Multi-Dimensional Arrays and Grid Traversal

Beginner12 min read•Updated: 2026-10-22

🔲 Multi-Dimensional Arrays and Grid Traversal

Introduction

Two-dimensional arrays represent tabular data: game boards (chess, tic-tac-toe), spreadsheet grids, and matrices in computer graphics.

📊 Matrix Representation in Modern C++

1#include <iostream>
2#include <array>
3#include <iomanip>
4 
5int main() {
6    // 3 rows, 3 columns matrix
7    constexpr std::size_t ROWS = 3;
8    constexpr std::size_t COLS = 3;
9 
10    std::array<std::array<int, COLS>, ROWS> matrix = {{
11        {1, 2, 3},
12        {4, 5, 6},
13        {7, 8, 9}
14    }};
15 
16    std::cout << "=== 2D Matrix Traversal ===\n";
17    for (std::size_t r = 0; r < ROWS; ++r) {
18        for (std::size_t c = 0; c < COLS; ++c) {
19            std::cout << std::setw(3) << matrix[r][c] << " ";
20        }
21        std::cout << "\n";
22    }
23 
24    // Calculating Main Diagonal Sum (Trace)
25    int diagonalSum = 0;
26    for (std::size_t i = 0; i < ROWS; ++i) {
27        diagonalSum += matrix[i][i];
28    }
29    std::cout << "Diagonal Sum (1 + 5 + 9): " << diagonalSum << "\n";
30 
31    return 0;
32}

⚡ Cache Locality & Row-Major Order

C++ stores multi-dimensional arrays in row-major order in memory:

1[Row 0, Col 0] [Row 0, Col 1] [Row 0, Col 2] [Row 1, Col 0] ...

Always iterate through rows in the outer loop and columns in the inner loop to exploit CPU cache line prefetching.

Next Lesson

Project 1: Scientific Calculator with Memory Registers

Continue learning with hands-on practice, examples, and exercises in the upcoming topic.

Related Lessons

Previous Lesson	Next Lesson
Fixed-Size Arrays with std::array vs C-Style Arrays	Project 1: Scientific Calculator with Memory Registers

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Project 1: Scientific Calculator with Memory Registers

Multi-Dimensional Arrays and Grid Traversal

Beginner12 min read•Updated: 2026-10-22

Study Materials

🔲 Multi-Dimensional Arrays and Grid Traversal

Introduction

Two-dimensional arrays represent tabular data: game boards (chess, tic-tac-toe), spreadsheet grids, and matrices in computer graphics.

📊 Matrix Representation in Modern C++

1#include <iostream>
2#include <array>
3#include <iomanip>
4 
5int main() {
6    // 3 rows, 3 columns matrix
7    constexpr std::size_t ROWS = 3;
8    constexpr std::size_t COLS = 3;
9 
10    std::array<std::array<int, COLS>, ROWS> matrix = {{
11        {1, 2, 3},
12        {4, 5, 6},
13        {7, 8, 9}
14    }};
15 
16    std::cout << "=== 2D Matrix Traversal ===\n";
17    for (std::size_t r = 0; r < ROWS; ++r) {
18        for (std::size_t c = 0; c < COLS; ++c) {
19            std::cout << std::setw(3) << matrix[r][c] << " ";
20        }
21        std::cout << "\n";
22    }
23 
24    // Calculating Main Diagonal Sum (Trace)
25    int diagonalSum = 0;
26    for (std::size_t i = 0; i < ROWS; ++i) {
27        diagonalSum += matrix[i][i];
28    }
29    std::cout << "Diagonal Sum (1 + 5 + 9): " << diagonalSum << "\n";
30 
31    return 0;
32}

⚡ Cache Locality & Row-Major Order

C++ stores multi-dimensional arrays in row-major order in memory:

1[Row 0, Col 0] [Row 0, Col 1] [Row 0, Col 2] [Row 1, Col 0] ...

Always iterate through rows in the outer loop and columns in the inner loop to exploit CPU cache line prefetching.

Next Lesson

Project 1: Scientific Calculator with Memory Registers

Continue learning with hands-on practice, examples, and exercises in the upcoming topic.

Related Lessons

Previous Lesson	Next Lesson
Fixed-Size Arrays with std::array vs C-Style Arrays	Project 1: Scientific Calculator with Memory Registers

Practice Quiz

Test your understanding of this lesson with 1 questions. Each question has one correct answer.

Previous Next