Serialize and Deserialize BST
<p>Serialization is converting a data structure or object into a sequence of bits so that it can be stored in a file or memory buffer, or transmitted across a network connection link to be reconstructed later in the same or another computer environment.</p>

<p>Design an algorithm to serialize and deserialize a <b>binary search tree</b>. There is no restriction on how your serialization/deserialization algorithm should work. You need to ensure that a binary search tree can be serialized to a string, and this string can be deserialized to the original tree structure.</p>

<p><b>The encoded string should be as compact as possible.</b></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> root = [2,1,3]
<strong>Output:</strong> [2,1,3]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> root = []
<strong>Output:</strong> []
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[0, 10<sup>4</sup>]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
	<li>The input tree is <strong>guaranteed</strong> to be a binary search tree.</li>
</ul>
Tree; Depth-First Search; Breadth-First Search; Design; Binary Search Tree; String; Binary Tree
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None


class Codec:
    def serialize(self, root: Optional[TreeNode]) -> str:
        """Encodes a tree to a single string."""

        def dfs(root: Optional[TreeNode]):
            if root is None:
                return
            nums.append(root.val)
            dfs(root.left)
            dfs(root.right)

        nums = []
        dfs(root)
        return " ".join(map(str, nums))

    def deserialize(self, data: str) -> Optional[TreeNode]:
        """Decodes your encoded data to tree."""

        def dfs(mi: int, mx: int) -> Optional[TreeNode]:
            nonlocal i
            if i == len(nums) or not mi <= nums[i] <= mx:
                return None
            x = nums[i]
            root = TreeNode(x)
            i += 1
            root.left = dfs(mi, x)
            root.right = dfs(x, mx)
            return root

        nums = list(map(int, data.split()))
        i = 0
        return dfs(-inf, inf)


# Your Codec object will be instantiated and called as such:
# Your Codec object will be instantiated and called as such:
# ser = Codec()
# deser = Codec()
# tree = ser.serialize(root)
# ans = deser.deserialize(tree)
# return ans
