# 104. Maximum Depth of Binary Tree

## Description

Given the root of a binary tree, return its maximum depth.

A binary tree's maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Example 1:

Input: root = [3,9,20,null,null,15,7]
Output: 3


Example 2:

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


Constraints:

• The number of nodes in the tree is in the range [0, 104].
• -100 <= Node.val <= 100

## Solutions

Solution 1: Recursion

Recursively traverse the left and right subtrees, calculate the maximum depth of the left and right subtrees, and then take the maximum value plus $1$.

The time complexity is $O(n)$, where $n$ is the number of nodes in the binary tree. Each node is traversed only once in the recursion.

• /**
* 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 int maxDepth(TreeNode root) {
if (root == null) {
return 0;
}
int l = maxDepth(root.left);
int r = maxDepth(root.right);
return 1 + Math.max(l, r);
}
}

• /**
* 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:
int maxDepth(TreeNode* root) {
if (!root) return 0;
int l = maxDepth(root->left), r = maxDepth(root->right);
return 1 + max(l, r);
}
};

• # 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 maxDepth(self, root: TreeNode) -> int:
if root is None:
return 0
l, r = self.maxDepth(root.left), self.maxDepth(root.right)
return 1 + max(l, r)


• /**
* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/
func maxDepth(root *TreeNode) int {
if root == nil {
return 0
}
l, r := maxDepth(root.Left), maxDepth(root.Right)
return 1 + max(l, r)
}

• /**
* 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 maxDepth(root: TreeNode | null): number {
if (root === null) {
return 0;
}
return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
}


• /**
* Definition for a binary tree node.
* function TreeNode(val, left, right) {
*     this.val = (val===undefined ? 0 : val)
*     this.left = (left===undefined ? null : left)
*     this.right = (right===undefined ? null : right)
* }
*/
/**
* @param {TreeNode} root
* @return {number}
*/
var maxDepth = function (root) {
if (!root) return 0;
const l = maxDepth(root.left);
const r = maxDepth(root.right);
return 1 + Math.max(l, r);
};


• // 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 dfs(root: &Option<Rc<RefCell<TreeNode>>>) -> i32 {
if root.is_none() {
return 0;
}
let node = root.as_ref().unwrap().borrow();
1 + Self::dfs(&node.left).max(Self::dfs(&node.right))
}

pub fn max_depth(root: Option<Rc<RefCell<TreeNode>>>) -> i32 {
Self::dfs(&root)
}
}