N-Queens (Count the Solutions)

/*
 * Problem : Count the N-Queens solutions.
 * Input   : One integer n.
 * Output  : The number of solutions.
 * Approach: One queen per row.
 * Time    : O(n!)
 * Space   : O(n)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
        // This method counts the ways to place queens in the rows row, row + 1, ..., n - 1.
        // The three arrays remember which columns and diagonals are already attacked.
        static int place(int row, int n, boolean[] columns, boolean[] diagonal1, boolean[] diagonal2) {
            // Step 1: All rows are filled. This is one valid solution.
            if (row == n) {
                return 1;
            }

            int count = 0;
            for (int column = 0; column < n; column++) {
                // Step 2: Cells on the same column or diagonal have the same index values. Skip attacked cells.
                if (columns[column] || diagonal1[row - column + n - 1] || diagonal2[row + column]) {
                    continue;
                }

                // Step 3: Place the queen, count the solutions for the next rows, then remove the queen.
                columns[column] = true;
                diagonal1[row - column + n - 1] = true;
                diagonal2[row + column] = true;
                count += place(row + 1, n, columns, diagonal1, diagonal2);
                columns[column] = false;
                diagonal1[row - column + n - 1] = false;
                diagonal2[row + column] = false;
            }
            return count;
        }

    // This method solves the task. It receives the input and returns the answer.
    static int solve(long n) {
        int size = (int) n;
        return place(0, size, new boolean[size], new boolean[2 * size], new boolean[2 * size]);
    }

    public static void main(String[] args) {
        long n = new Scanner(System.in).nextLong();
        System.out.println(solve(n));
    }
}