Pascal's Triangle

[Timmy Williams]

Hello all.
Started to read the art and science of Java and completing chapter exercises, below is pascals triangle as graphics program. I wanted to use the For loops which create the pyramid in combinations method. For this to work 3 If statements are used. I'm wondering if there is a better method to altering the values of the For loops to get the same outcome. At the moment if the pyramid size is increased in size I would need to add more if statements. Any advice greatly appreciated.

import acm.program.*;
import acm.graphics.*;


public class CombinationsGraphics extends GraphicsProgram {
 /* Width of each brick in pixels */
private static final int BRICK_WIDTH = 60;

/* Height of each brick in pixels */
private static final int BRICK_HEIGHT = 24;

/* Number of bricks in the base of the pyramid */
private static final int BRICKS_IN_BASE = 8;
			
			
	public void run() {

/* build bricks across in a row*/		
		for( int row = 0; row < BRICKS_IN_BASE; row++ ) {	
			
/* reduce bricks as rows increase*/			
			int bricksLeft = BRICKS_IN_BASE - row;		
			
/*build columns of bricks*/			
			for( int col = 0; col < bricksLeft; col++ ) {
				
/* centre pyramid in centre of screen*/				
				int x = getWidth() / 2 - (bricksLeft * BRICK_WIDTH) / 2 + col * BRICK_WIDTH;
				
				int	y = getHeight() - BRICK_HEIGHT - row * BRICK_HEIGHT;
			   	
/*build Pyramid and add to canvas */	
				
				GRect brick = new GRect( x , y  , BRICK_WIDTH, BRICK_HEIGHT);
				add(brick);
				
 /*Change value of bricksLeft to -1 to correct second row showing 3
 */			
			
			int valueForN = bricksLeft -1;
			
/* Change value for col and row for combination value of int K,	
 */			int total = 0;
			if ((col == 1 && row <= 5) || (row < 5 && col + row == 6)) total = 1;
			if ((col == 2 && row <= 3) || (row < 3 && col + row == 5)) total = 2;
			if ((col == 3 && row <= 1) || (row < 1 && col + row == 4)) total = 3;
	
/* Add Glabel to Canvas 
 */
			GLabel label = new GLabel (""+ combinations(valueForN, total)); 
			   	add (label, x+25, y + 20);
			   
			}		
		}	
	}
	
	   private int combinations(int n,  int k) {		
			return factorial(n) / (factorial(k) * factorial(n - k));
			
		   }
	   
	   private int factorial(int n) {
		      int result = 1;
		      for (int i = 1; i <= n; i++) {
		    	  result *= i; 
	  }
		      return result;
		   }
   
	   
	 }

[Knute Snortum]

You are right to think that if you have to add more if statements as your triangle gets bigger then there is something wrong with your algorithm.

You way to tackle the problem is to think about how you would create a Pascal Triangle by hand, that is, with a pencil and paper.  Only then try to turn the algorithm into Java code.

So how would you do this by hand?

[Campbell Ritchie]

... and welcome to the Ranch

[Timmy Williams]

Thank you for the welcome, finally cracked it.

public class CombinationsGraphics extends GraphicsProgram {
	
 /* Width of each brick in pixels */
private static final int BRICK_WIDTH = 60;

/* Height of each brick in pixels */
private static final int BRICK_HEIGHT = 24;

/* Number of bricks in the base of the pyramid */
private static final int BRICKS_IN_BASE = 10;

			
	
	public void run() {
       int brickSize = getHeight() / BRICKS_IN_BASE;
       
/* build bricks across in a row*/		
		for( int row = 0; row <= BRICKS_IN_BASE; row++ ) {
			
/*build columns of bricks*/		
			
			for( int col = 0; col <= row; col++ ) {
				
/* centre pyramid in centre of screen*/	
				
				int x = getWidth () / 2 - (row * BRICK_WIDTH) / 2 + col * BRICK_WIDTH;
				int	y = brickSize + BRICK_HEIGHT + row * BRICK_HEIGHT;

				
/*build Pyramid and add to canvas */	
				
				GRect brick = new GRect(x , y , BRICK_WIDTH, BRICK_HEIGHT);
				add(brick);
				
/* Add Glabel to Canvas 
  */
			GLabel label = new GLabel (""+ combinations(row, col)); 
			   	add (label, x+25, y + 20);
 
			}		
		}	
	}
	
	   private int combinations(int n,  int k) {			   		
			return factorial(n) / (factorial(k) * factorial(n - k));
			
		   }
	   
	   private int factorial(int n) {
		      int result = 1;
		      for (int i = 1; i <= n; i++) {
		    	  result *= i; 
		    	  
	  }
		      return result;
		   }
	  
	   
	 }

[Piet Souris]

Well done!

Years ago I made a similar Triangle, with two differences: 1) I let Java do all the centering calculations, and I determined a Pascal value as the sum of the two values above. In case you are interested:

public class TimmyWilliams {
    private final int depth = 10;
    private final Dimension dimension = new Dimension(50, 20);
    private final Font font = new Font("Serif", Font.BOLD, 18);
    
    public static void main(String... args) {
        SwingUtilities.invokeLater(TimmyWilliams::new);
    }

    TimmyWilliams() {
        var pascal = createPascalsTriangle(depth);
        
        var panel = new JPanel(new GridLayout(0, 1));
        for (int row = 0; row < depth; row++) {
            var p = new JPanel(new FlowLayout(FlowLayout.CENTER));
            if (row % 2 == 0) {
                p.setBorder(BorderFactory.createLoweredBevelBorder());
                p.setBackground(Color.LIGHT_GRAY);
            }
            else p.setBackground(Color.LIGHT_GRAY.brighter());
            for (int col = 0; col < row + 1; col++) {
                p.add(getLabel(pascal[row][col], dimension, font));
            }
            panel.add(p);
        }
        
        var frame = new JFrame("Pascals Triangle");
        frame.setContentPane(panel);
        frame.pack();
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);
    }
    
    private static int[][] createPascalsTriangle(int depth) {
        int[][] values = new int[depth][];
        values[0] = new int[]{1};
        for (int row = 1; row < depth; row++) {
            values[row] = new int[row + 1];
            for (int col = 0; col < row + 1; col++) {
                if (col == 0 || col == row) values[row][col] = 1;
                else values[row][col] = values[row - 1][col - 1] + values[row - 1][col];
            }
        }
        return values;
    }
    
    private static JLabel getLabel(int n, Dimension size, Font font) {
        var label = new JLabel();
        label.setMinimumSize(size);
        label.setPreferredSize(size);
        label.setMaximumSize(size);
        label.setFont(font);
        label.setText("" + n);
        return label;
    }
}

[Timmy Williams]

Thank you for attaching the way you created Pascals triangle, this has made me realise I have so much more to learn as most of the imports required I have never heard of. Arrays are coming next I will spend time going through your code as this will help with future questions from the book.