Maximum Depth of Binary Tree

This is the most intuitive and common approach. It leverages the recursive nature of a tree. The maximum depth of a tree is defined as 1 (for the root) plus the maximum of the depths of its left and right subtrees.

• If the root node is null, return 0.
• Calculate the depth of the left subtree by making a recursive call: leftDepth = maxDepth(root.left).
• Calculate the depth of the right subtree by making a recursive call: rightDepth = maxDepth(root.right).
• Return 1 + max(leftDepth, rightDepth).

The algorithm works by defining a function that calculates the depth of a subtree rooted at a given node.

• Base Case: If the current node is null, it represents an empty tree or the end of a path, which has a depth of 0.
• Recursive Step: For a non-null node, we recursively call the function on its left and right children to find the depths of the left and right subtrees (leftDepth and rightDepth).
• The depth of the tree rooted at the current node is then 1 + Math.max(leftDepth, rightDepth). The +1 accounts for the current node itself. The process starts by calling this function with the root of the entire tree.

/**
 * 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 leftDepth = maxDepth(root.left);
        int rightDepth = maxDepth(root.right);
        
        return Math.max(leftDepth, rightDepth) + 1;
    }
}