Check whether two trees are symmetrical or not

March 24, 2025

Check for symmetrical trees

In this article, we will learn the approach and code about how check whether two trees are symmetrical in C++. Two binary trees are said to be symmetrical if both the trees are mirror images of each other.

Check whether two binary trees are symmetrical or not

Check Whether Two Trees are Symmetrical or Not

Algorithm :

  • Create a recursive function isMirror() that takes two trees as an argument and returns 1 if trees are the mirrored and 0 if trees are not mirrored.
  • The isSMirror() function recursively checks two roots and subtrees under the root.
  • And isSymmetric() takes the root of the binary tree as an parameter and then will return true is isMirror() returns 1, otherwise it return 1.
  • If isSymmetric() returns 1 it means that given tree is symmetric, otherwise not  symmetric.
Check whether two trees are symmetrical or not

Find the size of binary tree

Find maximum in binary tree

Level Order Traversal LIne by Line

Check If binary tree if Foldable or not

Check for Children-Sum in Binary Tree

Code Implementation to check whether two trees are symmetrical or not in C++

Run 
#include<bits/stdc++.h>
using namespace std;

struct Node
{
  int val;
  Node *left;
  Node *right;
    Node (int x):val (x), left (NULL), right (NULL)
  {
  }
};

bool isSymmetric (Node * root1, Node * root2)
{
  if (root1 == NULL && root2 == NULL)
    {
      return true;
    }
  else if (root1 == NULL || root2 == NULL)
    {
      return false;
    }
  else
    {
      return (root1->val == root2->val) && isSymmetric (root1->left, root2->right) && isSymmetric (root1->right, root2->left);
    }
}

bool isSymmetricTree (Node * root)
{
  if (root == NULL)
    {
      return true;
    }
  else
    {
      return isSymmetric (root->left, root->right);
    }
}

int main ()
{
  // Construct two sample binary trees.
  Node *root1 = new Node (1);
  root1->left = new Node (2);
  root1->right = new Node (2);
  root1->left->left = new Node (3);
  root1->left->right = new Node (4);
  root1->right->left = new Node (4);
  root1->right->right = new Node (3);

  Node *root2 = new Node (1);
  root2->left = new Node (2);
  root2->right = new Node (2);
  root2->left->left = new Node (3);
  root2->left->right = new Node (4);
  root2->right->left = new Node (4);
  root2->right->right = new Node (5);

  // Check whether the two binary trees are symmetrical or not.
  bool isSymmetric1 = isSymmetricTree (root1);
  bool isSymmetric2 = isSymmetricTree (root2);

  if (isSymmetric1)
    {
      cout << "The first binary tree is symmetrical." << endl;
    }
  else
    {
      cout << "The first binary tree is not symmetrical." << endl;
    }

  if (isSymmetric2)
    {
      cout << "The second binary tree is symmetrical." << endl;
    }
  else
    {
      cout << "The second binary tree is not symmetrical." << endl;
    }

  return 0;
}

Output:
The first binary tree is symmetrical.
The second binary tree is not symmetrical.