<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 List, Optional
from collections import defaultdict
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
  
class Solution:
    def _dfs(self, u: TreeNode, ans: List, mp: defaultdict[TreeNode, int]):
        if not u: 
            dp_u = ""
            return dp_u
        # 如果是利用儿子结点信息计算，先递归再计算  

        # dp1[u]: u 子树的 pre_order
        # dp1[u] = f'{u.val}, dp1[v_l], dp1[v_r]'
        dp1_v_l = self._dfs(u.left, ans, mp)
        dp1_v_r = self._dfs(u.right, ans, mp)
        dp_u = f'{u.val}, {dp1_v_l}, {dp1_v_r}'

        mp[dp_u] += 1
        if mp[dp_u] == 2: ans.append(u)

        return dp_u
    def findDuplicateSubtrees(self, root: Optional[TreeNode]) -> List[Optional[TreeNode]]:
        ans = []
        mp = defaultdict(int)

        self._dfs(root, ans, mp)
        return ans
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