8.6.1. 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://apstudents.collegeboard.org/courses/ap-computer-science-a/free-response-questions-by-year.

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) */ }
}

8.6.1.1. 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 questions and code below, which displays how nested for loops work to display a block of numbers.

8.6.1.2. Algorithm

When approaching this problem, it can be helpful to look for keywords or hints that maybe be in the problem statement. This section contains a plain English explanation of one way to solve this problem as well as problems that test your understanding of how to write the code to do those things. Click on the buttons to reveal the questions.

9-10-5: Explain in plain English what your code will have to do to answer this question. Use the variable names given above.

There are many ways to solve this question, but we will only cover two in this section. Although it is a good exercise to be able to write the solution in multiple ways, you do not need to write both for the AP exam and you can just look at the problems below which relate to the method that is more intuitive to you.

If you want to solve this problem using nested for loops, complete the three questions below.

Alternatively, if you want to solve this problem using nested for each loops, complete the three questions below.

8.6.1.3. Try and Solve It

FRQ Gray Image A: write the code for the method countWhitePixels. When you are ready click “Run” to test your solution.

8.6.1.4. 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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