HELP: How can I integrate these patterns together?

I have a school project, I need to use two design patterns in my program. I decided to use the FACTORY and DECORATOR patterns like so:

- a string of numbers are sorted by choosing BubbleSort or QuickSort (factory pattern) from an interface window, decorated with 2 buttons (quick sort, bubble sort) and a label (where the result will be shown) - decorator pattern.

Here is the code for the window, the decorator pattern:


interface Window {

    public void draw(); // draws the Window

    public String getDescription(); // returns a description of the Window


public class decorator{

    public static void main(String[] args) {

        // create a decorated Window with horizontal and vertical scrollbars

        Window decoratedWindow = new HorizontalScrollBarDecorator (new VerticalScrollBarDecorator(new SimpleWindow()));

 		// Window decoratedWindow2 = new SimpleWindow();

        // print the Window's description

        System.out.println(decoratedWindow.getDescription());

        

    }

}


// abstract decorator class - note that it implements Window

abstract class WindowDecorator implements Window {

    protected Window decoratedWindow; // the Window being decorated

 

    public WindowDecorator (Window decoratedWindow) {

        this.decoratedWindow = decoratedWindow;

    }

}


// the first concrete decorator which adds vertical scrollbar functionality

class VerticalScrollBarDecorator extends WindowDecorator {

    public VerticalScrollBarDecorator (Window decoratedWindow) {

        super(decoratedWindow);

    }

 

    public void draw() {

        drawVerticalScrollBar();

        decoratedWindow.draw();

    }

 

    private void drawVerticalScrollBar() {

        // draw the vertical scrollbar

    }

 

    public String getDescription() {

        return decoratedWindow.getDescription() + ", including vertical scrollbars";

    }

}

 

class SimpleWindow implements Window{


    public void draw() {

        //draw window

      

    }

 

    public String getDescription() {

        return "simple window";

    }

}


// the second concrete decorator which adds horizontal scrollbar functionality

class HorizontalScrollBarDecorator extends WindowDecorator {

    public HorizontalScrollBarDecorator (Window decoratedWindow) {

        super(decoratedWindow);

    }

 

    public void draw() {

        drawHorizontalScrollBar();

        decoratedWindow.draw();

        decoratedWindow.setVisible(true);

    }

 

    private void drawHorizontalScrollBar() {

        // draw the horizontal scrollbar

    }

 

    public String getDescription() {

        return decoratedWindow.getDescription() + ", including horizontal scrollbars";

    }

}

}

Instead of HorizontalScrollBarDecorator and VerticalScrollBarDecorator I will have ButtonBubbleSort and ButtonQuickSort and another one called ResultLabel.
Thing is i don't know where to write down the code to actually show a window. I tried extending the JFrame class and using setsize() and setVisible(true) but in vain.

The second piece of code, the factory pattern is:

public interface SortInterface {

public void sort(double[] list);


public class QuickSort implements SortInterface {

public void sort(double[] a) {

 quicksort(a, 0, a.length - 1);

}

private void quicksort(double[] a, int left, int right) {

 if (right <= left) return;

 int i = partition(a, left, right);

 quicksort(a, left, i-1);

 quicksort(a, i+1, right);

}


private int partition(double[] a, int left, int right) {

 int i = left;

 int j = right;

 while (true) {

   while (a[i]< a[right])

     i++;

   while (less(a[right], a[--j]))

     if (j == left) break;

   if (i >= j) break;

   exch(a, i, j);

 }

 exch(a, i, right);

 return i;

}


private boolean less(double x, double y) {

 return (x < y);

}


private void exch(double[] a, int i, int j) {

 double swap = a[i];

 a[i] = a[j];

 a[j] = swap;

}

}


public class BubbleSort implements SortInterface {

public void sort(double[] list) {

 double temp;

 for(int i = 0; i < list.length; i++) {

   for(int j = 0; j < list.length - i; j++) {

     if(list[i] < list[j]) {

       temp = list[i];

       list[i] = list[j];

       list[j] = temp;

     }

   }

 }

}

}


public class SortingContext {

private SortInterface sorter = null;


public void sortDouble(double[] list) {

 sorter.sort(list);

}


public SortInterface getSorter() {

 return sorter;

}


public void setSorter(SortInterface sorter) {

 this.sorter = sorter;

}

}


public class SortingClient {

 public static void main(String[] args) {

  double[] list = {1,2.4,7.9,3.2,1.2,0.2,10.2,22.5,19.6,14,12,16,17};

  SortingContext context = new SortingContext();

  context.setSorter(new BubbleSort());

  context.sortDouble(list);

  for(int i =0; i< list.length; i++) {

   System.out.println(list[i]);

  }

 }

}

}

Where do I need to add the code? How can i combine the two of them? Please make me understand..

Thx in advance.