Unit 2 · Lesson 225 minAcademic review pending

Rows, columns, and nested loops

Represent tables and matrices with two-dimensional arrays and traverse them in row-major order.

Choose explanation

After this lesson

You should be able to

Index a two-dimensional array with valid row and column bounds.
Use nested loops for row, column, and whole-matrix operations.

A table stored row by row

int scores[3][4] represents three rows and four columns. scores[r][c] selects one element. Valid rows are 0–2 and valid columns are 0–3. In ordinary C arrays, each complete row is stored before the next row.

Nested loops mirror the shape: outer loop chooses a row and inner loop visits its columns. Use separate names and bounds; mixing row and column limits may compile but still access invalid memory.

Print a matrix

for (size_t r = 0; r < rows; r++) {
    for (size_t c = 0; c < cols; c++) {
        printf("%d ", matrix[r][c]);
    }
    printf("\n");
}

Choose the traversal for the question

A row total fixes r and varies c. A column total fixes c and varies r. A diagonal of a square matrix uses matching indexes matrix[i][i]. Naming the intended movement before coding prevents swapped-loop mistakes.

When passing a built-in two-dimensional array to a function, the compiler must know the later dimension so it can calculate row offsets. Variable-length array parameters can carry runtime dimensions in modern C implementations that support them.

Try it yourself

Compute the total of the main diagonal of a 3×3 integer matrix.

Need a hint?

Main-diagonal elements have the same row and column index.

Check the worked solution

Loop i from 0 through 2 and add matrix[i][i].

int total = 0;
for (size_t i = 0; i < 3; i++) {
    total += matrix[i][i];
}

Quick check

Which traversal computes one column total?

Select an answer to check your thinking.

Why this lesson exists

Syllabus mapping

Two-dimensional arrays

Maps to course outcomes CO3, CO5.