Interview Question for Software Development Engineer Intern at Amazon.com:

I utilized a depth-first traversal method, comparing the data within each node and recursively checking the left, then right child.

Don't know if this works or not...
<?php
class node{

    public $left;
    public $right;
    public $value;

    function _construct($value=null,$left=null,$right=null)
    {
        $this->value = $value;
        $this->left = $left;
        $this->right = $right;
    }

    // O(n) times inorder traversal
    function testEsqual($tree1,$tree2)
    {
        if($tree1->value ==null || $tree2->value==null)
            return false;
        if($tree1->value ==null && $tree2->value==null)
            return true;
        while($tree1->value!=null)
        {
            if($tree1->value == $tree2->value)
            {
                equal($tree1->left,$tree2->left);
                equal($tree1->right,$tree2->right);
            }
            else
            {
                return false;
            }
        }
    }
}
?>

How if we use in-order traversal? If my understanding is correct, two binary trees are equal if they contain the same elements (although at different positions in the tree)

bool AreEqual(Node* node1, Node* node2)
{
    if(
         (node1 == NULL && node2 != NULL) ||
         (node2 == NULL && node1 != NULL )
         return false;

         if(node1 == NULL && node2 == NULL)
              return true;

         if(node1->data != node2->data)
              return false;

         return( AreEqual(node1->left, node2->left) && AreEqual( node1->right, node2->right)
};

int main();
{

AreEqual(root1, root);

};

The solution by kvr doesn't cover a case when node1->data and node2->data are equal.
An additional if is required.