Serialization is the process of 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.

Design an algorithm to serialize and deserialize a binary search tree. There is no restriction on how your serialization/deserialization algorithm should work. You just 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.

The encoded string should be as compact as possible.

Note: Do not use class member/global/static variables to store states. Your serialize and deserialize algorithms should be stateless.

serialize用preorder traverse，deserialize用queue作輔助，左右分別遞迴

serialize　　    -- time: O(n), space: O(height)

deserialize　　-- time: O(n), space: O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Codec {

    // Encodes a tree to a single string.
    public String serialize(TreeNode root) {
        
 
if(root == null) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        preorder(root, sb);
        return sb.toString();
    }
    
    public void preorder(TreeNode root, StringBuilder sb) {
        if(root == null) {
            return;
        }
        sb.append(root.val).append(" ");
        preorder(root.left, sb);
        preorder(root.right, sb);
    }

    // Decodes your encoded data to tree.
    public TreeNode deserialize(String data) {
        if(data == "") {
            return null;
        }
        String[] vals = data.split(" ");
        Queue<Integer> q = new LinkedList<>();
        for(String val : vals) {
            q.offer(Integer.parseInt(val));
        }
        return deserialize(q);
    }
    
    public TreeNode deserialize(Queue<Integer> q) {
        if(q.isEmpty()) {
            return null;
        }
        TreeNode root = new TreeNode(q.poll());
        Queue<Integer> smallerQ = new LinkedList<>();
        while(!q.isEmpty() && q.peek() < root.val) {
            smallerQ.offer(q.poll());
        }
        root.left = deserialize(smallerQ);
        root.right = deserialize(q);
        return root;
    }
}

// Your Codec object will be instantiated and called as such:
// Codec codec = new Codec();
// codec.deserialize(codec.serialize(root));