[leetcode] 655. Print Binary Tree @ python

原題

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”, “”, “”, “”, “”, “”, “”, “”, “”, “”, “”, “”, “”, “”, “”]]

解法

觀察數組可得, 數組的長度是二叉樹的高度, 子數組的長度是2**h-1. 是以定義depth函數求二叉樹的高度, 并初始化res清單. 接下來是更新res的值, 使用遞歸, base case是當節點為空時, 傳回res. 然後每次遞歸根據左邊和右邊的index來求中間的index, 節點放在中間. 如此遞歸.

Time: O(h*h), h為樹的高度

Space: O(1)

代碼

class Solution:
    def printTree(self, root):
        """
        :type root: TreeNode
        :rtype: List[List[str]]
        """
        def height(root):
            if not root:
                return 0
            return 1 + max(height(root.left), height(root.right))
        
        def update(node, left, right, row, res):
            if not node:
                return 
            mid = (left + right)//2
            res[row][mid] = str(node.val)
            if node.left:
                update(node.left, left, mid-1, row+1, res)
            if node.right:
                update(node.right, mid+1, right, row+1, res)
                
        h = height(root)
        w = 2**h - 1
        res = [['']*w for i in range(h)]
        update(root, 0, w-1, 0, res)
        return res