1. Case Study 2 – Marking a Multiple-choice Test
In this case study, we learn:
How to design a solution for a given problem
How to use a two-dimensional array to represent a collection of multiple-choice test answers for a list of students
How to process the two-dimensional array
How to write, compile, run and test a program to implement the designed solution. 1 1 1

2. Problem Specification
The problem is to represent a collection of test answers for eight students, with each student having answers to ten questions , compare each set of test answers with the set of key answers, and count and print the number of correct answers. 2 2 2 2 2 2 2 2

3. How Would We Do it - Design?
Top-level design
1. Declare, create and initialise an array, answers[8]
[10] to represent the test answers
2. Declare, create and initialise an array, keys[10], to
represent the key answers
3. Count and print out the number of correct answers
of each student 3 3 3 3 3 3 3

4. How Would We Do it - Design?
Final design in pseudo code
1. Declare, create and initialise an array, answers[8][10], to
represent the test answers
2. Declare, create and initialise an array, keys[10], to
represent the correct answers
3.1. For i = 0 to number of rows
3.2. Set count to 0
3.3. For j = 0 to number of answers - 1
3.4. If answer[i][j] = key[j] then
3.5. Increment count by 1
3.6. Print out student j + count 4 4 4 4 4 4 4 4

5. Implementation public class GradeExam {
public static void main(String[] args) {
// Declare, create and initialise an array to represent answers
char[][] answers = {
{'A', 'B', 'A', 'C', 'C', 'D', 'E', 'E', 'A', 'D'},
{'D', 'B', 'A', 'B', 'C', 'A', 'E', 'E', 'A', 'D'},
{'E', 'D', 'D', 'A', 'C', 'B', 'E', 'E', 'A', 'D'},
{'C', 'B', 'A', 'E', 'D', 'C', 'E', 'E', 'A', 'D'},
{'A', 'B', 'D', 'C', 'C', 'D', 'E', 'E', 'A', 'D'},
{'B', 'B', 'E', 'C', 'C', 'D', 'E', 'E', 'A', 'D'},
{'B', 'B', 'A', 'C', 'C', 'D', 'E', 'E', 'A', 'D'},
{'E', 'B', 'E', 'C', 'C', 'D', 'E', 'E', 'A', 'D'}};
// Declare, create and initialise an array to represent correct answers
char[] keys = {'D', 'B', 'D', 'C', 'C', 'D', 'A', 'E', 'A', 'D'};
// Count correct answers of each students
for (int i = 0; i < answers.length; i++) {
// Count correct answers of an individual student
int correctCount = 0;
for (int j = 0; j < answers[i].length; j++) {
if (answers[i][j] == keys[j])
correctCount++; }
System.out.println("Student " + i + "'s correct count is " +
correctCount); 5 5 5 5 5 5 5 5 5 5 5 5 5

6. Two-dimensional Array Basics
Two subscripts are used in a two-dimensional array, one for the row and the other for the column, with the index for each subscript of int type starting from 0. 6 6 6 6 6 6 6 6 6

7. Processing Two-dimensional Arrays
Suppose an array, matrix, is created as follows:
int[][] matrix = new int[4][4];
Obtaining the lengths of two dimensional array:
A two-dimensional array is a one-dimensional array in which each element is also a one-dimensional array. The matrix is a one-dimensional array of 4 elements, matrix[0], matrix[1], matrix[2], matrix[3], each of which is a one-dimensional array of 4 integers.
The method length returns the length of a one-dimensional array. For example
matrix.length returns 4, and each of matrix[0].length, matrix[1].length, matrix[2].length, matrix[3].length returns 4. 7 7 7 7 7 7 7 7 7 7 7

8. Processing Two-dimensional Arrays
Initializing arrays with user input values:
java.util.Scanner input = new
Scanner(System.in);
System.out.println("Enter " + matrix.length + ”
rows and " + matrix[0].length + " columns: ");
for (int row = 0; row < matrix.length; row++) {
for (int column = 0; column <
matrix[row].length; column++) {
matrix[row][column] = input.nextInt(); } 8 8 8 8 8 8 8 8 8 8 8

9. Processing Two-dimensional Arrays
Printing arrays:
for (int row = 0; row < matrix.length; row++) {
for (int column = 0; column <
matrix[row].length; column++) {
System.out.print(matrix[row][column] + " "); }
System.out.println(); 9 9 9 9 9 9 9 9 9 9 9 9

10. Processing Two-dimensional Arrays
Summing all elements:
int total = 0;
for (int row = 0; row < matrix.length; row++) {
for (int column = 0; column <
matrix[row].length; column++) {
total += matrix[row][column]; } 10 10 10 10 10 10 10 10 10 10 10 10 10

11. Processing Two-dimensional Arrays
Finding the row with the largest sum:
int maxRow = 0;
int indexOfMaxRow = 0;
// Set sum of the first row to maxRow
for (int column = 0; column < matrix[0].length; column++) {
maxRow += matrix[0][column]; }
for (int row = 1; row < matrix.length; row++) {
int totalOfThisRow = 0;
for (int column = 0; column < matrix[row].length; column++)
totalOfThisRow += matrix[row][column];
if (totalOfThisRow > maxRow) {
maxRow = totalOfThisRow;
indexOfMaxRow = row;
System.out.println("Row " + indexOfMaxRow + " has the maximum sum of "
+ maxRow); 11 11 11 11 11 11 11 11 11 11 11 11 11 11

12. Processing Two-dimensional Arrays
Summing elements by column:
for (int column = 0; column < matrix[0].length;
column++) {
int total = 0;
for (int row = 0; row < matrix.length; row++)
total += matrix[row][column];
System.out.println("Sum for column " + column
+ " is “ + total); }
How to sum elements by row? 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12