Multi-dimensional arrays in C Sharp (C#) - Step-by-Step Execution

Concept Flow - Multi-dimensional arrays

Declare multi-dimensional array

↓

Allocate memory for rows and columns

↓

Access elements using two indices

↓

Modify or read element at [row, column

↓

Use nested loops to traverse all elements

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Done

This flow shows how a multi-dimensional array is declared, allocated, accessed by row and column indices, and traversed using nested loops.

Execution Sample

C Sharp (C#)

int[,] matrix = new int[2,3];
matrix[0,0] = 5;
matrix[1,2] = 10;
for(int i=0; i<2; i++) {
  for(int j=0; j<3; j++) {
    Console.Write(matrix[i,j] + " ");
  }
  Console.WriteLine();
}

This code creates a 2x3 integer array, sets two values, and prints all elements row by row.

Execution Table

Step	Action	Indices (i,j)	Value Set/Read	Output	Notes
1	Declare array	-	-	-	Create 2 rows and 3 columns, all initialized to 0
2	Set value	[0,0]	5	-	Set element at first row, first column to 5
3	Set value	[1,2]	10	-	Set element at second row, third column to 10
4	Start outer loop	i=0	-	-	Begin first row traversal
5	Start inner loop	i=0, j=0	-	5	Read matrix[0,0] = 5 and print
6	Inner loop	i=0, j=1	-	0	Default value 0 printed
7	Inner loop	i=0, j=2	-	0	Default value 0 printed
8	End inner loop	i=0	-	Line break	Move to next line after row 0
9	Outer loop	i=1	-	-	Begin second row traversal
10	Inner loop	i=1, j=0	-	0	Default value 0 printed
11	Inner loop	i=1, j=1	-	0	Default value 0 printed
12	Inner loop	i=1, j=2	-	10	Read matrix[1,2] = 10 and print
13	End inner loop	i=1	-	Line break	Move to next line after row 1
14	End outer loop	-	-	-	All elements printed, loops end

💡 Loops finish after i=1 and j=2, all elements accessed and printed.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 5	After Step 12	Final
matrix[0,0]	0	5	5	5	5	5
matrix[1,2]	0	0	10	10	10	10
i	-	-	-	0	1	-
j	-	-	-	0 to 2	0 to 2	-

Key Moments - 3 Insights

Why do we use two indices like matrix[i,j] instead of one?

Because the array has rows and columns, each index selects the row and column respectively, as shown in execution_table steps 5 and 12 where both i and j are used to access elements.

Why are some elements zero even though we only set two values?

In C#, multi-dimensional arrays of int are initialized with zeros by default, so elements not explicitly set remain zero, as seen in steps 6,7,10,11.

How do nested loops help in accessing all elements?

The outer loop selects the row (i), and the inner loop selects the column (j), together covering every element, demonstrated in execution_table steps 4-13.

Visual Quiz - 3 Questions

Look at the execution_table at step 5, what value is read from matrix[0,0]?

A 10

B 5

C 0

D Undefined

💡 Hint

Check the 'Value Set/Read' and 'Output' columns at step 5 in execution_table.

At which step does the inner loop finish printing the first row?

A Step 8

B Step 7

C Step 13

D Step 14

💡 Hint

Look for the 'End inner loop' action with a line break after row 0 in execution_table.

If we change matrix[1,2] = 10 to matrix[1,2] = 20, what changes in the output at step 12?

A Output remains 10

B Output changes to 0

C Output changes from 10 to 20

D No output at step 12

💡 Hint

Check the 'Value Set/Read' and 'Output' columns at step 12 in execution_table.

Concept Snapshot

Multi-dimensional arrays in C# use syntax: type[,] name = new type[rows, columns];
Access elements with two indices: array[row, column].
Elements default to zero for int arrays.
Use nested loops to traverse rows and columns.
Each index selects a dimension (row or column).
Useful for tables, grids, and matrices.

Full Transcript

This lesson shows how to work with multi-dimensional arrays in C#. We start by declaring an array with two dimensions, specifying rows and columns. Memory is allocated for all elements, which are initialized to zero by default for integers. We set specific elements using two indices, one for the row and one for the column. To read or print all elements, we use nested loops: the outer loop goes through rows, the inner loop through columns. Each element is accessed by matrix[i,j]. The execution table traces each step, showing how values are set and read, and how output is produced line by line. Key moments clarify why two indices are needed, why some elements remain zero, and how nested loops cover all elements. The visual quiz tests understanding of specific steps and output changes. The snapshot summarizes syntax and usage for quick reference.