package recursion;

public class NQueensII {
    private int count;
    
    public int totalNQueens(int n) {
        int[] positions = new int[n];
        this.count = 0;
        solve(positions, 0, n);
        return this.count;
    }
    
    private void solve(int[] positions, int row, int n) {
        if (row == n) {
            this.count++;
        } else {
            for (int i = 0; i < n; ++i) {
                if (isValid(positions, row, i)) {
                    positions[row] = i;
                    solve(positions, row + 1, n);
                }
            }
        }
    }
    
    private boolean isValid(int[] positions, int row, int candidate) {
        for (int i = 0; i < row; ++i) {
            if (positions[i] == candidate || Math.abs(i - row) == Math.abs(positions[i] - candidate))
                return false;
        }
        return true;
    }
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        NQueensII n = new NQueensII();
        System.out.println(n.totalNQueens(4));
    }

}