# 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.

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.

Video: (Rx4bPs0wkxU)