Problem Description
Given the root of a binary tree, return all duplicate subtrees. For each kind of duplicate subtrees, only the root node of any one of them needs to be returned. Two trees are duplicate if they have the same structure with the same node values.
Key Insights
- A subtree is defined as duplicate if it has the same structure and node values as another subtree in the binary tree.
- To identify duplicates, we can serialize each subtree and use a hash table to track occurrences.
- When a subtree is found that has already been seen (i.e., exists in the hash table), we add it to the result list, ensuring we only add it once.
Space and Time Complexity
Time Complexity: O(N) - Each node is processed once to determine the subtree structure. Space Complexity: O(N) - In the worst case, we store all subtrees in the hash table.
Solution
To find duplicate subtrees, we can use a depth-first search (DFS) approach. As we traverse the tree, we serialize each subtree into a string format (using a combination of node values and structure). We utilize a hash table to count occurrences of each serialized subtree. When we encounter a duplicate (i.e., a serialized subtree that has been seen before), we add it to our result list. This approach ensures we efficiently track duplicates without unnecessary comparisons.