<p>We run a&nbsp;preorder&nbsp;depth-first search (DFS) on the <code>root</code> of a binary tree.</p>

<p>At each node in this traversal, we output <code>D</code> dashes (where <code>D</code> is the depth of this node), then we output the value of this node.&nbsp; If the depth of a node is <code>D</code>, the depth of its immediate child is <code>D + 1</code>.&nbsp; The depth of the <code>root</code> node is <code>0</code>.</p>

<p>If a node has only one child, that child is guaranteed to be <strong>the left child</strong>.</p>

<p>Given the output <code>traversal</code> of this traversal, recover the tree and return <em>its</em> <code>root</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/09/10/recover_tree_ex1.png" style="width: 423px; height: 200px;" />
<pre>
<strong>Input:</strong> traversal = &quot;1-2--3--4-5--6--7&quot;
<strong>Output:</strong> [1,2,5,3,4,6,7]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/09/10/recover_tree_ex2.png" style="width: 432px; height: 250px;" />
<pre>
<strong>Input:</strong> traversal = &quot;1-2--3---4-5--6---7&quot;
<strong>Output:</strong> [1,2,5,3,null,6,null,4,null,7]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/09/10/recover_tree_ex3.png" style="width: 305px; height: 250px;" />
<pre>
<strong>Input:</strong> traversal = &quot;1-401--349---90--88&quot;
<strong>Output:</strong> [1,401,null,349,88,90]
</pre>

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

<ul>
	<li>The number of nodes in the original tree is in the range <code>[1, 1000]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>9</sup></code></li>
</ul>

# 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

# preorder: root, (left...), (right...)
class Solution:
    def recoverFromPreorder(self, traversal: str, depth=0) -> Optional[TreeNode]:
        if not traversal: return None
        root_val_bound = traversal.find('-')
        root = TreeNode(int(traversal[:root_val_bound if root_val_bound != -1 else None]))
        to_string = '-' * (depth + 1)
        pattern = re.compile(f'\d{to_string}\d')
        l_span = pattern.search(traversal)
        r_span = pattern.search(traversal, l_span.end()-1) if l_span else None
        if l_span: root.left = self.recoverFromPreorder(traversal[l_span.end()-1:(r_span.start()+1 if r_span else None)], depth+1)
        if r_span: root.right = self.recoverFromPreorder(traversal[r_span.end()-1:], depth+1)
        return root
17400