TreeIsomorphism

Write a function to detect if two trees are isomorphic. Two trees are called isomorphic if one of them can be obtained from other by a series of flips, i.e. by swapping left and right children of a number of nodes.

Any number of nodes at any level can have their children swapped. Two empty trees are isomorphic.

Example

For example, following two trees are isomorphic with following sub-trees flipped: 2 and 3, NULL and 6, 7 and 8.

Note

We simultaneously traverse both trees. Let the current internal nodes of two trees being traversed be n1 and n2 respectively. There are following two conditions for subtrees rooted with n1 and n2 to be isomorphic. 1) Data of n1 and n2 is same. 2) One of the following two is true for children of n1 and n2 ……a) Left child of n1 is isomorphic to left child of n2 and right child of n1 is isomorphic to right child of n2. ……b) Left child of n1 is isomorphic to right child of n2 and right child of n1 is isomorphic to left child of n2.

Code

class TreeIsomorphism 
{
    TreeNode root1, root2;

    /* Given a binary tree, print its nodes in reverse level order */
    boolean isIsomorphic(TreeNode n1, TreeNode n2) 
    {
        // Both roots are NULL, trees isomorphic by definition
        if (n1 == null && n2 == null)
            return true;

        // Exactly one of the n1 and n2 is NULL, trees not isomorphic
        if (n1 == null || n2 == null)
            return false;

        if (n1.val != n2.val)
            return false;

        return (isIsomorphic(n1.left, n2.left) && isIsomorphic(n1.right, n2.right)) || 
               (isIsomorphic(n1.left, n2.right) && isIsomorphic(n1.right, n2.left));
    }