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
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Tree 2
In the above images, both Tree1 and Tree2 are identical.
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:
- If both trees are empty then return 1.
- 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.
- 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 <iostream>using namespace std;// BST nodestruct Node { int data; struct Node* left; struct Node* right;};// Utility function to create a new Nodestruct 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 traversalvoid inorder(Node* root){ if (root == NULL) return; inorder(root->left); cout << root->data << " "; inorder(root->right);}// Function to check if two BSTs// are identicalint 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 codeint 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;} |
Java
// Java program to check if two BSTs// are identicalclass GFG{// BST nodestatic class Node{ int data; Node left; Node right;};// Utility function to create a new Nodestatic Node newNode(int data){ Node node = new Node(); node.data = data; node.left = null; node.right = null; return node;}// Function to perform inorder traversalstatic void inorder(Node root){ if (root == null) return; inorder(root.left); System.out.print(root.data + " "); inorder(root.right);}// Function to check if two BSTs// are identicalstatic 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) == 1 && isIdentical(root1.right, root2.right) == 1) return 1; else return 0; }}// Driver codepublic static void main(String[] args){ Node root1 = newNode(5); 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)==1) System.out.print("Both BSTs are identical"); else System.out.print("BSTs are not identical");}}// This code is contributed by 29AjayKumar |
Python3
# Python3 program to contrcut all unique# BSTs for keys from 1 to n# Binary Tree Node""" A utility function to create anew 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 traversaldef inorder(root) : if (root == None): return inorder(root.left) print(root.data, end = " ") inorder(root.right)# Function to check if two BSTs# are identicaldef 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 Codeif __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) |
C#
// C# program to check if two BSTs// are identicalusing System;class GFG{// BST nodeclass Node{ public int data; public Node left; public Node right;};// Utility function to create a new Nodestatic Node newNode(int data){ Node node = new Node(); node.data = data; node.left = null; node.right = null; return node;}// Function to perform inorder traversalstatic void inorder(Node root){ if (root == null) return; inorder(root.left); Console.Write(root.data + " "); inorder(root.right);}// Function to check if two BSTs// are identicalstatic 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) == 1 && isIdentical(root1.right, root2.right) == 1) return 1; else return 0; }}// Driver codepublic static void Main(String[] args){ Node root1 = newNode(5); 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) == 1) Console.Write("Both BSTs are identical"); else Console.Write("BSTs are not identical");}}// This code is contributed by PrinciRaj1992 |
Javascript
<script>// Javascript program to check if two BSTs// are identical// BST nodeclass Node{ // Utility function to create a new Node constructor(data) { this.data = data; this.left = this.right = null; }}// Function to perform inorder traversalfunction inorder(root){ if (root == null) return; inorder(root.left); document.write(root.data + " "); inorder(root.right);}// Function to check if two BSTs// are identicalfunction isIdentical(root1,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) == 1 && isIdentical(root1.right, root2.right) == 1) return 1; else return 0; }}// Driver codelet root1 = new Node(5); let root2 = new Node(5); root1.left = new Node(3); root1.right = new Node(8); root1.left.left = new Node(2); root1.left.right = new Node(4); root2.left = new Node(3); root2.right = new Node(8); root2.left.left = new Node(2); root2.left.right = new Node(4); if (isIdentical(root1, root2)==1) document.write("Both BSTs are identical"); else document.write("BSTs are not identical");// This code is contributed by avanitrachhadiya2155</script> |
Output:
Both BSTs are identical
Time Complexity: O(N)
Auxiliary Space: O(N)
