#include "s0216_combination_sum_iii.hpp"

void combinationSum3DFS(int k, int n, int begin, vector<int> &path, int sum,
                        vector<vector<int>> &result) {
  // 终止条件：高度达到上限且总和为 n
  if (path.size() == k && sum == n) {
    result.push_back(path);
    return;
  }

  // 开始迭代
  // 当总和 > n 时，剪枝
  for (int i = begin; i <= 9 && sum + i <= n; ++i) {
    sum += i;
    path.push_back(i);
    combinationSum3DFS(k, n, i + 1, path, sum, result);
    sum -= i;
    path.pop_back();
  }
}

vector<vector<int>> S0216::combinationSum3(int k, int n) {
  vector<int> path{};
  vector<vector<int>> result;
  combinationSum3DFS(k, n, 1, path, 0, result);
  return result;
}