private void helper(int r, boolean[] cols, boolean[] d1, boolean[] d2, int n, Map<String, Integer> res) {

if (r == n) {

res.put("num", res.get("num") + 1);

} else {

for (int c = 0; c < n; c++) {

int id1 = r - c + n, id2 = 2*n - r - c - 1;

if (!cols[c] && !d1[id1] && !d2[id2]) {

cols[c] = true; d1[id1] = true; d2[id2] = true;

helper(r+1, cols, d1, d2, n, res);

cols[c] = false; d1[id1] = false; d2[id2] = false;

}

}

}

}

public int totalNQueens(int n) {

Map<String, Integer> res = new HashMap<>();

res.put("num", 0);

helper(0, new boolean[n], new boolean[2*n], new boolean[2*n], n, res);

return res.get("num");

}

public static void main(String[] args) {

NQueensII52 nq = new NQueensII52();

System.out.println("---- 1");

System.out.println(nq.totalNQueens(1));

System.out.println("---- 4");

System.out.println(nq.totalNQueens(4));

System.out.println("---- 2");

System.out.println(nq.totalNQueens(2));

System.out.println("---- 3");

System.out.println(nq.totalNQueens(3));

System.out.println("---- 5");

System.out.println(nq.totalNQueens(5));

System.out.println("---- 6");

System.out.println(nq.totalNQueens(6));

}