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39. Combination Sum 👍

  • Time: $O(|\texttt{candidates}|^{\texttt{target}})$
  • Space: $O(\texttt{target})$
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class Solution {
 public:
  vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
    vector<vector<int>> ans;
    ranges::sort(candidates);
    dfs(candidates, 0, target, {}, ans);
    return ans;
  }

 private:
  void dfs(const vector<int>& A, int s, int target, vector<int>&& path,
           vector<vector<int>>& ans) {
    if (target < 0)
      return;
    if (target == 0) {
      ans.push_back(path);
      return;
    }

    for (int i = s; i < A.size(); ++i) {
      path.push_back(A[i]);
      dfs(A, i, target - A[i], std::move(path), ans);
      path.pop_back();
    }
  }
};

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class Solution {
  public List<List<Integer>> combinationSum(int[] candidates, int target) {
    List<List<Integer>> ans = new ArrayList<>();
    Arrays.sort(candidates);
    dfs(0, candidates, target, new ArrayList<>(), ans);
    return ans;
  }

  private void dfs(int s, int[] candidates, int target, List<Integer> path,
                   List<List<Integer>> ans) {
    if (target < 0)
      return;
    if (target == 0) {
      ans.add(new ArrayList<>(path));
      return;
    }

    for (int i = s; i < candidates.length; ++i) {
      path.add(candidates[i]);
      dfs(i, candidates, target - candidates[i], path, ans);
      path.remove(path.size() - 1);
    }
  }
}

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class Solution:
  def combinationSum(self, candidates: list[int],
                     target: int) -> list[list[int]]:
    ans = []

    def dfs(s: int, target: int, path: list[int]) -> None:
      if target < 0:
        return
      if target == 0:
        ans.append(path.clone())
        return

      for i in range(s, len(candidates)):
        path.append(candidates[i])
        dfs(i, target - candidates[i], path)
        path.pop()

    candidates.sort()
    dfs(0, target, [])
    return ans