<p>Given two integer arrays <code>preorder</code> and <code>inorder</code> where <code>preorder</code> is the preorder traversal of a binary tree and <code>inorder</code> is the inorder 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> preorder = [3,9,20,15,7], inorder = [9,3,15,20,7]
<strong>Output:</strong> [3,9,20,null,null,15,7]
</pre>

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

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

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

<ul>
	<li><code>1 &lt;= preorder.length &lt;= 3000</code></li>
	<li><code>inorder.length == preorder.length</code></li>
	<li><code>-3000 &lt;= preorder[i], inorder[i] &lt;= 3000</code></li>
	<li><code>preorder</code> and <code>inorder</code> consist of <strong>unique</strong> values.</li>
	<li>Each value of <code>inorder</code> also appears in <code>preorder</code>.</li>
	<li><code>preorder</code> is <strong>guaranteed</strong> to be the preorder traversal of the tree.</li>
	<li><code>inorder</code> is <strong>guaranteed</strong> to be the inorder 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, preorder: List[int], inorder: List[int]) -> Optional[TreeNode]:
        positions: Dict[int, int] = dict()
        for i, x in enumerate(inorder):
            positions[x] = i
        return self.buildTreeWithDict(preorder, inorder, positions, 0)

    def buildTreeWithDict(
        self,
        preorder: List[int],
        inorder: List[int],
        inorder_positions: Dict[int, int],
        shift: int,
    ) -> Optional[TreeNode]:
        if len(preorder) == 0:
            return None
        if len(preorder) == 1:
            return TreeNode(preorder[0])

        root_val = preorder[0]
        left_count = inorder_positions[root_val] - shift

        root = TreeNode(root_val)
        root.left = self.buildTreeWithDict(
            preorder[1 : 1 + left_count],
            inorder[:left_count],
            inorder_positions,
            shift,
        )
        root.right = self.buildTreeWithDict(
            preorder[left_count + 1 :],
            inorder[left_count + 1 :],
            inorder_positions,
            shift + left_count + 1,
        )
        return root

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