104. Maximum Depth of Binary Tree

Easy

Problem 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.

Examples

Example 1:
Input: root = [3,9,20,null,null,15,7]
Output: 3

Example 2:
Input: root = [1,null,2]
Output: 2
Jump to Solution: Python Java C++ JavaScript C#

Python Solution


# 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
def maxDepth(root: Optional[TreeNode]) -> int:
    if not root:
        return 0
    
    # Recursively find the depth of left and right subtrees
    left_depth = maxDepth(root.left)
    right_depth = maxDepth(root.right)
    
    # Return the maximum depth plus 1 for current node
    return max(left_depth, right_depth) + 1

Java Solution


/**
 * 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;
        }
        
        // Recursively find the depth of left and right subtrees
        int leftDepth = maxDepth(root.left);
        int rightDepth = maxDepth(root.right);
        
        // Return the maximum depth plus 1 for current node
        return Math.max(leftDepth, rightDepth) + 1;
    }
}

C++ Solution


/**
 * 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;
        }
        
        // Recursively find the depth of left and right subtrees
        int leftDepth = maxDepth(root->left);
        int rightDepth = maxDepth(root->right);
        
        // Return the maximum depth plus 1 for current node
        return max(leftDepth, rightDepth) + 1;
    }
};

JavaScript Solution


/**
 * 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;
    }
    
    // Recursively find the depth of left and right subtrees
    const leftDepth = maxDepth(root.left);
    const rightDepth = maxDepth(root.right);
    
    // Return the maximum depth plus 1 for current node
    return Math.max(leftDepth, rightDepth) + 1;
};

C# Solution


/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left;
 *     public TreeNode right;
 *     public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
public class Solution {
    public int MaxDepth(TreeNode root) {
        if (root == null) {
            return 0;
        }
        
        // Recursively find the depth of left and right subtrees
        int leftDepth = MaxDepth(root.left);
        int rightDepth = MaxDepth(root.right);
        
        // Return the maximum depth plus 1 for current node
        return Math.Max(leftDepth, rightDepth) + 1;
    }
}

Complexity Analysis

Solution Explanation

This solution uses recursive depth-first search:

Key points: