题目描述：

LeetCode 655. Print Binary Tree

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

1. The row number m should be equal to the height of the given binary tree.
2. The column number n should always be an odd number.
3. 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.
4. Each unused space should contain an empty string "".
5. 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].

题目大意：

将二叉树输出成m * n二维数组

行数m等于二叉树的高度

列数n总是奇数

根节点位于首行正中间，将其下的空间分成左右两半。递归此过程。

解题思路：

递归（Recursion）

根据深度 + 偏移量确定节点在二维数组中的位置

设树的总深度为height，则二维数组宽度width = (1 << height) - 1

根节点的位置offset = width >> 1，深度depth = 1

左子树根的位置为offset - (1 + width >> depth + 1)

右子树根的位置为offset + (1 + width >> depth + 1)

Python代码：

# 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]]
        """
        self.height = self.findDepth(root)
        self.width = (1 << self.height) - 1
        self.dmap = [[""] * self.width for x in range(self.height)]
        self.traverse(root, 1, self.width >> 1)
        return self.dmap
    def findDepth(self, root):
        if not root: return 0
        return 1 + max(self.findDepth(root.left), self.findDepth(root.right))
    def traverse(self, root, depth, offset):
        if not root: return
        self.dmap[depth - 1][offset] = str(root.val)
        gap = 1 + self.width >> depth + 1
        self.traverse(root.left, depth + 1, offset - gap)
        self.traverse(root.right, depth + 1, offset + gap)

 

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