# Check whether the two Binary Search Trees are Identical or Not

Given the root nodes of the two binary search trees. The task is to print 1 if the two Binary Search Trees are identical else print 0. Two trees are identical if they are identical structurally and nodes have the same values.

Tree 1

Tree 2

In the above images, both Tree1 and Tree2 are identical.

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

To identify if two trees are identical, we need to traverse both trees simultaneously, and while traversing we need to compare data and children of the trees.

Below is the step by step algorithm to check if two BSTs are identical:

1. If both trees are empty then return 1.
2. Else If both trees are non -empty
• Check data of the root nodes (tree1->data == tree2->data)
• Check left subtrees recursively i.e., call sameTree(tree1->left_subtree, tree2->left_subtree)
• Check right subtrees recursively i.e., call sameTree(tree1->right_subtree, tree2->right_subtree)
• If the values returned in the above three steps are true then return 1.
3. Else return 0 (one is empty and other is not).

Below is the implementation of the above approach:

## C++

 `// C++ program to check if two BSTs ` `// are identical ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// BST node ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node* left; ` `    ``struct` `Node* right; ` `}; ` ` `  `// Utility function to create a new Node ` `struct` `Node* newNode(``int` `data) ` `{ ` `    ``struct` `Node* node = (``struct` `Node*) ` `        ``malloc``(``sizeof``(``struct` `Node)); ` `    ``node->data = data; ` `    ``node->left = NULL; ` `    ``node->right = NULL; ` ` `  `    ``return` `node; ` `} ` ` `  `// Function to perform inorder traversal ` `void` `inorder(Node* root) ` `{ ` `    ``if` `(root == NULL) ` `        ``return``; ` ` `  `    ``inorder(root->left); ` ` `  `    ``cout << root->data << ``" "``; ` ` `  `    ``inorder(root->right); ` `} ` ` `  `// Function to check if two BSTs ` `// are identical ` `int` `isIdentical(Node* root1, Node* root2) ` `{ ` `    ``// Check if both the trees are empty ` `    ``if` `(root1 == NULL && root2 == NULL) ` `        ``return` `1; ` `    ``// If any one of the tree is non-empty ` `    ``// and other is empty, return false ` `    ``else` `if` `(root1 != NULL && root2 == NULL) ` `        ``return` `0; ` `    ``else` `if` `(root1 == NULL && root2 != NULL) ` `        ``return` `0; ` `    ``else` `{ ``// Check if current data of both trees equal ` `        ``// and recursively check for left and right subtrees ` `        ``if` `(root1->data == root2->data && isIdentical(root1->left, root2->left) ` `            ``&& isIdentical(root1->right, root2->right)) ` `            ``return` `1; ` `        ``else` `            ``return` `0; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``struct` `Node* root1 = newNode(5); ` `    ``struct` `Node* root2 = newNode(5); ` `    ``root1->left = newNode(3); ` `    ``root1->right = newNode(8); ` `    ``root1->left->left = newNode(2); ` `    ``root1->left->right = newNode(4); ` ` `  `    ``root2->left = newNode(3); ` `    ``root2->right = newNode(8); ` `    ``root2->left->left = newNode(2); ` `    ``root2->left->right = newNode(4); ` ` `  `    ``if` `(isIdentical(root1, root2)) ` `        ``cout << ``"Both BSTs are identical"``; ` `    ``else` `        ``cout << ``"BSTs are not identical"``; ` ` `  `    ``return` `0; ` `} `

## Python3

# Python3 program to contrcut all unique
# BSTs for keys from 1 to n

# 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 perform inorder traversal
def inorder(root) :

if (root == None):
return

inorder(root.left)

print(root.data, end = ” “)

inorder(root.right)

# Function to check if two BSTs
# are identical
def isIdentical(root1, root2) :

# Check if both the trees are empty
if (root1 == None and root2 == None) :
return 1

# If any one of the tree is non-empty
# and other is empty, return false
elif (root1 != None and root2 == None) :
return 0
elif (root1 == None and root2 != None) :
return 0
else: # Check if current data of both trees
# equal and recursively check for left
# and right subtrees
if (root1.data == root2.data and
isIdentical(root1.left, root2.left)
and isIdentical(root1.right, root2.right)) :
return 1
else:
return 0

# Driver Code
if __name__ == ‘__main__’:

root1 = newNode(5)
root2 = newNode(5)
root1.left = newNode(3)
root1.right = newNode(8)
root1.left.left = newNode(2)
root1.left.right = newNode(4)

root2.left = newNode(3)
root2.right = newNode(8)
root2.left.left = newNode(2)
root2.left.right = newNode(4)

if (isIdentical(root1, root2)):
print(“Both BSTs are identical”)
else:
print(“BSTs are not identical”)

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

Output:

```Both BSTs are identical
```

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