Check if a binary tree is the mirror image of itself

Given a binary tree, how do we write a program to check if it is the mirror image of itself. This binary tree is also called a symmetric tree.

A binary tree is called a symmetric tree if it’s left and right sub-trees are mirror images of each other.

For example Let us consider the following examples of some symmetric and asymmetric trees.

    1
   / Symmetric
2 2

    1
   / Asymmetric
2   3

      1
     /
    2   2 Symmetric
   /
3       3

We can design a recursive algorithm like the following.

An empty tree is a symmetric tree.
At each node we check the following
1. If the left value and right value are same
2. If the left sub-tree of left node and right sub-tree of the right node are mirror images
3. If the right sub-tree of left node and left sub-tree of the right node are mirror images
If all the above conditions are satisfied then the tree is symmetric.

Here is the C++ implementation of this.