Multidimensional Arrays

So far, we have looked at one-dimensional arrays, where each element is accessed using a single integer index. E.g., if quiz is an array of double elements with length 3, then there are 3 double variables which belong to the array, quiz[0], quiz[1], and quiz[2]. We call this kind of array a one-dimensional array.

A multidimensional array is one in which the elements (variables) in the array are accessed using multiple index values. For example, a two-dimensional array has its elements arranged like a grid. For example:

#define NUM_STUDENTS 3
#define NUM_QUIZZES 2

...

double quiz[NUM_STUDENTS][NUM_QUIZZES];

In this example, the array quiz has two dimensions. Because NUM_STUDENTS is 3 and NUM_QUIZZES is 2, the size of the array is 3x2. By convention, we think of the first dimension of a two-dimensional array as representing rows, and the second dimension as representing columns.

Conceptually, the array is arranged like this:

quiz[0][0] quiz[0][1]
quiz[1][0] quiz[1][1]
quiz[2][0] quiz[2][1]

Because there are 3 rows and 2 columns, the array contains 6 elements.

We could use this array to store multiple quiz grades for multiple students. I.e., if student is an integer index value in the range 0..2 representing a particular student, and quiz_num is an integer index value in the range 0..1 representing a particular quiz, then

quiz[student][quiz_num]

is a double variable recording a particular quiz score.

Here is what a program to store quiz grades for multiple students, and then compute each student’s quiz average, might look like:

#include <stdio.h>

#define NUM_STUDENTS 3
#define NUM_QUIZZES 2

int main(void)
{
    double quiz[NUM_STUDENTS][NUM_QUIZZES];

    int j, i;

    // Allow the user to enter the quiz grade data
    for (j = 0; j < NUM_STUDENTS; j++) {
        printf("Enter grades for student %i:\n", j + 1);

        for (i = 0; i < NUM_QUIZZES; i++) {
            printf("Quiz %i grade: ", i + 1);
            scanf("%lf", &quiz[j][i]);
        }
    }

    // Now compute each student's quiz average
    for (j = 0; j < NUM_STUDENTS; j++) {
        double quiz_average;

        // Code to compute the average would go here...

        printf("Student %i's average is %.2lf\n", j + 1, quiz_average);
    }

    return 0;
}

Example run (user input in bold):

Enter grades for student 1:
Quiz 1 grade: 100
Quiz 2 grade: 80
Enter grades for student 2:
Quiz 1 grade: 85
Quiz 2 grade: 92
Enter grades for student 3:
Quiz 1 grade: 74
Quiz 2 grade: 89
Student 1's average is 90.00
Student 2's average is 88.50
Student 3's average is 81.50

It is possible to have 3, 4, and even higher numbers of dimensions in an array.

quiz[0][0]	quiz[0][1]
quiz[1][0]	quiz[1][1]
quiz[2][0]	quiz[2][1]