Queens2.java

Below is the syntax highlighted version of Queens2.java from §2.3 Recursion.

/******************************************************************************
 *  Compilation:  javac Queens2.java
 *  Execution:    java Queens2 n
 *
 *  Solve the n queens problem by enumerating all n! permutations,
 *  pruning off useless branches. Solves n = 30 in a reasonable amount
 *  of time.
 *
 *  % java Queens2 3
 *
 *  % java Queens2 4
 *  * * Q *
 *  Q * * *
 *  * * * Q
 *  * Q * *
 *
 ******************************************************************************/


public class Queens2 {

   /***************************************************************************
    * Prints n-by-n placement of queens in ASCII.
    ***************************************************************************/
    public static void printQueens(int[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (a[i] == j) StdOut.print("Q ");
                else           StdOut.print("* ");
            }
            StdOut.println();
        }
        StdOut.println();
    }

   /***************************************************************************
    * Solve the n queens problem by brute force.
    ***************************************************************************/
    public static void swap(int[] a, int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    // try all n! permutations, but prune useless ones
    public static void enumerate(int[] a, boolean[] diag1, boolean[] diag2, int k) {
        int n = a.length;

        // found one, so print out and stop
        if (k == 0) {
            printQueens(a);
            // System.exit(0);
        }

        for (int i = 0; i < k; i++) {
            swap(a, i, k-1);
            int j = k-1;

            // if placement of new queen is ok, then enumerate
            if (!diag1[j + a[j]] && !diag2[n + j - a[j]]) {
                diag1[j + a[j]] = true;
                diag2[n + j - a[j]] = true;
                enumerate(a, diag1, diag2, k-1);
                diag1[j + a[j]] = false;
                diag2[n + j - a[j]] = false;
            }
            swap(a, i, k-1);
        }
    }


    public static void main(String[] args) {
        int n = Integer.parseInt(args[0]);
        int[] a         = new int[n];         // a[i] = row of queen in ith column
        boolean[] diag1 = new boolean[2*n];   // is ith top diagonal occupied?
        boolean[] diag2 = new boolean[2*n];   // is ith bottom diagonal occupied?
        for (int i = 0; i < n; i++)
            a[i] = i;
        enumerate(a, diag1, diag2, n);
    }

}