Check if 2 trees are mirror of each other

In this tutorial we shall see how to check if 2 trees are mirror to each other.

Problem Statement:

You are given root node of 2 trees. You need to check if those 2 trees are mirror to each other.

For example:

Below 2 trees are mirror to each other.

As you can see above, except root node, the left child will become right and vice versa. This is the meaning of mirror of binary tree.

From the above image we can arrive at below points that return true.

1. If the current is root node, then continue.
2. If the left child of the tree 1 is equal to the right child value return true.
3. If the right child value is equal to the left child value, return true.
4. If both are NULL, then return true.

We can also define below false statements:

1. If right child exists in tree 1 and no child at tree 2 return false, same holds for vice versa.
2. If the right child value is different than the left child value of tree 2, return false.

Solution in C++

#include <iostream>
#include <queue>
#include <stack>
using namespace std;

// structure to hold binary tree node
struct Node
{
    int data;
    Node *left, *right;

    Node(int data)
    {
        this->data = data;
        this->left = this->right = nullptr;
    }
};


bool check_if_mirror(Node *node1, Node *node2) 
{
    if (node1 == NULL && node2 == NULL) 
    {
      return true;
    }

    if (node1 == NULL || node2 == NULL) 
    {
      return false;
    }

    return node1->data == node2->data 
        && check_if_mirror(node1->left, node2->right) 
        && check_if_mirror(node1->right, node2->left);
  }


int main()  
{  
    Node* root = nullptr;
    /* Binary tree:
              16
            /   \
           /     \
          10      25
         /  \    /  \
        /    \  /    \
       7    15 18     30

    */

    root = new Node(16);
    root->left = new Node(10);
    root->right = new Node(25);
    root->left->left = new Node(7);
    root->left->right = new Node(15);
    root->right->left = new Node(18);
    root->right->right = new Node(30);



    Node* root_1 = nullptr;
    /* Binary tree:
              16
            /   \
           /     \
          25      10
         /  \    /  \
        /    \  /    \
       30    18 15     7

    */

    root_1 = new Node(16);
    root_1->left = new Node(25);
    root_1->right = new Node(10);
    root_1->left->left = new Node(30);
    root_1->left->right = new Node(18);
    root_1->right->left = new Node(15);
    root_1->right->right = new Node(7);

    if(check_if_mirror(root, root_1))
    {
        cout<<"Both are mirror"<<endl;
    } else {
        cout<<"Both are not mirror"<<endl;
    }

    return 0;  
}

Output:

Both are mirror

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