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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.

../_images/grayImageA.png

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.

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.

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

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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