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Symmetric Tree

A symmetric tree is a mirror image of itself around the root node. A recursive or iterative approach can determine whether or not a binary tree is symmetric. Let’s take a look at the examples of Symmetric Tree and determine whether they’re true or false.

Symmetric Tree Problem Statement

Given a binary tree, check whether it is a mirror of itself i.e. symmetric around its center.

Example One



Learn how to Construct the Binary Tree with the inorder and preorder traversal.

Example Two



Learn how to solve the Mirror Image of Binary Tree problem.

Example Three





  • 0 <= number of nodes in the tree <= 5 * 104
  • 0 <= value in a tree node <= 105

Know how to Validate a Binary Search Tree.

Code for Symmetric Tree:

Following is the code to solve the symmetric tree problem. 


Asymptotic complexity in terms of the number of nodes ( = `n`) and the height ( = `h`) of the tree rooted at `root`:

* Time: O(n).

* Auxiliary space: O(h).

* Total space: O(n).


// Helper function which returns true if trees with roots as root1 and root2 are mirror images.

bool check_if_mirror(BinaryTreeNode* root1, BinaryTreeNode* root2){

   if (root1 == NULL && root2 == NULL){

       return true;


   if(root1 == NULL || root2 == NULL){

       return false;


   if (root1->value == root2->value){

       return check_if_mirror(root1->left, root2->right) && check_if_mirror(root1->right, root2->left);


   return false;


bool check_if_symmetric(BinaryTreeNode *root) {

   return check_if_mirror(root, root);


Find out how to Build a Balanced BST from a Sorted Array.

We hope that these solutions to the Symmetric Tree problem will help you level up your coding skills. Data structures are the foundation of programming languages, and the Binary Search Tree is a tree that allows for fast search, insert, and delete operations on sorted data. It also allows you to find the item that is closest to you. Routing Tables, Sorting, Decision Trees, and Data Compression are just a few of the many applications of Symmetric Tree.

Because of the widespread use of Tree Data Structure, companies such as Amazon and Zomato include Symmetric Tree interview questions and other Binary Tree Data Structure problems in their tech interviews. 

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