C Multidimensional Arrays

An array can have more than one dimension. A two-dimensional array is a table with rows and columns, such as a seating plan, a game board or the marks of several students in several subjects.

Declaring a 2D array

Give the number of rows, then the number of columns. Each row's values go in their own braces.

#include <stdio.h>

int main(void) {
    int table[2][3] = {
        {1, 2, 3},
        {4, 5, 6}
    };
    printf("table[0][0] = %d\n", table[0][0]);
    printf("table[1][2] = %d\n", table[1][2]);
    return 0;
}

table[0][0] = 1
table[1][2] = 6

table[1][2] is row 1, column 2: the third value of the second row. Both indexes start at 0.

Looping over rows and columns

Two nested loops visit every element: the outer loop goes over the rows, the inner loop over the columns of one row.

#include <stdio.h>

int main(void) {
    int marks[3][4] = {
        {80, 72, 91, 65},
        {58, 77, 69, 84},
        {93, 88, 79, 90}
    };
    for (int s = 0; s < 3; s++) {
        int total = 0;
        printf("Student %d:", s + 1);
        for (int sub = 0; sub < 4; sub++) {
            printf(" %3d", marks[s][sub]);
            total += marks[s][sub];
        }
        printf("  total %d\n", total);
    }
    return 0;
}

Student 1:  80  72  91  65  total 308
Student 2:  58  77  69  84  total 288
Student 3:  93  88  79  90  total 350

Adding two matrices

In mathematics a table of numbers is a matrix. Adding two matrices adds the elements at the same position:

#include <stdio.h>

int main(void) {
    int a[2][2] = {{1, 2}, {3, 4}};
    int b[2][2] = {{10, 20}, {30, 40}};
    int sum[2][2];
    for (int r = 0; r < 2; r++) {
        for (int c = 0; c < 2; c++) {
            sum[r][c] = a[r][c] + b[r][c];
        }
    }
    for (int r = 0; r < 2; r++) {
        printf("%d %d\n", sum[r][0], sum[r][1]);
    }
    return 0;
}

11 22
33 44

How it is stored

In memory a 2D array is one long row of values: first all of row 0, then all of row 1, and so on. That is why, when you pass a 2D array to a function, the number of columns must be given: void print(int t[][4], int rows).

Common mistakes

• Swapping the indexes: table[col][row] instead of table[row][col]. Name the loop variables row and col to keep them straight.
• Using the wrong limit in the inner loop: the inner loop counts columns, the outer loop rows.
• Going past the last row or column: like any array, indexes run from 0 to size − 1, and C does not check them. Safe mode in the editor catches it.

Arrays can have more than two dimensions too, such as int cube[3][3][3], but two are by far the most common.

Practice exercises

1. Print the total of each column of the marks table.
2. Build a 3 by 3 tic-tac-toe board of characters filled with '.', put an 'X' in the middle and print it.
3. Print the multiplication table from 1 to 5 as a 5 by 5 grid stored in a 2D array.