Question.java

package Q8_12_Eight_Queens;

import java.util.ArrayList;

public class Question {
	public static int GRID_SIZE = 8;
	
	/* Check if (row1, column1) is a valid spot for a queen by checking if there
	 * is a queen in the same column or diagonal. We don't need to check it for queens
	 * in the same row because the calling placeQueen only attempts to place one queen at
	 * a time. We know this row is empty. 
	 */
	public static boolean checkValid(Integer[] columns, int row1, int column1) {
		for (int row2 = 0; row2 < row1; row2++) {
			int column2 = columns[row2];
			/* Check if (row2, column2) invalidates (row1, column1) as a queen spot. */
			
			/* Check if rows have a queen in the same column */
			if (column1 == column2) { 
				return false;
			}
			
			/* Check diagonals: if the distance between the columns equals the distance
			 * between the rows, then they’re in the same diagonal. */
			int columnDistance = Math.abs(column2 - column1); 
			int rowDistance = row1 - row2; // row1 > row2, so no need to use absolute value
		    if (columnDistance == rowDistance) {
		    	return false;
		    }
		}
		return true;
	}
	
	public static void placeQueens(int row, Integer[] columns, ArrayList<Integer[]> results) {
		if (row == GRID_SIZE) { // Found valid placement
			results.add(columns.clone()); 
		} else {
			for (int col = 0; col < GRID_SIZE; col++) {			
				if (checkValid(columns, row, col)) {
					columns[row] = col;	// Place queen
					placeQueens(row + 1, columns, results);	
				}		
			}
		}
	}
	
	public static void clear(Integer[] columns) {
		for (int i = 0; i < GRID_SIZE; i++) {
			columns[i] = -1;
		}
	}
	
	public static void printBoard(Integer[] columns) {
        drawLine();
        for(int i = 0; i < GRID_SIZE; i++){
			System.out.print("|");
			for (int j = 0; j < GRID_SIZE; j++){
			    if (columns[i] == j) {
			    	System.out.print("Q|");
			    } else {
			    	System.out.print(" |");
			    }
			}
            System.out.print("\n");
            drawLine();
		}
		System.out.println("");
	}

    private static void drawLine() {
        StringBuilder line = new StringBuilder();
        for (int i=0;i<GRID_SIZE*2+1;i++)
            line.append('-');
        System.out.println(line.toString());
    }


	
	public static void printBoards(ArrayList<Integer[]> boards) {
		for (int i = 0; i < boards.size(); i++) {
			Integer[] board = boards.get(i);
			printBoard(board);
		}
	}
	   
	public static void main(String[] args) {
		ArrayList<Integer[]> results = new ArrayList<Integer[]>();
		Integer[] columns = new Integer[GRID_SIZE];
		clear(columns);
		placeQueens(0, columns, results);
		printBoards(results);
		System.out.println(results.size());
	}
}