Maximum Depth of a Binary Tree - Explained Visually

Why it works

The recursion touches every node exactly once and does constant work per node, so it is O(n) time. Space is the call stack at its deepest - O(h) where h is tree height, O(log n) for balanced trees and O(n) for a degenerate chain.

The problem

Given the root of a binary tree, return its maximum depth. The maximum depth is the number of nodes along the longest path from the root down to the farthest leaf.

Hints

• Think recursively: the depth of a tree is 1 + max depth of its subtrees.
• Base case: if root is None, return 0.
• Alternatively, use BFS and count levels.

Test cases

Reference starter code

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def max_depth(root):
    # Recursive or iterative
    pass

# Build tree [3,9,20,None,None,15,7]
root = TreeNode(3)
root.left = TreeNode(9)
root.right = TreeNode(20)
root.right.left = TreeNode(15)
root.right.right = TreeNode(7)

print(max_depth(root))   # 3
print(max_depth(None))   # 0

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