/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    void bfs(vector<vector<int>>& levels,
             vector<const TreeNode*>& current_level,
             vector<const TreeNode*>& next_level) {
        if (current_level.empty()) {
            return;
        }
        levels.push_back({});
        vector<int>& level = levels.back();
        level.reserve(current_level.size());
        for (const TreeNode* node : current_level) {
            level.push_back(node->val);
            if (node->left) {
                next_level.push_back(node->left);
            }
            if (node->right) {
                next_level.push_back(node->right);
            }
        }
        current_level.clear(); // New next level.
        bfs(levels, next_level, current_level);
    }

    vector<vector<int>> levelOrder(TreeNode* root) {
        if (!root) return {};
        vector<vector<int>> levels;
        vector<const TreeNode*> current_level({root});
        vector<const TreeNode*> next_level;
        bfs(levels, current_level, next_level);
        return levels;
    }
};