Given a binary tree, write a function to get the maximum width of the given tree. The width of a tree is the maximum width among all levels. The binary tree has the same structure as a full binary tree, but some nodes are null. 
The width of one level is defined as the length between the end-nodes (the leftmost and right most non-null nodes in the level, where the null nodes between the end-nodes are also counted into the length calculation.
Example 1:
Input: 
           1
         /   \
        3     2
       / \     \  
      5   3     9 
Output: 4
Explanation: The maximum width existing in the third level with the length 4 (5,3,null,9).
Example 2:
Input: 
          1
         /  
        3    
       / \       
      5   3     
Output: 2
Explanation: The maximum width existing in the third level with the length 2 (5,3).
Example 3:
Input: 
          1
         / \
        3   2 
       /        
      5      
Output: 2
Explanation: The maximum width existing in the second level with the length 2 (3,2).
Example 4:
Input: 
          1
         / \
        3   2
       /     \  
      5       9 
     /         \
    6           7
Output: 8
Explanation:The maximum width existing in the fourth level with the length 8 (6,null,null,null,null,null,null,7).
Note:
Answer will in the range of 32-bit signed integer.
class Solution:
     def widthOfBinaryTree(self, root):
         """
         :type root: TreeNode
         :rtype: int
         """
         
         table = {}
         
         stack = [(root, [])]
         while stack:
             node, path = stack.pop()
             if not node:
                 continue
             
             table.setdefault(len(path), []).append(path)
             
             stack.append((node.left, path + ['0']))
             stack.append((node.right, path + ['1']))
             
         
         maxwidth = 0
         for n in sorted(table):
             paths = table[n]
             if len(paths) < 1:
                 continue
             if len(paths) == 1:
                 maxwidth = max(1, maxwidth)
                 continue
                 
             values = list(map(lambda p: int(''.join(p), 2), paths))
             width = max(values) - min(values) + 1
             
             maxwidth = max(maxwidth, width)
             
         return maxwidth
class Solution:
     def widthOfBinaryTree(self, root):
         """
         :type root: TreeNode
         :rtype: int
         """
         
         table = {}
         
         stack = [(root, [])]
         while stack:
             node, path = stack.pop()
             if not node:
                 continue
             
             table.setdefault(len(path), []).append(path)
             
             stack.append((node.left, path + ['0']))
             stack.append((node.right, path + ['1']))
             
         
         maxwidth = 0
         for n in sorted(table):
             paths = table[n]
             if len(paths) < 1:
                 continue
             if len(paths) == 1:
                 maxwidth = max(1, maxwidth)
                 continue
                 
             values = list(map(lambda p: int(''.join(p), 2), paths))
             width = max(values) - min(values) + 1
             
             maxwidth = max(maxwidth, width)
             
         return maxwidth