Given the root of a binary tree, construct a string consisting of parenthesis and integers from a binary tree with the preorder traversal way, and return it.

Omit all the empty parenthesis pairs that do not affect the one-to-one mapping relationship between the string and the original binary tree.

Example 1:

Input: root = [1,2,3,4]
Output: "1(2(4))(3)"
Explanation: Originally, it needs to be "1(2(4)())(3()())", but you need to omit all the unnecessary empty parenthesis pairs. And it will be "1(2(4))(3)"

Example 2:

Input: root = [1,2,3,null,4]
Output: "1(2()(4))(3)"
Explanation: Almost the same as the first example, except we cannot omit the first parenthesis pair to break the one-to-one mapping relationship between the input and the output.

Constraints:

• The number of nodes in the tree is in the range [1, 104].
• 1000 <= Node.val <= 1000

// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
// 
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
		// Option 타입은 열거형으로 "Rc<RefCell<TreeNode>>" 값의 존재 여부를 알려준다.
    pub fn tree2str(root: Option<Rc<RefCell<TreeNode>>>) -> String {
        match root {
						// root 에 값이 있다면, 값을 출력하고 자식 노드 순회
            Some(node) => {
                let node_ref = node.borrow();
                let mut result = node_ref.val.to_string();

                if node_ref.left.is_some() || node_ref.right.is_some() {
                    result.push('(');
                    result.push_str(&Solution::tree2str(node_ref.left.clone()));
                    result.push(')');

                    if node_ref.right.is_some() {
                        result.push('(');
                        result.push_str(&Solution::tree2str(node_ref.right.clone()));
                        result.push(')');
                    }
                }

                result
            }

						// root 가 비어 있다면, 빈 문자열 출력            
            None => String::new(),
        }
    }
}