` `    ``# First update the left subtree``    ``arrayToBST(arr, root.left)` `    ``# now update root's data delete the value from array``    ``root.data ``=` `arr[``0``]``    ``arr.pop(``0``)` `    ``# Finally update the right subtree``    ``arrayToBST(arr, root.right)` `# This function converts a given binary tree to BST``def` `binaryTreeToBST(root):``    ` `    ``# Base Case: Tree is empty``    ``if` `root ``is` `None``:``        ``return``    ` `    ``# Count the number of nodes in Binary Tree so that``    ``# we know the size of temporary array to be created``    ``n ``=` `countNodes(root)` `    ``# Create the temp array and store the inorder traversal``    ``# of tree``    ``arr ``=` `[]``    ``storeInorder(root, arr)``    ` `    ``# Sort the array``    ``arr.sort()` `    ``# copy array elements back to binary tree``    ``arrayToBST(arr, root)` `# Print the inorder traversal of the tree``def` `printInorder(root):``    ``if` `root ``is` `None``:``        ``return``    ``printInorder(root.left)``    ``print` `(root.data,end``=``" "``)``    ``printInorder(root.right)` `# Driver program to test above function``root ``=` `Node(``10``)``root.left ``=` `Node(``30``)``root.right ``=` `Node(``15``)``root.left.left ``=` `Node(``20``)``root.right.right ``=` `Node(``5``)` `# Convert binary tree to BST``binaryTreeToBST(root)` `print` `(``"Following is the inorder traversal of the converted BST"``)``printInorder(root)` `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

## C#

 `using` `System;` `public` `class` `Node``{``    ``public` `int` `data;``    ``public` `Node left;``    ``public` `Node right;``}` `public` `class` `GFG{``    ` `    ``// index pointer to pointer to the array index``    ``static` `int` `index;`` ` ` ` `    ``/* A helper function that stores inorder traversal of a tree rooted``    ``with node */``    ``static` `void` `storeInorder(Node node, ``int``[] inorder)``    ``{``        ``// Base Case``        ``if` `(node == ``null``)``            ``return``;`` ` `        ``/* first store the left subtree */``        ``storeInorder(node.left, inorder);`` ` `        ``/* Copy the root's data */``        ``inorder[index] = node.data;``        ``index++; ``// increase index for next entry`` ` `        ``/* finally store the right subtree */``        ``storeInorder(node.right, inorder);``    ``}`` ` `    ``/* A helper function to count nodes in a Binary Tree */``    ``static` `int` `countNodes(Node root)``    ``{``        ``if` `(root == ``null``)``            ``return` `0;``        ``return` `countNodes(root.left) + countNodes(root.right) + 1;``    ``}`` ` `    ``/* A helper function that copies contents of arr[] to Binary Tree.``    ``This function basically does Inorder traversal of Binary Tree and``    ``one by one copy arr[] elements to Binary Tree nodes */``    ``static` `void` `arrayToBST(``int``[] arr, Node root)``    ``{``        ``// Base Case``        ``if` `(root == ``null``)``            ``return``;`` ` `        ``/* first update the left subtree */``        ``arrayToBST(arr, root.left);`` ` `        ``/* Now update root's data and increment index */``        ``root.data = arr[index];``        ``index++;`` ` `        ``/* finally update the right subtree */``        ``arrayToBST(arr, root.right);``    ``}`` ` `    ``// This function converts a given Binary Tree to BST``    ``static` `void` `binaryTreeToBST(Node root)``    ``{``        ``// base case: tree is empty``        ``if` `(root == ``null``)``            ``return``;`` ` `        ``/* Count the number of nodes in Binary Tree so that``        ``we know the size of temporary array to be created */``        ``int` `n = countNodes(root);`` ` `        ``// Create a temp array arr[] and store inorder traversal of tree in arr[]``        ``int``[] arr = ``new` `int``[n];`` ` `        ``storeInorder(root, arr);`` ` `        ``// Sort the array using library function for quick sort``        ``Array.Sort(arr);``         ` `         ` `        ``// Copy array elements back to Binary Tree``        ``index = 0;``        ``arrayToBST(arr, root);``    ``}`` ` `    ``/* Utility function to create a new Binary Tree node */``    ``static` `Node newNode(``int` `data)``    ``{``        ``Node temp = ``new` `Node();``        ``temp.data = data;``        ``temp.left = ``null``;``        ``temp.right = ``null``;``        ``return` `temp;``    ``}`` ` `    ``/* Utility function to print inorder traversal of Binary Tree */``    ``static` `void` `printInorder(Node node)``    ``{``        ``if` `(node == ``null``)``            ``return``;`` ` `        ``/* first recur on left child */``        ``printInorder(node.left);`` ` `        ``/* then print the data of node */``        ``Console.Write(node.data + ``" "``);`` ` `        ``/* now recur on right child */``        ``printInorder(node.right);``    ``}`` ` `    ``/* Driver function to test above functions */``    ` `    ``static` `public` `void` `Main (){``        ` `        ``Node root = ``null``;`` ` `        ``/* Constructing tree given in the above figure``            ``10``            ``/ \``            ``30 15``        ``/     \``        ``20     5 */``        ``root = newNode(10);``        ``root.left = newNode(30);``        ``root.right = newNode(15);``        ``root.left.left = newNode(20);``        ``root.right.right = newNode(5);`` ` `        ``// convert Binary Tree to BST``        ``binaryTreeToBST(root);`` ` `        ``Console.WriteLine(``"Following is Inorder Traversal of the converted BST: "``);``        ``printInorder(root);``        ` `    ``}``}` `// This code is contributed by avanitrachhadiya2155`

## Javascript

 ``
Output
```Following is the inorder traversal of the converted BST
5 10 15 20 30```

Complexity Analysis:

• Time Complexity: O(nlogn). This is the complexity of the sorting algorithm which we are using after first in-order traversal, rest of the operations take place in linear time.
• Auxiliary Space: O(n). Use of data structure ‘array’ to store in-order traversal.

We will be covering another method for this problem which converts the tree using O(height of the tree) extra space.