What are some algorithms for comparing the differences between two trees?

Question

I'm looking to find the differences while comparing two tree structures.

The nodes will be strings. And I would like to capture at what level of the tree it is occurring.

For example finding the differences between these two trees:

Answer 1

The basic idea is to traverse the both tree level by level. Once you find,

the nodes are not the same

or

the nodes are not samely structured

means you found a difference here! now you can mark the level or the node, whatever you want.

PSEDOCODE :

function getDiff(Tree root, Tree root1){
   Queue queue->push(root);
   Queue queue1->push(root1);
   level = 1;
   while(queue->size() != 0 && queue1->size() != 0){
      if(queue->size() != queue1->size()) {
            PRINT: "THE TREE AREN'T IN SAME STRUCTURE :/";
            return;
      }

      size = queue->size();
      /* traversing both trees level-by-level */
      while(size-- > 0){
           Tree temp = queue->peek();
           Tree temp1 = queue1->peek();

           queue->pop();
           queue1->pop();

            if(!temp->node != temp1->node) {
                  PROCESS: level;
            }
            if(temp->left != null && temp1->left != null) {
                queue->push(temp->left);
                queue1->push(temp1->left);
            }

            if(temp->right!= null && temp1->right!= null) {
                queue->push(temp->right);
                queue1->push(temp1->right);
            }
        }
        /* increase level */
        level += 1;
    }
}

NOTE: CHANGE THE PSEDOCODE INTO YOUR FAVOURITE LANGUAGE :)

Answer 2

What about a simple hash, List all values from root to leaf of the first tree and hash them. then list all values from root to leaf of the second tree and compare to the first one with O(1) time complexity. One can split the second tree (ig based on the first layer) and use multi thread, In python, just put them on a set; and it's all done. or hash both of them and do a .difference()