Maximum Depth of Binary Tree

Easy Trees & BST Recursion Original on LeetCode

Maximum Depth of Binary Tree is a easy trees & bst problem solved with the recursion pattern. The best approach, recursive dfs, runs in O(n) time and O(h) space. Below are 2 approaches in Java, from level order (bfs) up.

Problem

Return the maximum depth of a binary tree: the number of nodes on the longest path from the root down to a leaf.

Examples

Example 1

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

Example 2

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

Constraints

The tree has 0 to 10^4 nodes.

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Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

Approach	Time	Space
Level order (BFS)	`O(n)`	`O(w)`
Recursive DFS	`O(n)`	`O(h)`

1Level order (BFS)

TimeO(n)

SpaceO(w)w = maximum width of the tree.

Count the number of levels with a queue.

Process the queue level by level; depth++ per level.

Java

class Solution {
    public int maxDepth(TreeNode root) {
        if (root == null) return 0;
        Queue<TreeNode> q = new ArrayDeque<>();
        q.add(root);
        int depth = 0;
        while (!q.isEmpty()) {
            depth++;
            for (int i = q.size(); i > 0; i--) {
                TreeNode n = q.poll();
                if (n.left != null) q.add(n.left);
                if (n.right != null) q.add(n.right);
            }
        }
        return depth;
    }
}

2Recursive DFS

TimeO(n)

SpaceO(h)

An empty tree has depth 0. Any other node is one deeper than the deeper of its two subtrees.

if root == null return 0.
return 1 + max(maxDepth(left), maxDepth(right)).

Java

class Solution {
    public int maxDepth(TreeNode root) {
        if (root == null) return 0;
        return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
    }
}

Edge cases to test

Empty tree (0)
Skewed tree (depth n)

Hints

Hint 1

depth(node) = 1 + max(depth(left), depth(right)).

FAQ

What is the best time complexity for Maximum Depth of Binary Tree?

Recursive DFS runs in O(n) time and O(h) extra space.

Which pattern does Maximum Depth of Binary Tree use?

It is a trees & bst problem that uses the recursion pattern. Other problems with the same pattern: Binary Tree Inorder Traversal (Recursive), Binary Tree Preorder Traversal (Recursive), Binary Tree Postorder Traversal (Recursive).

Is there a brute force solution for Maximum Depth of Binary Tree?

Yes. Level order (BFS) takes O(n) time and O(w) space. Count the number of levels with a queue.

Which edge cases should I test for Maximum Depth of Binary Tree?

Empty tree (0); Skewed tree (depth n).