給一個二叉樹，要求進行列印，也就是在一個高度*寬度的矩陣裡面列印就好了，每個子樹的root列印在當前子區間的中間就好了

Print a binary tree in an m*n 2D string array following these rules:

The row number m should be equal to the height of the given binary tree.
The column number n should always be an odd number.
The root node's value (in string format) should be put
 
 in the exactly middle of the first row it can be put. The column and the row where the root node belongs will separate the rest space into two parts (left-bottom part and right-bottom part). You should print the left subtree in the left-bottom part and print the right subtree in the right-bottom part. The left-bottom part and
 
 the right-bottom part should have the same size. Even if one subtree is none while the other is not, you don't need to print anything for the none subtree but still need to leave the space as large as that for the other subtree. However, if two subtrees are none, then you don't need to leave space for
 
 both of them.
Each unused space should contain an empty string "".
Print the subtrees following the same rules.
Example 1:
Input:
     1
    /
   2
Output:
[["", "1", ""],
 ["2", "", ""]]
Example 2:
Input:
     1
    / \
   2   3
    \
     4
Output:
[["", "", "", "1", "", "", ""],
 ["", "2", "", "", "", "3", ""],
 ["", "", "4", "", "", "", ""]]
Example 3:
Input:
      1
     / \
    2   5
   / 
  3 
 / 
4 
Output:

[["",  "",  "", "",  "", "", "", "1", "",  "",  "",  "",  "", "", ""]
 ["",  "",  "", "2", "", "", "", "",  "",  "",  "",  "5", "", "", ""]
 ["",  "3", "", "",  "", "", "", "",  "",  "",  "",  "",  "", "", ""]
 ["4", "",  "", "",  "", "", "", "",  "",  "",  "",  "",  "", "", ""]]
Note: The height of binary tree is in the range of [1, 10].

總的來說就是，第一次dfs獲得樹的高度，第二次列印，注意根據當前層高計算相應的移動位置就可以了

# 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 printTree(self, root):
        """
        :type root: TreeNode
        :rtype: List[List[str]]
        """
        import math
        def dfs(root, h):
            if root:
                return max(dfs(root.left,h+1), dfs(root.right,h+1))
            else :
                return h
        height = dfs(root, 0)
        width = 2 ** height -1
        # 初始化
        res = [ ["" for j in range(width)] for i in range(height)]
        # dfs print
        def dfs_print(res,root,h,pos):
            if root:
                res[h - 1][pos] = '%d' % root.val
                dfs_print(res, root.left, h+1, pos-2**(height - h - 1))
                dfs_print(res, root.right, h+1, pos+2**(height - h - 1))
        dfs_print(res,root,1,width/2)
        return res