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52. N-Queens II 👍

  • Time: $O(n \cdot n!)$
  • Space: $O(n \cdot n!)$
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class Solution {
 public:
  int totalNQueens(int n) {
    int ans = 0;
    dfs(n, 0, vector<bool>(n), vector<bool>(2 * n - 1), vector<bool>(2 * n - 1),
        ans);
    return ans;
  }

 private:
  void dfs(int n, int i, vector<bool>&& cols, vector<bool>&& diag1,
           vector<bool>&& diag2, int& ans) {
    if (i == n) {
      ++ans;
      return;
    }

    for (int j = 0; j < n; ++j) {
      if (cols[j] || diag1[i + j] || diag2[j - i + n - 1])
        continue;
      cols[j] = diag1[i + j] = diag2[j - i + n - 1] = true;
      dfs(n, i + 1, std::move(cols), std::move(diag1), std::move(diag2), ans);
      cols[j] = diag1[i + j] = diag2[j - i + n - 1] = false;
    }
  }
};

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class Solution {
  public int totalNQueens(int n) {
    dfs(n, 0, new boolean[n], new boolean[2 * n - 1], new boolean[2 * n - 1]);
    return ans;
  }

  private int ans = 0;

  private void dfs(int n, int i, boolean[] cols, boolean[] diag1, boolean[] diag2) {
    if (i == n) {
      ++ans;
      return;
    }

    for (int j = 0; j < cols.length; ++j) {
      if (cols[j] || diag1[i + j] || diag2[j - i + n - 1])
        continue;
      cols[j] = diag1[i + j] = diag2[j - i + n - 1] = true;
      dfs(n, i + 1, cols, diag1, diag2);
      cols[j] = diag1[i + j] = diag2[j - i + n - 1] = false;
    }
  }
}

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class Solution:
  def totalNQueens(self, n: int) -> int:
    ans = 0
    cols = [False] * n
    diag1 = [False] * (2 * n - 1)
    diag2 = [False] * (2 * n - 1)

    def dfs(i: int) -> None:
      nonlocal ans
      if i == n:
        ans += 1
        return

      for j in range(n):
        if cols[j] or diag1[i + j] or diag2[j - i + n - 1]:
          continue
        cols[j] = diag1[i + j] = diag2[j - i + n - 1] = True
        dfs(i + 1)
        cols[j] = diag1[i + j] = diag2[j - i + n - 1] = False

    dfs(0)
    return ans