<p>Given two integer arrays <code>inorder</code> and <code>postorder</code> where <code>inorder</code> is the inorder traversal of a binary tree and <code>postorder</code> is the postorder traversal of the same tree, construct and return <em>the binary tree</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/19/tree.jpg" style="width: 277px; height: 302px;" />
<pre>
<strong>Input:</strong> inorder = [9,3,15,20,7], postorder = [9,15,7,20,3]
<strong>Output:</strong> [3,9,20,null,null,15,7]
</pre>

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

<pre>
<strong>Input:</strong> inorder = [-1], postorder = [-1]
<strong>Output:</strong> [-1]
</pre>

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

<ul>
	<li><code>1 &lt;= inorder.length &lt;= 3000</code></li>
	<li><code>postorder.length == inorder.length</code></li>
	<li><code>-3000 &lt;= inorder[i], postorder[i] &lt;= 3000</code></li>
	<li><code>inorder</code> and <code>postorder</code> consist of <strong>unique</strong> values.</li>
	<li>Each value of <code>postorder</code> also appears in <code>inorder</code>.</li>
	<li><code>inorder</code> is <strong>guaranteed</strong> to be the inorder traversal of the tree.</li>
	<li><code>postorder</code> is <strong>guaranteed</strong> to be the postorder traversal of the tree.</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 buildTree(self, inorder: List[int], postorder: List[int]) -> Optional[TreeNode]:
        # find mid
        # find left
        # find right
        n = len(inorder)

        if n == 1:
            return TreeNode(inorder[0])

        inorder_mapping = {inorder[i]: i for i in range(n)}

        def build(inorder_range, postorder_range):
            # inorder_range = [start, end]
            if (
                inorder_range[0] > inorder_range[1]
                or postorder_range[0] > postorder_range[1]
            ):
                return None

            root_index = postorder_range[1]
            root = TreeNode(postorder[root_index])

            mid = inorder_mapping[root.val]

            left_len = mid - inorder_range[0]
            left_pos_end = postorder_range[0] + left_len - 1

            right_len = inorder_range[1] - mid

            root.left = build(
                (inorder_range[0], mid - 1),
                (postorder_range[0], left_pos_end),
            )
            root.right = build(
                (mid + 1, inorder_range[1]), (left_pos_end + 1, postorder_range[1] - 1)
            )

            return root

        root = build((0, n - 1), (0, n - 1))
        return root

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