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.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Codec {
    private int i;
    private List<String> nums;
    private final int inf = 1 << 30;

    // Encodes a tree to a single string.
    public String serialize(TreeNode root) {
        nums = new ArrayList<>();
        dfs(root);
        return String.join(" ", nums);
    }

    // Decodes your encoded data to tree.
    public TreeNode deserialize(String data) {
        if (data == null || "".equals(data)) {
            return null;
        }
        i = 0;
        nums = Arrays.asList(data.split(" "));
        return dfs(-inf, inf);
    }

    private void dfs(TreeNode root) {
        if (root == null) {
            return;
        }
        nums.add(String.valueOf(root.val));
        dfs(root.left);
        dfs(root.right);
    }

    private TreeNode dfs(int mi, int mx) {
        if (i == nums.size()) {
            return null;
        }
        int x = Integer.parseInt(nums.get(i));
        if (x < mi || x > mx) {
            return null;
        }
        TreeNode root = new TreeNode(x);
        ++i;
        root.left = dfs(mi, x);
        root.right = dfs(x, mx);
        return root;
    }
}

// Your Codec object will be instantiated and called as such:
// Codec ser = new Codec();
// Codec deser = new Codec();
// String tree = ser.serialize(root);
// TreeNode ans = deser.deserialize(tree);
// return ans;