# 655. Print Binary Tree

## Description

Given the root of a binary tree, construct a 0-indexed m x n string matrix res that represents a formatted layout of the tree. The formatted layout matrix should be constructed using the following rules:

• The height of the tree is height and the number of rows m should be equal to height + 1.
• The number of columns n should be equal to 2height+1 - 1.
• Place the root node in the middle of the top row (more formally, at location res[0][(n-1)/2]).
• For each node that has been placed in the matrix at position res[r][c], place its left child at res[r+1][c-2height-r-1] and its right child at res[r+1][c+2height-r-1].
• Continue this process until all the nodes in the tree have been placed.
• Any empty cells should contain the empty string "".

Return the constructed matrix res.

Example 1:

Input: root = [1,2]
Output:
[["","1",""],
["2","",""]]


Example 2:

Input: root = [1,2,3,null,4]
Output:
[["","","","1","","",""],
["","2","","","","3",""],
["","","4","","","",""]]


Constraints:

• The number of nodes in the tree is in the range [1, 210].
• -99 <= Node.val <= 99
• The depth of the tree will be in the range [1, 10].

## Solutions

• /**
* 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) {
}
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));
}
}

• /**
* 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));
}
};

• # 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: Optional[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


• /**
* 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
}

• /**
* Definition for a binary tree node.
* class TreeNode {
*     val: number
*     left: TreeNode | null
*     right: TreeNode | null
*     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
*         this.val = (val===undefined ? 0 : val)
*         this.left = (left===undefined ? null : left)
*         this.right = (right===undefined ? null : right)
*     }
* }
*/

function printTree(root: TreeNode | null): string[][] {
const getHeight = (root: TreeNode | null, h: number) => {
if (root == null) {
return h - 1;
}
return Math.max(getHeight(root.left, h + 1), getHeight(root.right, h + 1));
};

const height = getHeight(root, 0);
const m = height + 1;
const n = 2 ** (height + 1) - 1;
const res: string[][] = Array.from({ length: m }, () => new Array(n).fill(''));
const dfs = (root: TreeNode | null, i: number, j: number) => {
if (root === null) {
return;
}
const { val, left, right } = root;
res[i][j] = val + '';
dfs(left, i + 1, j - 2 ** (height - i - 1));
dfs(right, i + 1, j + 2 ** (height - i - 1));
};
dfs(root, 0, (n - 1) >>> 1);
return res;
}


• // Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
fn get_height(root: &Option<Rc<RefCell<TreeNode>>>, h: u32) -> u32 {
if let Some(node) = root {
let node = node.borrow();
return Self::get_height(&node.left, h + 1).max(Self::get_height(&node.right, h + 1));
}
h - 1
}

fn dfs(
root: &Option<Rc<RefCell<TreeNode>>>,
i: usize,
j: usize,
res: &mut Vec<Vec<String>>,
height: u32
) {
if root.is_none() {
return;
}
let node = root.as_ref().unwrap().borrow();
res[i][j] = node.val.to_string();
Self::dfs(&node.left, i + 1, j - (2usize).pow(height - (i as u32) - 1), res, height);
Self::dfs(&node.right, i + 1, j + (2usize).pow(height - (i as u32) - 1), res, height);
}

pub fn print_tree(root: Option<Rc<RefCell<TreeNode>>>) -> Vec<Vec<String>> {
let height = Self::get_height(&root, 0);
let m = (height + 1) as usize;
let n = (2usize).pow(height + 1) - 1;
let mut res = vec![vec![String::new(); n]; m];
Self::dfs(&root, 0, (n - 1) >> 1, &mut res, height);
res
}
}