104. Maximum Depth of Binary Tree

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.

Solution

Approach 1: Recursion.

Approach 2: Iteration.

Code (Python)

Approach 1:

    def maxDepth(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        # recursive -- DFS
        if not root:
            return 0
        return max(self.maxDepth(root.left), self.maxDepth(root.right)) + 1

Approach 2:

    def maxDepth(self, root):
        # iterative -- BFS
        if not root:
            return 0
        level = [root]
        depth = 0
        while level:
            depth += 1
            next_level = []
            for node in level:
                for child in (node.left, node.right):
                    if child:
                        next_level.append(child)
            level = next_level
        return depth

Code (C++)

Approach 1:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int maxDepth(TreeNode* root) {
        if (root == NULL) return 0;
        return 1 + std::max(maxDepth(root->left), maxDepth(root->right));
    }
};

Approach 2:

class Solution {
public:
    int maxDepth(TreeNode* root) {
        if (root == NULL) return 0;
        stack<pair<TreeNode*, int>> nodeStack;
        nodeStack.push(pair<TreeNode*, int>(root, 1));
        int max = 0;
        while (!nodeStack.empty())
        {
            TreeNode *node = nodeStack.top().first;
            int depth = nodeStack.top().second;
            nodeStack.pop();
            if (depth > max) max = depth;
            if (node->left != NULL)
                nodeStack.push(pair<TreeNode*, int>(node->left, depth+1));
            if (node->right != NULL)
                nodeStack.push(pair<TreeNode*, int>(node->right, depth+1));
        }
        return max;
    }
};