<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]:
        subtrees = {}
        nodes = {}
        parents = {}

        root = preorder[0]
        nodes[root] = TreeNode(val=root)
        parents[root] = None

        root_index_inorder = inorder.index(root)
        subtrees[root] = (inorder[0: root_index_inorder], inorder[root_index_inorder + 1: len(inorder)])

        curr = root

        for i in range(1, len(preorder)):
            node_to_add = preorder[i]
            left_subtree, right_subtree = subtrees[curr]
            while True:
                if node_to_add in left_subtree:
                    new_node = TreeNode(node_to_add)
                    nodes[curr].left = new_node
                    parents[node_to_add] = curr
                    nodes[node_to_add] = new_node

                    pivot = left_subtree.index(node_to_add)
                    subtrees[node_to_add] = (left_subtree[0: pivot], left_subtree[pivot + 1: len(left_subtree)])
                    curr = node_to_add
                    break
                elif node_to_add in right_subtree:
                    new_node = TreeNode(val=node_to_add)
                    nodes[curr].right = new_node
                    parents[node_to_add] = curr
                    nodes[node_to_add] = new_node

                    pivot = right_subtree.index(node_to_add)
                    subtrees[node_to_add] = (right_subtree[0: pivot], right_subtree[pivot + 1: len(right_subtree)])
                    curr = node_to_add
                    break
                else:
                    curr = parents[curr]
                    left_subtree, right_subtree = subtrees[curr]

        return nodes[root]
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