You can use N-Queens I 's method counting for the result. But it wont pass the leetcode test.

Use bit operation will be much faster:

1 class Solution { 2 private: 3     int count, rec; 4 public: 5     void getQueen(int row, int ld, int rd) { 6         if (row == rec) { 7             count++; 8             return; 9         } else {10             int nonOccupied = rec & ~(row | rd | ld), occupy;11             while (nonOccupied != 0) {12                 occupy = nonOccupied & (~nonOccupied + 1);13                 nonOccupied -= occupy;14                 getQueen(row + occupy, (ld + occupy) << 1, (rd + occupy) >> 1);15             }16         }17     }18     int totalNQueens(int n) {19         count = 0;20         rec = (1 << n) - 1;21         getQueen(0, 0, 0);22         return count;23     }24 };