<p>Given the <code>root</code> of a binary search tree, return <em>a <strong>balanced</strong> binary search tree with the same node values</em>. If there is more than one answer, return <strong>any of them</strong>.</p>

<p>A binary search tree is <strong>balanced</strong> if the depth of the two subtrees of every node never differs by more than <code>1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/balance1-tree.jpg" style="width: 500px; height: 319px;" />
<pre>
<strong>Input:</strong> root = [1,null,2,null,3,null,4,null,null]
<strong>Output:</strong> [2,1,3,null,null,null,4]
<b>Explanation:</b> This is not the only correct answer, [3,1,4,null,2] is also correct.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/balanced2-tree.jpg" style="width: 224px; height: 145px;" />
<pre>
<strong>Input:</strong> root = [2,1,3]
<strong>Output:</strong> [2,1,3]
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def _inorderTraversal(self, root: TreeNode) -> Iterator[TreeNode]:

        if root is None:
            return 
            
        yield from self._inorderTraversal(root.left)
        yield root
        yield from self._inorderTraversal(root.right)

    def balanceBST(self, root: TreeNode) -> TreeNode:
        values = list(self._inorderTraversal(root))

        def _balanceBST(
            start: int,
            stop: int,
        ):
            if start > stop:
                return None

            middle =((stop + start) // 2)
            node = values[middle]
            node.left = _balanceBST(start, middle - 1)
            node.right = _balanceBST(middle + 1, stop)

            return node

        return _balanceBST(0, len(values) - 1)  # type: ignore

20500