Eight queen problem in Java

Here is a solution to eight queen puzzle in Java. You should note the following

• This is a brute force solution for NxN board
• The way we solve it is - first solve it for eight rook - i.e. first take care of horizontal and vertical lines only (the way a rook moves) and then omit the solutions having collision on diagonals 
• To solve the N-rook problem we generate all possible permutations of N (corresponding to the fact that one queen occupies one column) - so this solution is not at all going to scale
• The only way to learn anything in life is to do it yourself - even though this is a simple brute force solution or whatever - doing it gives me more pleasure than reading other's elegant solutions.

Next step - is probably to port this to javascript and generate the boards using HTML5 canvas. 

/*
 * 8-queen problem  using brute force searching
 * This solutions uses following strategies 
 *
 * 1 - fix one queen in one column and generate all
 * non-conflicting permutations - N! in total  
 * this is akin to solving the N-rook problem
 * 2- eliminate from N! permutations - that do not 
 * pass the additional diagonal test 
 * 
 * @author Rajeev Jha
 * @version 1.0
 *
 */

import java.util.Set;
import java.util.HashSet;

public class queen8 {

    private int[] columns ;
    private char[] colNames ;
    private int size ;
    private int solutions ;
    
    public queen8(int N) { 
        this.columns = new int[N] ; 
     for(int i=0 ; i < N ; i++) this.columns[i] = i+1 ;

        this.colNames = new char[N] ; 
        char a = 'A' ;
     for(int i=0 ; i < N ; i++) this.colNames[i] = (char) (a + i) ;

        this.size = N ;
        this.solutions = 0 ;
    }

    private void solve() {
        this.generate(this.size);
    }

    /* 
     * permutation generator using a backtracking algo
     * from http://www.cs.princeton.edu/~rs/talks/perms.pdf */

    private void generate(int N){
     int c ;
        /* factorial 1, 1! case,just one possibility,print that ..*/
        if ( N == 0 ) test_diagonal(); 
        //algorithm adjusted for zero-based indexes ..
        for(c = 0 ; c < N ; c++){
            swap(c,N-1);
            generate(N-1);
            swap(c,N-1);
        }
    
    } 

    /* swap for permutation */
    private void swap(int x, int y){
     int tmp = this.columns[x] ;
        this.columns[x] = this.columns[y] ;
        this.columns[y] = tmp ;
    
    }

    /* for position of a queen in a column (a permutation)
     * diagonal positions are given by moving 
     * one row up in next column and one row down in 
     * previous column */

    private void test_diagonal(){
        int x ;

     for(int i = 0 ; i < this.columns.length ; i++) {
            x = this.columns[i] ;
            for(int j = i+1, k = 1; j < this.columns.length ; j++, k++) {
                if((x+k) == this.columns[j]) return ;
                if((x-k) == this.columns[j]) return ;
            }
        }

        // diagonal test passed
        print_board();
    }

    private void print_board() {

     for(int i = 0 ; i < this.columns.length ; i++) {
            System.out.print(this.colNames[i]);
            System.out.print(this.columns[i] + " ");
        }

        System.out.println();
        this.solutions++ ;

    }

    private int getNumSolutions() {
        return this.solutions ;
    }
   
    public static void main(String[] args) throws Exception {
        queen8 board = new queen8(8);
        board.solve();
        System.out.println(" \n Total " + board.getNumSolutions() + " solutions " );

    }
}

And here are the solutions

rjha@mint13 ~/code/fun $ javac queen8.java 
rjha@mint13 ~/code/fun $ java -classpath . queen8 
A4 B2 C7 D3 E6 F8 G5 H1 
A5 B2 C4 D7 E3 F8 G6 H1 
A3 B5 C2 D8 E6 F4 G7 H1 
A3 B6 C4 D2 E8 F5 G7 H1 
A4 B7 C5 D3 E1 F6 G8 H2 
A5 B7 C1 D3 E8 F6 G4 H2 
A4 B6 C8 D3 E1 F7 G5 H2 
A3 B6 C8 D1 E4 F7 G5 H2 
A5 B3 C8 D4 E7 F1 G6 H2 
A5 B7 C4 D1 E3 F8 G6 H2 
A4 B1 C5 D8 E6 F3 G7 H2 
A3 B6 C4 D1 E8 F5 G7 H2 
A6 B4 C2 D8 E5 F7 G1 H3 
A5 B2 C6 D1 E7 F4 G8 H3 
A6 B4 C7 D1 E8 F2 G5 H3 
A1 B7 C4 D6 E8 F2 G5 H3 
A6 B2 C7 D1 E4 F8 G5 H3 
A6 B8 C2 D4 E1 F7 G5 H3 
A5 B8 C4 D1 E7 F2 G6 H3 
A4 B8 C1 D5 E7 F2 G6 H3 
A4 B7 C1 D8 E5 F2 G6 H3 
A4 B2 C7 D5 E1 F8 G6 H3 
A2 B5 C7 D4 E1 F8 G6 H3 
A5 B7 C1 D4 E2 F8 G6 H3 
A2 B7 C5 D8 E1 F4 G6 H3 
A1 B7 C5 D8 E2 F4 G6 H3 
A5 B1 C4 D6 E8 F2 G7 H3 
A6 B4 C1 D5 E8 F2 G7 H3 
A6 B3 C7 D2 E8 F5 G1 H4 
A2 B7 C3 D6 E8 F5 G1 H4 
A5 B1 C8 D6 E3 F7 G2 H4 
A1 B5 C8 D6 E3 F7 G2 H4 
A3 B6 C8 D1 E5 F7 G2 H4 
A7 B5 C3 D1 E6 F8 G2 H4 
A6 B3 C1 D7 E5 F8 G2 H4 
A7 B3 C1 D6 E8 F5 G2 H4 
A5 B7 C2 D6 E3 F1 G8 H4 
A3 B6 C2 D7 E5 F1 G8 H4 
A6 B2 C7 D1 E3 F5 G8 H4 
A7 B3 C8 D2 E5 F1 G6 H4 
A5 B3 C1 D7 E2 F8 G6 H4 
A2 B5 C7 D1 E3 F8 G6 H4 
A3 B6 C2 D5 E8 F1 G7 H4 
A6 B1 C5 D2 E8 F3 G7 H4 
A8 B3 C1 D6 E2 F5 G7 H4 
A2 B8 C6 D1 E3 F5 G7 H4 
A3 B7 C2 D8 E6 F4 G1 H5 
A6 B3 C7 D2 E4 F8 G1 H5 
A4 B2 C7 D3 E6 F8 G1 H5 
A1 B6 C8 D3 E7 F4 G2 H5 
A7 B1 C3 D8 E6 F4 G2 H5 
A6 B3 C7 D4 E1 F8 G2 H5 
A3 B8 C4 D7 E1 F6 G2 H5 
A7 B4 C2 D8 E6 F1 G3 H5 
A4 B6 C8 D2 E7 F1 G3 H5 
A2 B6 C1 D7 E4 F8 G3 H5 
A3 B6 C2 D7 E1 F4 G8 H5 
A7 B2 C6 D3 E1 F4 G8 H5 
A2 B4 C6 D8 E3 F1 G7 H5 
A3 B6 C8 D2 E4 F1 G7 H5 
A8 B4 C1 D3 E6 F2 G7 H5 
A4 B8 C1 D3 E6 F2 G7 H5 
A6 B3 C1 D8 E4 F2 G7 H5 
A2 B6 C8 D3 E1 F4 G7 H5 
A4 B7 C3 D8 E2 F5 G1 H6 
A4 B8 C5 D3 E1 F7 G2 H6 
A3 B5 C8 D4 E1 F7 G2 H6 
A7 B4 C2 D5 E8 F1 G3 H6 
A5 B7 C2 D4 E8 F1 G3 H6 
A4 B2 C8 D5 E7 F1 G3 H6 
A4 B1 C5 D8 E2 F7 G3 H6 
A5 B1 C8 D4 E2 F7 G3 H6 
A5 B2 C8 D1 E4 F7 G3 H6 
A8 B2 C4 D1 E7 F5 G3 H6 
A7 B2 C4 D1 E8 F5 G3 H6 
A3 B7 C2 D8 E5 F1 G4 H6 
A3 B1 C7 D5 E8 F2 G4 H6 
A8 B2 C5 D3 E1 F7 G4 H6 
A3 B5 C2 D8 E1 F7 G4 H6 
A3 B5 C7 D1 E4 F2 G8 H6 
A5 B2 C4 D6 E8 F3 G1 H7 
A6 B3 C5 D8 E1 F4 G2 H7 
A5 B8 C4 D1 E3 F6 G2 H7 
A4 B2 C5 D8 E6 F1 G3 H7 
A4 B6 C1 D5 E2 F8 G3 H7 
A5 B3 C1 D6 E8 F2 G4 H7 
A6 B3 C1 D8 E5 F2 G4 H7 
A4 B2 C8 D6 E1 F3 G5 H7 
A6 B3 C5 D7 E1 F4 G2 H8 
A6 B4 C7 D1 E3 F5 G2 H8 
A4 B7 C5 D2 E6 F1 G3 H8 
A5 B7 C2 D6 E3 F1 G4 H8 
 
 Total 92 solutions