# Time:  O(n)
# Space: O(h)

# You need to construct a string consists of parenthesis and integers from a binary tree with
# the preorder traversing way.
#
# The null node needs to be represented by empty parenthesis pair "()".
# And you need to omit all the empty parenthesis pairs that don't affect 
# the one-to-one mapping relationship between the string and the original binary tree.
#
# Example 1:
# Input: Binary tree: [1,2,3,4]
#       1
#      /   \
#     2     3
#   /    
#   4     
#
# Output: "1(2(4))(3)"
#
# Explanation: Originallay 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: Binary tree: [1,2,3,null,4]
#       1
#      /   \
#     2     3
#      \  
#       4 
#
# Output: "1(2()(4))(3)"
#
# Explanation: Almost the same as the first example, 
# except we can't omit the first parenthesis pair to break the one-to-one mapping relationship
# between the input and the output.


# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def tree2str(self, t):
        """
        :type t: TreeNode
        :rtype: str
        """
        if not t: return ""
        s = str(t.val)
        if t.left or t.right:
            s += "(" + self.tree2str(t.left) + ")"
        if t.right:
            s += "(" + self.tree2str(t.right) + ")"
        return s