<p>Given a binary tree <code>root</code> and a&nbsp;linked list with&nbsp;<code>head</code>&nbsp;as the first node.&nbsp;</p>

<p>Return True if all the elements in the linked list starting from the <code>head</code> correspond to some <em>downward path</em> connected in the binary tree&nbsp;otherwise return False.</p>

<p>In this context downward path means a path that starts at some node and goes downwards.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/sample_1_1720.png" style="width: 220px; height: 280px;" /></strong></p>

<pre>
<strong>Input:</strong> head = [4,2,8], root = [1,4,4,null,2,2,null,1,null,6,8,null,null,null,null,1,3]
<strong>Output:</strong> true
<strong>Explanation:</strong> Nodes in blue form a subpath in the binary Tree.  
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/sample_2_1720.png" style="width: 220px; height: 280px;" /></strong></p>

<pre>
<strong>Input:</strong> head = [1,4,2,6], root = [1,4,4,null,2,2,null,1,null,6,8,null,null,null,null,1,3]
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> head = [1,4,2,6,8], root = [1,4,4,null,2,2,null,1,null,6,8,null,null,null,null,1,3]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no path in the binary tree that contains all the elements of the linked list from <code>head</code>.
</pre>

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

<ul>
	<li>The number of nodes in the tree will be in the range <code>[1, 2500]</code>.</li>
	<li>The number of nodes in the list will be in the range <code>[1, 100]</code>.</li>
	<li><code>1 &lt;= Node.val&nbsp;&lt;= 100</code>&nbsp;for each node in the linked list and binary tree.</li>
</ul>

class Solution:
    def isSubPath(self, head: Optional[ListNode], root: Optional[TreeNode]) -> bool:
        
        self.graph = collections.defaultdict(list)
        self.lst = []
        tmp = head
        while tmp != None:
            self.lst.append(tmp)
            tmp = tmp.next

        def helper(root, parent):
            if not root: return
            if parent != None:
                self.graph[parent].append(root)
                self.graph[root].append(parent)

            helper(root.left, root)
            helper(root.right, root)
        
        helper(root, None)

        self.ans = False
        self.seen = set()


        def dfs(root, depth):
            if depth==len(self.lst):
                self.ans = True
                return
            for v in self.graph[root]:
                if v in self.seen: continue
                if v.val == self.lst[depth].val:
                    self.seen.add(v)
                    dfs(v, depth+1)
                    self.seen.remove(v)
        
        def dfs2(root):
            if not root:
                return
            
            if root.val==head.val:
                self.seen.add(root)
                dfs(root, 1)
                self.seen.remove(root)
            
            dfs2(root.left)
            dfs2(root.right)

        dfs2(root)
        return self.ans
20500