<p>Given the <code>root</code>&nbsp;of a binary tree, return all <strong>duplicate subtrees</strong>.</p>

<p>For each kind of duplicate subtrees, you only need to return the root node of any <b>one</b> of them.</p>

<p>Two trees are <strong>duplicate</strong> if they have the <strong>same structure</strong> with the <strong>same node values</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/16/e1.jpg" style="width: 450px; height: 354px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,null,2,4,null,null,4]
<strong>Output:</strong> [[2,4],[4]]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/16/e2.jpg" style="width: 321px; height: 201px;" />
<pre>
<strong>Input:</strong> root = [2,1,1]
<strong>Output:</strong> [[1]]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/16/e33.jpg" style="width: 450px; height: 303px;" />
<pre>
<strong>Input:</strong> root = [2,2,2,3,null,3,null]
<strong>Output:</strong> [[2,3],[3]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of the nodes in the tree will be in the range <code>[1, 5000]</code></li>
	<li><code>-200 &lt;= Node.val &lt;= 200</code></li>
</ul>

from typing import Optional, List
from collections import defaultdict
import uuid

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right

class Solution:
  def __init__(self):
    self.id_counts = defaultdict(int)
    self.triplet_to_id = defaultdict()
    self.id_to_node = defaultdict()
    self.duplicate_subtree_ids = set()
    self.none_id = str(uuid.uuid4())

  def traverse(self, node: TreeNode) -> str:
    if not node:
      return self.none_id
    triplet = (self.traverse(node.left), node.val, self.traverse(node.right))
    if triplet not in self.triplet_to_id:
      triplet_id = str(uuid.uuid4())
      self.triplet_to_id[triplet] = triplet_id
      self.id_to_node[triplet_id] = node

    triplet_id = self.triplet_to_id[triplet]
    self.id_counts[triplet_id] += 1

    if self.id_counts[triplet_id] >= 2:
      self.duplicate_subtree_ids.add(triplet_id)

    return triplet_id


  def findDuplicateSubtrees(self, root: Optional[TreeNode]) -> List[Optional[TreeNode]]:
    self.traverse(root)
    ret_val = [self.id_to_node[id] for id in self.duplicate_subtree_ids]
    return ret_val
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