FRQ4 - 2D Arrays

Section 15.13 FRQ4 - 2D Arrays - Part 1

From the 2025 Course and Exam Description:

Free-Response Question 4: 2D Array. Students will be provided with a scenario and its associated class(es). Students will write one method of a given class based on provided specifications and examples. The method requires students to use, analyze, and manipulate data in a 2D array structure.

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FRQ 4 requires the following skills:

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Iterate through a 2D array

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Access elements of a 2D array

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Call methods on elements of a 2D array

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Subsection 15.13.1 2013 FRQ 4 - SkyView - Part (a)

The following is a free response question from 2013. It was question 4 on the exam on https://secure-media.collegeboard.org/digitalServices/pdf/ap/apcentral/ap13_frq_comp_sci.pdf.

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Note 15.13.1. JuiceMind AI-Graded FRQ Practice.

This is also available as an AI-graded FRQ on the JuiceMind IDE for AP exam practice with rubrics and AI instant feedback. Teachers must create free accounts and assign the FRQ on JuiceMind for students to access it.

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Question 4. A telescope scans a rectangular area of the night sky and collects the data into a 1-dimensional array. Each data value scanned is a number representing the amount of light detected by the telescope. The telescope scans back and forth across the sky (alternating between left to right and right to left) in the pattern indicated below by the arrows. The back-and-forth ordering of the values received from the scan is called telescope order.

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Figure 15.13.2. The first row is left to right and the second is right to left and so on.
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The telescope records the data in telescope order into a 1-dimensional array of double values. This 1-dimensional array of information received from a single scan will be transferred into a 2-dimensional array, which reconstructs the original view of the rectangular area of the sky. This 2-dimensional array is part of the SkyView class, shown below. In this question you will write a constructor and a method for this class.

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public class SkyView {
    /** A rectangular array that holds the data representing a rectangular area of the sky. */
    private double[][] view;

    /**
     * Constructs a SkyView object from a 1-dimensional array of scan data.
     *
     * @param numRows the number of rows represented in the view Precondition: numRows > 0
     * @param numCols the number of columns represented in the view Precondition: numCols > 0
     * @param scanned the scan data received from the telescope, stored in telescope order
     *     Precondition: scanned.length == numRows * numCols Postcondition: view has been created as
     *     a rectangular 2-dimensional array with numRows rows and numCols columns and the values in
     *     scanned have been copied to view and are ordered as in the original rectangular area of
     *     sky.
     */
    public SkyView(int numRows, int numCols, double[] scanned) {
        /* to be implemented in part (a) */
    }

    /**
     * Returns the average of the values in a rectangular section of view.
     *
     * @param startRow the first row index of the section
     * @param endRow the last row index of the section
     * @param startCol the first column index of the section
     * @param endCol the last column index of the section Precondition: 0 <= startRow <= endRow <
     *     view.length Precondition: 0 <= startCol <= endCol < view[0].length
     * @return the average of the values in the specified section of view
     */
    public double getAverage(int startRow, int endRow, int startCol, int endCol) {
        /* to be implemented in part (b) */
    }

    // There may be other instance variables, constructors, and methods
}

Part a. Write the constructor for the SkyView class. The constructor initializes the view instance variable to a 2-dimensional array with numRows rows and numCols columns. The information from scanned, which is stored in the telescope order, is copied into view to reconstruct the sky view as originally seen by the telescope. The information in scanned must be rearranged as it is stored into view so that the sky view is oriented properly.

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For example, suppose scanned contains values, as shown in the following array.

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Figure 15.13.3. First example scanned array values
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Using the scanned array above, a SkyView object created with new SkyView(4, 3, values), would have view initialized with the following values.

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Figure 15.13.4. The resulting view from the first example scanned array
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For another example, suppose scanned contains the following values.

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Figure 15.13.5. Second example scanned array values
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A SkyView object created with new SkyView(3, 2, values), would have view initialized with the following values.

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Figure 15.13.6. The resulting view from the second example scanned array
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Complete the SkyView constructor in the class below.

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The code below declares the class, the view, and a constructor for you to finish writing. It also has a main method for testing the constructor.

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Activity 15.13.1.

Complete the SkyView constructor in the class below.

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public class SkyView {
    private double[][] view;

/** This is a main method for testing the class */
    public static void main(String[] args) {
        double[] values = {0.3, 0.7, 0.8, 0.4, 1.4, 1.1, 0.2, 0.5, 0.1, 1.6, 0.6, 0.9};
        SkyView sView = new SkyView(4, 3, values);
        System.out.println("It should print the following:");
        System.out.println("0.3, 0.7, 0.8,");
        System.out.println("1.1, 1.4, 0.4,");
        System.out.println("0.2, 0.5, 0.1,");
        System.out.println("0.9, 0.6, 1.6,");
        System.out.println();
        System.out.println("Your results");
        for (int row = 0; row < sView.view.length; row++) {
            for (int col = 0; col < sView.view[0].length; col++) {
                System.out.print(sView.view[row][col] + ", ");
            }
            System.out.println();
        }

System.out.println();

double[] val2 = {0.3, 0.7, 0.8, 0.4, 1.4, 1.1};
        sView = new SkyView(3, 2, val2);
        System.out.println("It should print the following:");
        System.out.println("0.3, 0.7,");
        System.out.println("0.4, 0.8,");
        System.out.println("1.4, 1.1,");
        System.out.println();
        System.out.println("Your results");
        for (int row = 0; row < sView.view.length; row++) {
            for (int col = 0; col < sView.view[0].length; col++) {
                System.out.print(sView.view[row][col] + ", ");
            }
            System.out.println();
        }
    } // end of main

public String toString() {
        String output = "";
        for (int row = 0; row < view.length; row++) {
            for (int col = 0; col < view[row].length; col++) {
                output += view[row][col] + ", ";
            }
            output += "\n";
        }
        return output;
    }
} // end of class
====
import static org.junit.Assert.*;

import org.junit.*;

import java.io.*;

// import java.util.Arrays;
// import java.util.ArrayList;

public class RunestoneTests extends CodeTestHelper {
    public RunestoneTests() {
        super("SkyView");
        // CodeTestHelper.sort = true;
    }

@Test
    public void testMain1() {
        boolean passed = false;

double[] val2 = {0.3, 0.7, 0.4, 0.8, 1.4, 1.1};
        SkyView sView = new SkyView(3, 2, val2);
        String expect = "0.3, 0.7,\n0.8, 0.4,\n1.4, 1.1,";

String output = sView.toString().trim();

passed = getResults(expect, output, "Checking for expected output");
        assertTrue(passed);
    }

@Test
    public void testMain2() {
        boolean passed = false;

double[] val2 = {0.3, 0.7, 0.4, 0.8, 1.4, 1.1};
        SkyView sView = new SkyView(2, 3, val2);
        String expect = "0.3, 0.7, 0.4, \n1.1, 1.4, 0.8,";

String output = sView.toString().trim();

passed = getResults(expect, output, "Checking for expected output");
        assertTrue(passed);
    }
}

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Subsection 15.13.2 2013 FRQ 4 - SkyView - Part (b)

SkyView Part B is from the 2103 AP Computer Science A Exam at https://secure-media.collegeboard.org/digitalServices/pdf/ap/apcentral/ap13_frq_comp_sci.pdf.

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Note 15.13.7. JuiceMind AI-Graded FRQ Practice.

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Part b. Write the SkyView method getAverage, which returns the average of the elements of the section of view with row indexes from startRow through endRow, inclusive, and column indexes from startCol through endCol, inclusive.

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For example, if nightSky is a SkyView object where view contains the values shown below, the call nightSky.getAverage(1, 2, 0, 1) should return 0.8. (The average is (1.1 + 1.4 + 0.2 + 0.5) / 4, which equals 0.8). The section being averaged is indicated by the dark outline in the table below.

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Figure 15.13.8. Example values with the region for the getAverage outlined
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Activity 15.13.2.

Finish writing the getAverage method in the class below.

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public class SkyView {
    private double[][] view;

/**
     * Constructs a SkyView object from a 1-dimensional array of scan data.
     *
     * @param numRows the number of rows represented in the view Precondition: numRows > 0
     * @param numCols the number of columns represented in the view Precondition: numCols > 0
     * @param scanned the scan data received from the telescope, stored in telescope order
     *     Precondition: scanned.length == numRows * numCols Postcondition: view has been created as
     *     a rectangular 2-dimensional array with numRows rows and numCols columns and the values in
     *     scanned have been copied to view and are ordered as in the original rectangular area of
     *     sky.
     */
    public SkyView(int numRows, int numCols, double[] scanned) {
        view = new double[numRows][numCols];
        int scannedIndex = 0;
        for (int r = 0; r < numRows; r++) {
            // if even row number go left to right */
            if (r % 2 == 0) {
                for (int c = 0; c < numCols; c++) {
                    view[r][c] = scanned[scannedIndex];
                    scannedIndex++;
                }
            } else {
                for (int c = numCols - 1; c >= 0; c--) {
                    view[r][c] = scanned[scannedIndex];
                    scannedIndex++;
                }
            }
        }
    }

/**
     * Returns the average of the values in a rectangular section of view.
     *
     * @param startRow the first row index of the section
     * @param endRow the last row index of the section
     * @param startCol the first column index of the section
     * @param endCol the last column index of the section Precondition: 0 <= startRow <= endRow <
     *     view.length Precondition: 0 <= startCol <= endCol < view[0].length
     * @return the average of the values in the specified section of view
     */
    public double getAverage(int startRow, int endRow, int startCol, int endCol) {
        // *** Finish writing this method! ***
    }

/** This is a main method for testing getAverage */
    public static void main(String[] args) {
        double[] startArray = {0.3, 0.7, 0.8, 0.4, 1.4, 1.1, 0.2, 0.5, 0.1, 1.6, 0.6, 0.9};
        SkyView sView = new SkyView(4, 3, startArray);
        System.out.println(
                "getAverage(1,2,0,1) should return 0.8 and returns "
                        + sView.getAverage(1, 2, 0, 1));
    } // end of main
} // end of class
====

import static org.junit.Assert.*;

import org.junit.*;

import java.io.*;

// import java.util.Arrays;
// import java.util.ArrayList;

public class RunestoneTests extends CodeTestHelper {
    public RunestoneTests() {
        super("SkyView");
        // CodeTestHelper.sort = true;
    }

@Test
    public void testMain1() {
        boolean passed = false;

double[] val2 = {0.3, 0.7, 0.4, 0.8, 1.4, 1.1};

String view = "0.3, 0.7,\n0.8, 0.4,\n1.4,1.1,";

SkyView sView = new SkyView(3, 2, val2);
        String expect = "getAverage(1,2,0,1)  --> 0.925";

String output = "getAverage(1,2,0,1)  --> " + sView.getAverage(1, 2, 0, 1);

passed = getResults(expect, output, "Checking for expected output from:\n" + view);
        assertTrue(passed);
    }

@Test
    public void testMain2() {
        boolean passed = false;

double[] val2 = {0.3, 0.7, 0.4, 0.8, 1.4, 1.1};
        String view = "0.3, 0.7, 0.4,\n1.1, 1.4,  0.8,";
        SkyView sView = new SkyView(2, 3, val2);
        String expect = "getAverage(1,2,0,1) --> 0.875";

String output = "getAverage(1,2,0,1)  --> " + sView.getAverage(0, 1, 0, 1);

passed = getResults(expect, output, "Checking for expected output from:\n" + view);
        assertTrue(passed);
    }
}

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