606 Construct String from Binary Tree

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.

Complexity: O(n) time and space

The Idea: The first thing to recognize is that the numbers follow a preorder traversal - so the creative bit comes where the parenthesis are placed. Every non-null leaf and subtree are encapsulated with parenthesis. We also make sure to be one step ahead as to avoid null leafs.

# 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 ""

        str_val = str(t.val)
        if t.left:
            str_val += "(" + self.tree2str(t.left) + ")"
        elif t.right:
            str_val += "()"
        if t.right:
            str_val += "(" + self.tree2str(t.right) + ")"

        return str_val