<p>Given the <code>root</code> of a binary tree, construct a <strong>0-indexed</strong> <code>m x n</code> string matrix <code>res</code> that represents a <strong>formatted layout</strong> of the tree. The formatted layout matrix should be constructed using the following rules:</p>

<ul>
	<li>The <strong>height</strong> of the tree is <code>height</code>&nbsp;and the number of rows <code>m</code> should be equal to <code>height + 1</code>.</li>
	<li>The number of columns <code>n</code> should be equal to <code>2<sup>height+1</sup> - 1</code>.</li>
	<li>Place the <strong>root node</strong> in the <strong>middle</strong> of the <strong>top row</strong> (more formally, at location <code>res[0][(n-1)/2]</code>).</li>
	<li>For each node that has been placed in the matrix at position <code>res[r][c]</code>, place its <strong>left child</strong> at <code>res[r+1][c-2<sup>height-r-1</sup>]</code> and its <strong>right child</strong> at <code>res[r+1][c+2<sup>height-r-1</sup>]</code>.</li>
	<li>Continue this process until all the nodes in the tree have been placed.</li>
	<li>Any empty cells should contain the empty string <code>&quot;&quot;</code>.</li>
</ul>

<p>Return <em>the constructed matrix </em><code>res</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/03/print1-tree.jpg" style="width: 141px; height: 181px;" />
<pre>
<strong>Input:</strong> root = [1,2]
<strong>Output:</strong> 
[[&quot;&quot;,&quot;1&quot;,&quot;&quot;],
&nbsp;[&quot;2&quot;,&quot;&quot;,&quot;&quot;]]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/03/print2-tree.jpg" style="width: 207px; height: 302px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,null,4]
<strong>Output:</strong> 
[[&quot;&quot;,&quot;&quot;,&quot;&quot;,&quot;1&quot;,&quot;&quot;,&quot;&quot;,&quot;&quot;],
&nbsp;[&quot;&quot;,&quot;2&quot;,&quot;&quot;,&quot;&quot;,&quot;&quot;,&quot;3&quot;,&quot;&quot;],
&nbsp;[&quot;&quot;,&quot;&quot;,&quot;4&quot;,&quot;&quot;,&quot;&quot;,&quot;&quot;,&quot;&quot;]]
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 2<sup>10</sup>]</code>.</li>
	<li><code>-99 &lt;= Node.val &lt;= 99</code></li>
	<li>The depth of the tree will be in the range <code>[1, 10]</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 getDepth(self, node: Optional[TreeNode], depth: int) -> int:
        if not node or (not node.right and not node.left):
            return depth
        left = self.getDepth(node.left, depth + 1)
        right = self.getDepth(node.right, depth + 1)
        return max(left, right)

    def print_tree_recurse(self, queue: List[int], max_depth: int, curr_depth: int) -> List[Optional[List[str]]]:
        if curr_depth <= max_depth:
            new_queue = []
            line = []
            for entry in queue:
                if entry == None:
                    new_queue += [None, None]
                else:
                    new_queue += [entry.left, entry.right]
                line += (
                    [""] * (2 ** (max_depth - curr_depth) - 1)  + 
                    ["" if not entry else str(entry.val)] + 
                    [""] * (2 ** (max_depth - curr_depth) - 1) + [""]
                )
            
            return [line[:-1]] + self.print_tree_recurse(new_queue, max_depth, curr_depth + 1)
        return []


    def printTree(self, root: Optional[TreeNode]) -> List[List[str]]:
        max_depth = self.getDepth(root, 0)
        return self.print_tree_recurse([root], max_depth, 0)

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