# LeetCode 104. Maximum Depth of Binary Tree

## Description

Given a binary tree, find its maximum depth.

The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Note: A leaf is a node with no children.

Example:

Given binary tree `[3,9,20,null,null,15,7]`,

```    3
/ \
9  20
/  \
15   7```

return its depth = 3.Accepted

## Explanation

List all scenarios of what a binary tree could be like:

1. when a binary tree is null, simply return maximum depth as 0
2. when a binary tree just have a root node, return maximum depth as 1
3. when a binary tree has a root node and child nodes, maximum depth would be the depth of the bigger side between left and right subtrees plus 1.

## Java Solution

```/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
class Solution {
public int maxDepth(TreeNode root) {
if (root == null) {
return 0;
}

int leftDepth = maxDepth(root.left);
int rightDepth = maxDepth(root.right);

return Math.max(leftDepth, rightDepth) + 1;
}
}```

## Python Solution

``````# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
def maxDepth(self, root: TreeNode) -> int:
if root == None:
return 0

left = self.maxDepth(root.left)
right = self.maxDepth(root.right)

max_depth = max(left, right) + 1

return max_depth
``````
• Time Complexity: O(N)
• Space Complexity: O(log(N))