public static void main(String[] args) {

NQueens2 nq = new NQueens2();

nq.totalNQueens(1);

}

public int totalNQueens(int n) {

ArrayList<Integer> cols = new ArrayList<Integer>();

return totalNQueensHelp(n, cols, 0);

}

public boolean isValid(ArrayList<Integer> cols, int col) {

for (int i = 0; i < cols.size(); i++) {

if (col == cols.get(i) || (cols.size() - i == Math.abs(col - cols.get(i)))) {

return false;

}

}

return true;

}

public int totalNQueensHelp(int n, ArrayList<Integer> cols, int total) {

if (cols.size() == n) {

// get a new solution.

return total + 1;

}

int newTotal = total;

for (int i = 0; i < cols.size(); i ++) {

if (!isValid(cols, i)) { // this is not a solution.

continue;

}

cols.add(i);

newTotal = totalNQueensHelp(n, cols, newTotal);

cols.remove(cols.size() - 1);

}

return newTotal;

}