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655. 输出二叉树

English Version

题目描述

在一个 m*n 的二维字符串数组中输出二叉树，并遵守以下规则：

  1. 行数 m 应当等于给定二叉树的高度。
  2. 列数 n 应当总是奇数。
  3. 根节点的值（以字符串格式给出）应当放在可放置的第一行正中间。根节点所在的行与列会将剩余空间划分为两部分（左下部分和右下部分）。你应该将左子树输出在左下部分，右子树输出在右下部分。左下和右下部分应当有相同的大小。即使一个子树为空而另一个非空，你不需要为空的子树输出任何东西，但仍需要为另一个子树留出足够的空间。然而，如果两个子树都为空则不需要为它们留出任何空间。
  4. 每个未使用的空间应包含一个空的字符串""。
  5. 使用相同的规则输出子树。

示例 1:

输入:
     1
    /
   2
输出:
[["", "1", ""],
 ["2", "", ""]]

示例 2:

输入:
     1
    / \
   2   3
    \
     4
输出:
[["", "", "", "1", "", "", ""],
 ["", "2", "", "", "", "3", ""],
 ["", "", "4", "", "", "", ""]]

示例 3:

输入:
      1
     / \
    2   5
   / 
  3 
 / 
4 
输出:
[["",  "",  "", "",  "", "", "", "1", "",  "",  "",  "",  "", "", ""]
 ["",  "",  "", "2", "", "", "", "",  "",  "",  "",  "5", "", "", ""]
 ["",  "3", "", "",  "", "", "", "",  "",  "",  "",  "",  "", "", ""]
 ["4", "",  "", "",  "", "", "", "",  "",  "",  "",  "",  "", "", ""]]

注意: 二叉树的高度在范围 [1, 10] 中。

解法

中文题意不容易读懂，可以参考英文版本的题目描述。

先求二叉树的高度 h，然后根据 h 求得结果列表的行数和列数 m, n。

根据 m, n 初始化结果列表，然后 dfs 遍历二叉树，依次在每个位置填入二叉树节点值（字符串形式）即可。

Python3

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def printTree(self, root: TreeNode) -> List[List[str]]:
        def height(root):
            if root is None:
                return -1
            return 1 + max(height(root.left), height(root.right))

        def dfs(root, r, c):
            if root is None:
                return
            ans[r][c] = str(root.val)
            dfs(root.left, r + 1, c - 2 ** (h - r - 1))
            dfs(root.right, r + 1, c + 2 ** (h - r - 1))

        h = height(root)
        m, n = h + 1, 2 ** (h + 1) - 1
        ans = [[""] * n for _ in range(m)]
        dfs(root, 0, (n - 1) // 2)
        return ans

Java

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public List<List<String>> printTree(TreeNode root) {
        int h = height(root);
        int m = h + 1, n = (1 << (h + 1)) - 1;
        String[][] res = new String[m][n];
        for (int i = 0; i < m; ++i) {
            Arrays.fill(res[i], "");
        }
        dfs(root, res, h, 0, (n - 1) / 2);
        List<List<String>> ans = new ArrayList<>();
        for (String[] t : res) {
            ans.add(Arrays.asList(t));
        }
        return ans;
    }

    private void dfs(TreeNode root, String[][] res, int h, int r, int c) {
        if (root == null) {
            return;
        }
        res[r][c] = String.valueOf(root.val);
        dfs(root.left, res, h, r + 1, c - (1 << (h - r - 1)));
        dfs(root.right, res, h, r + 1, c + (1 << (h - r - 1)));
    }

    private int height(TreeNode root) {
        if (root == null) {
            return -1;
        }
        return 1 + Math.max(height(root.left), height(root.right));
    }
}

C++

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    vector<vector<string>> printTree(TreeNode* root) {
        int h = height(root);
        int m = h + 1, n = (1 << (h + 1)) - 1;
        vector<vector<string>> ans(m, vector<string>(n, ""));
        dfs(root, ans, h, 0, (n - 1) / 2);
        return ans;
    }

    void dfs(TreeNode* root, vector<vector<string>>& ans, int h, int r, int c) {
        if (!root) return;
        ans[r][c] = to_string(root->val);
        dfs(root->left, ans, h, r + 1, c - pow(2, h - r - 1));
        dfs(root->right, ans, h, r + 1, c + pow(2, h - r - 1));
    }

    int height(TreeNode* root) {
        if (!root) return -1;
        return 1 + max(height(root->left), height(root->right));
    }
};

Go

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func printTree(root *TreeNode) [][]string {
	var height func(root *TreeNode) int
	height = func(root *TreeNode) int {
		if root == nil {
			return -1
		}
		return 1 + max(height(root.Left), height(root.Right))
	}
	h := height(root)
	m, n := h+1, (1<<(h+1))-1
	ans := make([][]string, m)
	for i := range ans {
		ans[i] = make([]string, n)
		for j := range ans[i] {
			ans[i][j] = ""
		}
	}
	var dfs func(root *TreeNode, r, c int)
	dfs = func(root *TreeNode, r, c int) {
		if root == nil {
			return
		}
		ans[r][c] = strconv.Itoa(root.Val)
		dfs(root.Left, r+1, c-int(math.Pow(float64(2), float64(h-r-1))))
		dfs(root.Right, r+1, c+int(math.Pow(float64(2), float64(h-r-1))))
	}

	dfs(root, 0, (n-1)/2)
	return ans
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

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