Find Duplicate Subtrees

To solve finding duplicate subtrees efficiently, I would use a post-order traversal combined with a hash map to serialize each subtree. The core challenge is creating a unique string representation for every subtree structure. I will define a recursive function that returns a serialized string for the current node. For any given node, I first recursively process its left and right children. Then, I construct a signature by combining the left signature, the right signature, and the current node's value, separated by specific delimiters like commas or pipes to avoid ambiguity. For example, a tree with root 1, left child 2, and right child 3 might serialize as '2,3,1'. As we traverse, we store these signatures in a HashMap. The key is the signature string, and the value is a list of root nodes that produced it. If a signature appears for the second time, we know we found a duplicate, so we add the current root to our results list. By using post-order, we guarantee that when we process a node, its entire subtree has already been uniquely identified. This approach runs in O(N) time where N is the number of nodes, assuming string hashing is efficient, and uses O(N) space for the map. This method aligns well with Meta's focus on scalable, efficient algorithms that handle complex data relationships without redundant computation.