Two-dimensional arrays in C - Step-by-Step Execution

Concept Flow - Two-dimensional arrays

Declare 2D array

↓

Initialize elements

↓

Access element at row i, col j

↓

Use nested loops to traverse

↓

Perform operations on elements

↓

End

This flow shows how a 2D array is declared, initialized, accessed by row and column, traversed with nested loops, and used for operations.

Execution Sample

C

int arr[2][3] = {{1, 2, 3}, {4, 5, 6}};
for(int i=0; i<2; i++) {
  for(int j=0; j<3; j++) {
    printf("%d ", arr[i][j]);
  }
  printf("\n");
}

This code declares a 2x3 array, initializes it, and prints all elements row by row.

Execution Table

Step	i (row)	j (col)	Condition i<2	Condition j<3	Action	Output
1	0	0	True	True	Print arr[0][0] = 1	1
2	0	1	True	True	Print arr[0][1] = 2	2
3	0	2	True	True	Print arr[0][2] = 3	3
4	0	3	True	False	End inner loop, print newline	\n
5	1	0	True	True	Print arr[1][0] = 4	4
6	1	1	True	True	Print arr[1][1] = 5	5
7	1	2	True	True	Print arr[1][2] = 6	6
8	1	3	True	False	End inner loop, print newline	\n
9	2	0	False	N/A	End outer loop

💡 Outer loop ends when i=2, condition i<2 is False

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	After Step 8	Final
i	0	0	0	0	0	1	1	1	1	2
j	0	0	1	2	3	0	1	2	3	0

Key Moments - 3 Insights

Why do we need two loops to traverse a 2D array?

Because a 2D array has rows and columns, the outer loop goes through rows (i), and the inner loop goes through columns (j), as shown in steps 1-8 in the execution_table.

What happens when the inner loop condition j<3 becomes false?

The inner loop ends, and the program prints a newline (step 4 and 8), then the outer loop increments i to move to the next row.

Why does the outer loop stop when i equals 2?

Because the array has 2 rows (indices 0 and 1), when i reaches 2, condition i<2 is false (step 9), so the loop ends.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of j after step 3?

A 2

B 3

C 1

D 0

💡 Hint

Check the 'j (col)' column in execution_table at step 3 and step 4.

At which step does the outer loop condition i<2 become false?

A Step 8

B Step 7

C Step 9

D Step 4

💡 Hint

Look at the 'Condition i<2' column in execution_table for the step where it is False.

If the array had 3 rows instead of 2, how would the execution_table change?

A There would be more steps with i=2 iterating over j from 0 to 2

B The inner loop would run fewer times

C The outer loop would end earlier

D The output would be empty

💡 Hint

Check how the outer loop variable i controls the number of rows in variable_tracker and execution_table.

Concept Snapshot

Two-dimensional arrays store data in rows and columns.
Declare with: type name[rows][cols];
Access with arr[i][j], where i=row, j=column.
Use nested loops: outer for rows, inner for columns.
Useful for matrices, grids, tables.
Indexing starts at 0.

Full Transcript

This lesson shows how two-dimensional arrays work in C. We start by declaring a 2D array with fixed rows and columns. Each element is accessed by two indexes: row and column. To process all elements, we use nested loops: the outer loop goes through each row, and the inner loop goes through each column in that row. The execution table traces each step of printing the array elements, showing how the indexes i and j change. Key moments clarify why two loops are needed, what happens when inner loop ends, and when the outer loop stops. The visual quiz tests understanding of loop variables and array size effects. The snapshot summarizes the syntax and usage of 2D arrays.