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10.15.1. Free Response - Gray Image A

The following is part a of a free response question from 2012. It was question 4 on the exam. You can see all the free response questions from past exams at https://apstudent.collegeboard.org/apcourse/ap-computer-science-a/exam-practice.

Question 4. A grayscale image is represented by a 2-dimensional rectangular array of pixels (picture elements). A pixel is an integer value that represents a shade of gray. In this question, pixel values can be in the range from 0 through 255, inclusive. A black pixel is represented by 0, and a white pixel is represented by 255. The declaration of the GrayImage class is shown below.

public class GrayImage
{
   public static final int BLACK = 0;
   public static final int WHITE = 255;

   /** The 2-dimensional representation of this image.
    *  Guaranteed not to be null.
    *  All values in the array are within the range
    *  [BLACK, WHITE], inclusive.
    */
   private int[][] pixelValues;

   /** @return the total number of white pixels in
    *    this image.
    * Postcondition: this image has not been changed.
    */
   public int countWhitePixels()
   { /* to be implemented in part (a) */ }
}

Part a. Write the method countWhitePixels that returns the number of pixels in the image that contain the value WHITE. For example, assume that pixelValues contains the following image.

Figure 1: Example 2D array

A call to countWhitePixels method would return 5 because there are 5 entries (shown in boldface) that have the value WHITE.

public class GrayImage
{
   public static final int BLACK = 0;
   public static final int WHITE = 255;

   /** The 2-dimensional representation of this image.
    *  Guaranteed not to be null.
    *  All values in the array are within the range
    *  [BLACK, WHITE], inclusive.
    */
   private int[][] pixelValues;

   /** @return the total number of white pixels in
    *    this image.
    * Postcondition: this image has not been changed.
    */
   public int countWhitePixels()
   { /* to be implemented in part (a) */ }
}

10.15.1.1. How to solve this problem

To solve this problem, we will need to loop through the entire 2D array, looking for instances of a WHITE pixel, keeping track of our count during the loop.

9-10-1-1: Which loop should you use to solve this problem?

• single for each loop
• This is a two-dimensional array so you would need a nested for-each loop.
• nested for loop
• For a two-dimensional array you can use a nested for loop or you could also use a nested for-each loop.
• nested while loop
• You could use a nested while loop, but since you know the numbers of rows and columns a nested for loop is usually better since with a while loop you could forget to increment the row or column index.

Looping through a 2D array is more complicated than the simple arrays we usually see, requiring nested for loops. Check out the code below, which displays how nested for loops work to display a block of numbers.

public class Test { public static void main(String[] args) { for (int i = 0; i < 5; i++) { for (int j = 0; j < 5; j++) { System.out.print(j); } System.out.println(); } } }

Try to write the code for the method countWhitePixels. When you are ready click “Run” to test your solution.

public class GrayImage { public static final int BLACK = 0; public static final int WHITE = 255; /** The 2-dimensional representation of this image. * Guaranteed not to be null. * All values in the array are within the range * [BLACK, WHITE], inclusive. */ private int[][] pixelValues; /** constructor that takes a 2D array */ public GrayImage(int[][] theArray) { pixelValues = theArray; } /** @return the total number of white pixels in * this image. * Postcondition: this image has not been changed. */ public int countWhitePixels() { } /** main for testing */ public static void main (String[] args) { int[][] values = { {255, 184, 178, 84, 129}, {84, 255, 255, 130, 94}, {78, 255, 0, 0, 78}, {84, 130, 255, 130, 84} }; GrayImage image = new GrayImage(values); System.out.println("count white should be 5 and is " + image.countWhitePixels()); } }

10.15.1.2. Video - One way to code the solution

The following video is also on YouTube at https://youtu.be/Rx4bPs0wkxU. It walks through coding a solution.

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