# Unit 4C - Free Response - Gray Image A Each coding exercise has its own folder. Open its `.java` file and press **Run** to try it. **Run Tests** checks every graded exercise in this lesson at once. 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 [Past AP CSA Exams](https://www.savemyexams.com/ap/computer-science/college-board/a/past-papers/) . **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. ```java 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. ![Example 2D array](images/grayImageA.png) *Example 2D array* A call to `countWhitePixels` method would return 5 because there are 5 entries (shown in boldface) that have the value `WHITE`. ```java 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) */ } } ``` ## 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. > Check your understanding: What kind of loop could you use to solve this problem? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#frgia_1 > Check your understanding: What is another kind of loop you could use to solve this problem? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#frgia_1b 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. ```java // Nested indexed for loops public class NestedIndexedForLoops { 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(); } } } ``` ```java // Nested for each loops public class NestedForEachLoops { public static void main(String[] args) { int[][] arr = new int[5][5]; for (int[] row : arr) { for (int ent : row) { System.out.print(ent); } System.out.println(); } } } ``` ## 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. Explain in plain English what your code will have to do to answer this question. Use the variable names given above. > Discuss this with your class, or answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#gray_image_A > Check your understanding: Which class is `countWhitePixels` a method in? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg_ans > Check your understanding: What array will you be modifying in this method? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg1_ans 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. > Check your understanding: What could you write for the outer for loop so that it iterates through the rows of the array? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg2_ans > Check your understanding: What could you write for the inner for loop so that it iterates through the columns of the array? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg3_ans > Check your understanding: how could you check if the current value is white? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg4_ans Alternatively, if you want to solve this problem using nested for each loops, complete the three questions below. > Check your understanding: What could you write for the outer for loop so that it iterates through the rows of the array? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg5_ans > Check your understanding: What could you write for the inner for loop so that it iterates through the columns of the array? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg6_ans > Check your understanding: How will you check if pv is white? — answer it on CS Awesome: https://runestone.academy/ns/books/published/csawesome2/grayImageA.html#2012GreyScale_alg7_ans ## Try and Solve It ### Exercise 1 FRQ Gray Image A: write the code for the method `countWhitePixels`. When you are ready click “Run” to test your solution. > Open the `01-lcfrgia2` folder and edit `GrayImage.java`. Press **Run** to try it; **Run Tests** checks it (4 tests). ## Video - One way to code the solution The following video is also on YouTube at [https://youtu.be/Rx4bPs0wkxU](https://youtu.be/Rx4bPs0wkxU). It walks through coding a solution.