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].

宽度搜索获取每层
[[1],                                     0
[2],[3],
[4],[5],[6],[7]]

需要变成的目标
[["", "", "", "1", "", "", ""],
 ["", "2", "", "", "", "3", ""],
 ["4", "", "5", "", "6", "", "7"]]

index变化
0 -> 3
0, 1 -> 1, 5
0, 1, 2, 3 -> 0, 2, 4, 6 


规律
假设总depth = n， 当前depth 为 i, res = n-i

首元素 index = 2**(res) -1
其他元素 = 首元素index + 2**(res+1) * index

通项： new_index = 2**(res) - 1 + 2**(res+1) * index

可以可以利用numpy的特性简化计算

import numpy as np

class Solution(object):
    def printTree(self, root):
        """imporpt
        :type root: TreeNode
        :rtype: List[List[str]]
        """
        def extend_layer(final_depth, current_depth, layer):
            res_depth = final_depth - current_depth
            final_length = 2 ** final_depth - 1
            index = np.array(range(len(layer)))

            new_index = 2 ** res_depth - 1 + 2 ** (res_depth + 1) * index
            extended_layer = [""] * final_length

            for i in range(len(layer)):
                extended_layer[new_index[i]] = layer[i]

            return extended_layer

        result = [[str(root.val)]]
        now_layer = [root]
        depth = 1
        while True:
            next_layer = []
            for node in now_layer:
                if not node:
                    next_layer.append(None)
                    next_layer.append(None)
                    continue

                next_layer.append(node.left)
                next_layer.append(node.right)

            next_layer_val = [str(node.val) if node else "" for node in next_layer]

            if all([val is '' for val in next_layer_val]):
                break

            result.append(next_layer_val)
            now_layer = next_layer
            depth += 1
        
        print(result)
        extended_ret = []
        for i, line in enumerate(result):
            current_depth = i + 1
            extended_ret.append(extend_layer(depth, current_depth, line))
        return extended_ret

public class Solution {
    public List<List<String>> printTree(TreeNode root) {
        int height = getHeight(root);
        String[][] res = new String[height][(1 << height) - 1];
        for(String[] arr:res)
            Arrays.fill(arr,"");
        List<List<String>> ans = new ArrayList<>();
        fill(res, root, 0, 0, res[0].length);
        for(String[] arr:res)
            ans.add(Arrays.asList(arr));
        return ans;
    }
    public void fill(String[][] res, TreeNode root, int i, int l, int r) {
        if (root == null)
            return;
        res[i][(l + r) / 2] = "" + root.val;
        fill(res, root.left, i + 1, l, (l + r) / 2);
        fill(res, root.right, i + 1, (l + r + 1) / 2, r);
    }
    public int getHeight(TreeNode root) {
        if (root == null)
            return 0;
        return 1 + Math.max(getHeight(root.left), getHeight(root.right));
    }
}

def test():
    print('hello')
    with open('test','w') as f:
        f.write('hello')

import cProfile
cProfile.run('test()')

$ python haha.py 
hello
         5 function calls in 0.000 seconds

   Ordered by: standard name

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.000    0.000    0.000    0.000 <string>:1(<module>)
        1    0.000    0.000    0.000    0.000 haha.py:1(test)
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
        1    0.000    0.000    0.000    0.000 {method 'write' of 'file' objects}
        1    0.000    0.000    0.000    0.000 {open}