[leetcode-52-N-Queens II]

Follow up for N-Queens problem.

Now, instead outputting board configurations, return the total number of distinct solutions.

思路：

典型8皇后，回溯法，验证是否能放皇后位置，判断同一列，左上45°和135°方向。

bool isValid(vector<string>& nQueens, int row, int col, int &n)
     {
         for (int i = 0; i < row;i++)
         {
             if (nQueens[i][col] == 'Q')return false;
         }
         for (int i = row - 1, j = col - 1; i >= 0&&j >= 0;i--,j--)
         {
             if (nQueens[i][j] == 'Q')return false;
         }
         for (int i = row - 1, j = col + 1; i >= 0&&j < n;i--,j++)
         {
             if (nQueens[i][j] == 'Q')return false;
         }
         return true;
     }
void totalNQueens(int& n, int row, vector<string>& nQueens, int& total)
     {
         if (row == n)
         {
             total += 1;
             return;
         }
         for (int col = 0; col < n;col++)
         {
             if (isValid(nQueens, row, col, n))
             {
                 nQueens[row][col] = 'Q';
                 totalNQueens(n, row + 1, nQueens, total);
                 nQueens[row][col] = '.';
             }
         }
     }
     int totalNQueens(int n)
     {
         vector<string> nQueens(n, string(n, '.'));
         int total = 0;
         totalNQueens(n, 0, nQueens, total);
         return total;
     }