Multi-dimensional arrays in C++ - Step-by-Step Execution

Concept Flow - Multi-dimensional arrays

Declare multi-dimensional array

↓

Access element by row and column indices

↓

Modify or read element

↓

Use nested loops to traverse rows and columns

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Process or output elements

↓

End

This flow shows how to declare, access, and traverse a multi-dimensional array using nested loops.

Execution Sample

C++

#include <iostream>
using namespace std;

int main() {
  int arr[2][3] = {{1,2,3},{4,5,6}};
  for(int i=0; i<2; i++) {
    for(int j=0; j<3; j++) {
      cout << arr[i][j] << ' ';
    }
    cout << '\n';
  }
  return 0;
}

This code declares a 2x3 array and prints all its elements row by row.

Execution Table

Step	i	j	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	Inner loop ends, 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	Inner loop ends, print newline	\n
9	2	0	False	N/A	Outer loop ends

💡 Outer loop i=2 is not less than 2, so loop ends.

Variable Tracker

Variable	Start	After Step 1	After Step 4	After Step 5	After Step 8	Final
i	0	0	0	1	1	2
j	0	0	3	0	3	N/A

Key Moments - 3 Insights

Why does the inner loop reset j to 0 after finishing one row?

Because the inner loop runs for each row, j must start at 0 to access columns from the beginning each time (see steps 4 and 5 in execution_table).

Why do we use two loops instead of one to access all elements?

A multi-dimensional array has rows and columns, so one loop goes through rows (i), and the inner loop goes through columns (j) to cover every element (see nested loops in code).

What happens if we try to access arr[2][0]?

It is out of bounds because the array has only 2 rows indexed 0 and 1. Accessing arr[2][0] causes undefined behavior (see exit condition i<2 in execution_table).

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of j after step 4?

A 2

B 0

C 3

D 1

💡 Hint

Check the 'j' column in execution_table row for step 4.

At which step does the outer loop condition become false?

A Step 8

B Step 9

C Step 4

D Step 1

💡 Hint

Look at the 'Condition i<2' column in execution_table.

If the array size changed to arr[3][3], how many total elements would the loops print?

A 9

B 6

C 3

D 5

💡 Hint

Multiply the number of rows by columns to find total elements.

Concept Snapshot

Multi-dimensional arrays store data in rows and columns.
Declare with syntax: type name[rows][columns];
Access elements with arr[row][column].
Use nested loops to traverse all elements.
Outer loop for rows, inner loop for columns.
Indexing starts at 0 and goes to size-1.

Full Transcript

This lesson shows how multi-dimensional arrays work in C++. We declare an array with two dimensions, like int arr[2][3]. We access elements using two indices: row and column. To print all elements, we use nested loops: the outer loop goes through rows, and the inner loop goes through columns. Each loop runs until its condition is false. The inner loop resets its index after finishing a row. Trying to access outside the declared size causes errors. This visual trace shows each step of the loops and the values of variables i and j as they change.