1  import javafx.application.Application;
  2  import javafx.geometry.Pos;
  3  import javafx.stage.Stage;
  4  import javafx.scene.Scene;
  5  import javafx.scene.control.Label;
  6  import javafx.scene.image.Image;
  7  import javafx.scene.image.ImageView;
  8  import javafx.scene.layout.GridPane;
  9  
 10  public class EightQueens extends Application {
 11    public static final int SIZE = 8; // The size of the chess board
 12    // queens are placed at (i, queens[i])
 13    // -1 indicates that no queen is currently placed in the ith row
 14    // Initially, place a queen at (0, 0) in the 0th row
 15    private int[] queens = {-1, -1, -1, -1, -1, -1, -1, -1}; 
 16  
 17    @Override // Override the start method in the Application class
 18    public void start(Stage primaryStage) {
 19      search(); // Search for a solution 
 20          
 21      // Display chess board
 22      GridPane chessBoard = new GridPane();
 23      chessBoard.setAlignment(Pos.CENTER);
 24      Label[][] labels = new Label[SIZE][SIZE];
 25      for (int i = 0; i < SIZE; i++)
 26        for (int j = 0; j < SIZE; j++) {
 27          chessBoard.add(labels[i][j] = new Label(), j, i);
 28          labels[i][j].setStyle("-fx-border-color: black");
 29          labels[i][j].setPrefSize(55, 55);
 30        }
 31  
 32      // Display queens
 33      Image image = new Image("image/queen.jpg");
 34      for (int i = 0; i < SIZE; i++)
 35        labels[i][queens[i]].setGraphic(new ImageView(image));
 36        
 37      // Create a scene and place it in the stage
 38      Scene scene = new Scene(chessBoard, 55 * SIZE, 55 * SIZE);
 39      primaryStage.setTitle("EightQueens"); // Set the stage title
 40      primaryStage.setScene(scene); // Place the scene in the stage
 41      primaryStage.show(); // Display the stage
 42    }
 43  
 44    /** Search for a solution */
 45    private boolean search() {
 46      // k is the current row to be considered
 47      // We are looking for a position in the kth row to place a queen
 48      int k = 0;
 49      while (k >= 0 && k < SIZE) {
 50        // Find a position to place a queen in the kth row
 51        int j = findPosition(k);
 52        if (j < 0) {
 53          queens[k] = -1;
 54          k--; // Backtrack to the previous row
 55        } else {
 56          queens[k] = j;
 57          k++;
 58        }
 59      }
 60      
 61      if (k == -1)
 62        return false; // No solution
 63      else
 64        return true; // A solution is found
 65    }
 66  
 67    public int findPosition(int k) {
 68      int start = queens[k] + 1; // Search for a new placement
 69  
 70      for (int j = start; j < SIZE; j++) {
 71        if (isValid(k, j))
 72          return j; // (k, j) is the place to put the queen now
 73      }
 74  
 75      return -1;
 76    }
 77    
 78    /** Return true if a queen can be placed at (row, column) */
 79    public boolean isValid(int row, int column) {
 80      for (int i = 1; i <= row; i++)
 81        if (queens[row - i] == column // Check column
 82          || queens[row - i] == column - i // Check upleft diagonal
 83          || queens[row - i] == column + i) // Check upright diagonal
 84          return false; // There is a conflict
 85      return true; // No conflict
 86    }
 87  
 88    /**
 89     * The main method is only needed for the IDE with limited
 90     * JavaFX support. Not needed for running from the command line.
 91     */
 92    public static void main(String[] args) {
 93      launch(args);
 94    }
 95  }