<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
class Solution:
    def recoverFromPreorder(self, traversal: str) -> Optional[TreeNode]:
        n = len(traversal)
        if n == 0: return None
        i, j = 0, 0
        def getNumber(i):
            num = 0
            while i < n and traversal[i].isdigit():
                num = num * 10 + int(traversal[i])
                i += 1
            return num, i

        def constructTree(depth):
            nonlocal i, j
            num, i = getNumber(i)
            node = TreeNode(num)
            for j in range(i, n):
                if traversal[j] != '-':
                    break
            else:
                return node
            # print(i, j)
            if j - i == depth:
                i = j
                node.left = constructTree(depth + 1)
            else:
                return node
            if j - i == depth:
                i = j
                node.right = constructTree(depth + 1)
            else:
                return node
            return node
        return constructTree(1)

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