# Binary Tree to Binary Search Tree Conversion using STL set

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.

This solution will use Sets of C++ STL instead of array based solution.

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

#### Solution

1. Copy the items of binary tree in a set while doing inorder traversal. This takes O(n log n) time. Note that set in C++ STL is implemented using a Self Balancing Binary Search Tree like Red Black Tree, AVL Tree, etc
2. There is no need to sort the set as sets in C++ are implemented using Self-balancing binary search trees due to which each operation such as insertion, searching, deletion etc takes O(log n) time.
3. Now simply copy the items of set one by one from beginning to the tree while doing inorder traversal of tree. Care should be taken as when copying each item of set from its beginning, we first copy it to the tree while doing inorder traversal, then remove it from the set as well.

Now the above solution is simpler and easier to implement than the array based conversion of Binary tree to Binary search tree explained here- Conversion of Binary Tree to Binary Search tree (Set-1), where we had to separately make a function to sort the items of the array after copying the items from tree to it.

Program to convert a binary tree to binary search tree using set.

## C++

 `/* CPP program to convert a Binary tree to BST  ` `   ``using sets as containers. */` `#include ` `using` `namespace` `std; ` ` `  `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// function to store the nodes in set while ` `// doing inorder traversal. ` `void` `storeinorderInSet(Node* root, set<``int``>& s) ` `{ ` `    ``if` `(!root) ` `        ``return``; ` ` `  `    ``// visit the left subtree first ` `    ``storeinorderInSet(root->left, s); ` ` `  `    ``// insertion takes order of O(logn) for sets ` `    ``s.insert(root->data);  ` ` `  `    ``// visit the right subtree ` `    ``storeinorderInSet(root->right, s); ` ` `  `} ``// Time complexity  = O(nlogn) ` ` `  `// function to copy items of set one by one  ` `// to the tree while doing inorder traversal ` `void` `setToBST(set<``int``>& s, Node* root) ` `{ ` `    ``// base condition ` `    ``if` `(!root) ` `        ``return``; ` ` `  `    ``// first move to the left subtree and  ` `    ``// update items ` `    ``setToBST(s, root->left); ` ` `  `    ``// iterator initially pointing to the ` `    ``// beginning of set ` `    ``auto` `it = s.begin(); ` ` `  `    ``// copying the item at beginning of  ` `    ``// set(sorted) to the tree. ` `    ``root->data = *it;  ` ` `  `    ``// now erasing the beginning item from set. ` `    ``s.erase(it); ` ` `  `    ``// now move to right subtree and update items ` `    ``setToBST(s, root->right); ` ` `  `} ``// T(n) = O(nlogn) time ` ` `  `// Converts Binary tree to BST. ` `void` `binaryTreeToBST(Node* root) ` `{ ` `    ``set<``int``> s; ` ` `  `    ``// populating the set with the tree's  ` `    ``// inorder traversal data ` `    ``storeinorderInSet(root, s); ` ` `  `    ``// now sets are by default sorted as ` `    ``// they are implemented using self- ` `    ``// balancing BST ` ` `  `    ``// copying items from set to the tree  ` `    ``// while inorder traversal which makes a BST ` `    ``setToBST(s, root); ` ` `  `} ``// Time complexity  =  O(nlogn),  ` `  ``// Auxiliary Space = O(n) for set. ` ` `  `// helper function to create a node ` `Node* newNode(``int` `data) ` `{ ` `    ``// dynamically allocating memory ` `    ``Node* temp = ``new` `Node(); ` `    ``temp->data = data; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `temp; ` `} ` ` `  `// function to do inorder traversal ` `void` `inorder(Node* root) ` `{ ` `    ``if` `(!root) ` `        ``return``; ` `    ``inorder(root->left); ` `    ``cout << root->data << ``" "``; ` `    ``inorder(root->right); ` `} ` ` `  `int` `main() ` `{ ` `    ``Node* root = newNode(5); ` `    ``root->left = newNode(7); ` `    ``root->right = newNode(9); ` `    ``root->right->left = newNode(10); ` `    ``root->left->left = newNode(1); ` `    ``root->left->right = newNode(6); ` `    ``root->right->right = newNode(11); ` ` `  `    ``/* Constructing tree given in the above figure ` `           ``5 ` `         ``/   ` `        ``7     9 ` `       ``/    / ` `      ``1  6   10 11   */` ` `  `    ``// converting the above Binary tree to BST ` `    ``binaryTreeToBST(root); ` `    ``cout << ``"Inorder traversal of BST is: "` `<< endl; ` `    ``inorder(root); ` `    ``return` `0; ` `} `

## Python3

# Python3 program to convert a Binary tree
# to BST using sets as containers.

# Binary Tree Node
“”” A utility function to create a
new BST node “””
class newNode:

# Construct to create a newNode
def __init__(self, data):
self.data = data
self.left = None
self.right = None

# function to store the nodes in set
# while doing inorder traversal.
def storeinorderInSet(root, s):

if (not root) :
return

# visit the left subtree first
storeinorderInSet(root.left, s)

# insertion takes order of O(logn)
# for sets

# visit the right subtree
storeinorderInSet(root.right, s)

# Time complexity = O(nlogn)

# function to copy items of set one by one
# to the tree while doing inorder traversal
def setToBST(s, root) :

# base condition
if (not root):
return

# first move to the left subtree and
# update items
setToBST(s, root.left)

# iterator initially pointing to
# the beginning of set
it = next(iter(s))

# copying the item at beginning of
# set(sorted) to the tree.
root.data = it

# now erasing the beginning item from set.
s.remove(it)

# now move to right subtree
# and update items
setToBST(s, root.right)

# T(n) = O(nlogn) time

# Converts Binary tree to BST.
def binaryTreeToBST(root):

s = set()

# populating the set with the tree’s
# inorder traversal data
storeinorderInSet(root, s)

# now sets are by default sorted as
# they are implemented using self-
# balancing BST

# copying items from set to the tree
# while inorder traversal which makes a BST
setToBST(s, root)

# Time complexity = O(nlogn),
# Auxiliary Space = O(n) for set.

# function to do inorder traversal
def inorder(root) :

if (not root) :
return
inorder(root.left)
print(root.data, end = ” “)
inorder(root.right)

# Driver Code
if __name__ == ‘__main__’:

root = newNode(5)
root.left = newNode(7)
root.right = newNode(9)
root.right.left = newNode(10)
root.left.left = newNode(1)
root.left.right = newNode(6)
root.right.right = newNode(11)

“”” Constructing tree given in
the above figure
5
/
7 9
/ /
1 6 10 11 “””

# converting the above Binary tree to BST
binaryTreeToBST(root)
print(“Inorder traversal of BST is: “)
inorder(root)

# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)

Output:

```Inorder traversal of BST is:
1 5 6 7 9 10 11
```

Time Complexity: O(n Log n)
Auxiliary Space: (n)