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3437. Permutations III 👍

  • Time: $O(n \cdot n!)$
  • Space: $O(n \cdot n!)$
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class Solution {
 public:
  vector<vector<int>> permute(int n) {
    vector<vector<int>> ans;
    dfs(n, vector<bool>(n + 1), {}, ans);
    return ans;
  }

 private:
  void dfs(int n, vector<bool>&& used, vector<int>&& path,
           vector<vector<int>>& ans) {
    if (path.size() == n) {
      ans.push_back(path);
      return;
    }
    for (int num = 1; num <= n; ++num) {
      if (used[num])
        continue;
      if (!path.empty() && path.back() % 2 == num % 2)
        continue;
      used[num] = true;
      path.push_back(num);
      dfs(n, std::move(used), std::move(path), ans);
      path.pop_back();
      used[num] = false;
    }
  }
};

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class Solution {
  public int[][] permute(int n) {
    List<List<Integer>> ans = new ArrayList<>();
    dfs(n, new boolean[n + 1], new ArrayList<>(), ans);
    return ans.stream()
        .map(A -> A.stream().mapToInt(Integer::intValue).toArray())
        .toArray(int[][] ::new);
  }

  private void dfs(int n, boolean[] used, List<Integer> path, List<List<Integer>> ans) {
    if (path.size() == n) {
      ans.add(new ArrayList<>(path));
      return;
    }

    for (int num = 1; num <= n; ++num) {
      if (used[num])
        continue;
      if (!path.isEmpty() && path.get(path.size() - 1) % 2 == num % 2)
        continue;
      used[num] = true;
      path.add(num);
      dfs(n, used, path, ans);
      path.remove(path.size() - 1);
      used[num] = false;
    }
  }
}

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class Solution:
  def permute(self, n: int) -> list[list[int]]:
    ans = []
    used = [False] * (n + 1)

    def dfs(path: list[int]) -> None:
      if len(path) == n:
        ans.append(path.copy())
        return
      for num in range(1, n + 1):
        if used[num]:
          continue
        if path and path[-1] % 2 == num % 2:
          continue
        used[num] = True
        path.append(num)
        dfs(path)
        path.pop()
        used[num] = False

    dfs([])
    return ans