Find the trace of a square matrix using a function

LAB B05 · 01

Understand the task.

Aim: Find the trace of a square matrix using a function.

Review the related theory in Unit 4.

LAB B05 · 02

Know what goes in and what comes out.

First the square-matrix order, from 1 to 5. Then order × order integers from -20 to 20, entered row by row.

3
1 2 3
4 5 6
7 8 9

Trace = 15

Source programs read the documented input directly, without prompt text, so the same sample works in the embedded compiler’s STDIN field.

LAB B05 · 03

Plan the steps before writing code.

1. Read and validate order.
2. Read all matrix elements with nested loops.
3. Call trace(matrix, order).
4. Inside trace, initialize total to zero and add matrix[i][i] for every valid i.
5. Return total and display it in main.

LAB B05 · 04

One complete program. Ready to run.

#include <stdio.h>
#define MAX 5
int trace(int matrix[][MAX], int order);
int main(void)
{
    int matrix[MAX][MAX], order, i, j;
    if (scanf("%d", &order) != 1 || order < 1 || order > MAX) {
        puts("Enter a square-matrix order from 1 to 5."); return 1;
    }
    for (i = 0; i < order; i++) {
        for (j = 0; j < order; j++) {
            if (scanf("%d", &matrix[i][j]) != 1 || matrix[i][j] < -20 || matrix[i][j] > 20) {
                puts("Enter matrix values from -20 to 20."); return 1;
            }
        }
    }
    printf("Trace = %d\n", trace(matrix, order));
    return 0;
}
int trace(int matrix[][MAX], int order)
{
    int i, total = 0;
    for (i = 0; i < order; i++) total += matrix[i][i];
    return total;
}

gcc B05-matrix-trace.c -o program

LAB B05 · 05

Connect each statement to its purpose.

• The main diagonal is [0][0], [1][1], …, [order - 1][order - 1].
• The function does not add every matrix element or the opposite diagonal.
• In a 2D-array parameter, the trailing dimension MAX is specified so the compiler can calculate row strides.
• order describes the entered square within the fixed MAX × MAX array; main passes it explicitly.

LAB B05 · 06

Follow the sample calculation.

LAB B05 · 07

Check more than one input.

Time and storage

Reading takes O(n²) time. The trace function itself takes O(n) time and O(1) extra working space.

Start with the sample, then test a boundary and a case that changes the result. A correct sample alone does not establish that every input is handled correctly.

LAB B05 · 08

Use the real C compiler.

Choose an example and load it into the embedded C compiler. Select I/O inside the compiler, check the sample STDIN, and press Run. Change the input or edit the source to explore a different case.

3
1 2 3
4 5 6
7 8 9

Trace = 15

#include <stdio.h>
#define MAX 5
int trace(int matrix[][MAX], int order);
int main(void)
{
    int matrix[MAX][MAX], order, i, j;
    if (scanf("%d", &order) != 1 || order < 1 || order > MAX) {
        puts("Enter a square-matrix order from 1 to 5."); return 1;
    }
    for (i = 0; i < order; i++) {
        for (j = 0; j < order; j++) {
            if (scanf("%d", &matrix[i][j]) != 1 || matrix[i][j] < -20 || matrix[i][j] > 20) {
                puts("Enter matrix values from -20 to 20."); return 1;
            }
        }
    }
    printf("Trace = %d\n", trace(matrix, order));
    return 0;
}
int trace(int matrix[][MAX], int order)
{
    int i, total = 0;
    for (i = 0; i < order; i++) total += matrix[i][i];
    return total;
}

LAB B05 · 09

Explain why the program works.

LAB B05 · 10

Build the next skill.

Read the viva answers, try the extra cases, and return to the lab index to mark this exercise as practised.