51.N Queen.cpp

class Solution {
  public:
    bool isSafe1(int row, int col, vector < string > board, int n) {
      // check upper element
      int duprow = row;
      int dupcol = col;
      
      //check upper left diagonal
      while (row >= 0 && col >= 0) {
        if (board[row][col] == 'Q')
          return false;
        row--;
        col--;
      }

      col = dupcol;
      row = duprow;
      //check left col on the same row
      while (col >= 0) {
        if (board[row][col] == 'Q')
          return false;
        col--;
      }

      row = duprow;
      col = dupcol;
      //check lower left diagonal
      while (row < n && col >= 0) {
        if (board[row][col] == 'Q')
          return false;
        row++;
        col--;
      }
      return true;
    }

  public:
    void solve(int col, vector < string > & board, vector < vector < string >> & ans, int n)     {
      if (col == n) {
        ans.push_back(board);
        return;
      }
      for (int row = 0; row < n; row++) {
        if (isSafe1(row, col, board, n)) {
          board[row][col] = 'Q';
          solve(col + 1, board, ans, n);
          board[row][col] = '.';
        }
      }
    }

  public:
    vector < vector < string >> solveNQueens(int n) {
      vector < vector < string >> ans;
      vector < string > board(n, string(n,'.'));
      solve(0, board, ans, n);
      return ans;
    }
};