Queens.java

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

/******************************************************************************
 *  Compilation:  javac Queens.java
 *  Execution:    java Queens n
 *
 *  Solve the 8 queens problem using recursion and backtracing.
 *  Prints out all solutions.
 *
 *  Limitations: works for n <= 25, but slows down considerably
 *  for larger n.
 *
 *  Remark: this program implicitly enumerates all n^n possible
 *  placements (instead of n!), but the backtracing prunes off
 *  most of them, so it's not necessarily worth the extra
 *  complication of enumerating only permutations.
 *
 *
 *  % java Queens 3
 *
 *  % java Queens 4
 *  * Q * *
 *  * * * Q
 *  Q * * *
 *  * * Q *
 *
 *  * * Q *
 *  Q * * *
 *  * * * Q
 *  * Q * *
 *
 *  % java Queens 8
 *  Q * * * * * * *
 *  * * * * Q * * *
 *  * * * * * * * Q
 *  * * * * * Q * *
 *  * * Q * * * * *
 *  * * * * * * Q *
 *  * Q * * * * * *
 *  * * * Q * * * *
 *
 *  ...
 *
 ******************************************************************************/

public class Queens {

   /***************************************************************************
    * Return true if queen placement q[n] does not conflict with
    * other queens q[0] through q[n-1]
    ***************************************************************************/
    public static boolean isConsistent(int[] q, int n) {
        for (int i = 0; i < n; i++) {
            if (q[i] == q[n])             return false;   // same column
            if ((q[i] - q[n]) == (n - i)) return false;   // same major diagonal
            if ((q[n] - q[i]) == (n - i)) return false;   // same minor diagonal
        }
        return true;
    }

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


   /***************************************************************************
    *  Try all permutations using backtracking
    ***************************************************************************/
    public static void enumerate(int n) {
        int[] a = new int[n];
        enumerate(a, 0);
    }

    public static void enumerate(int[] q, int k) {
        int n = q.length;
        if (k == n) printQueens(q);
        else {
            for (int i = 0; i < n; i++) {
                q[k] = i;
                if (isConsistent(q, k)) enumerate(q, k+1);
            }
        }
    }


    public static void main(String[] args) {
        int n = Integer.parseInt(args[0]);
        enumerate(n);
    }

}