Traversing elements present in a 2-Dimensional Array/Matrix

In this article we will go through code examples in different languages to traverse/iterate a 2 dimensional array. Traversal or iterating means visiting or accessing all elements in present in the given array.

Let’s consider the use-case we used in previous articles: There are 4 students in a class and we need to store marks obtained by each student in 3 different subjects. In order to achieve this, we create a 2-dimensional array with 4 rows and 3 columns, Each row contains marks in all the subjects obtained by the student.

[
 [81, 75, 92], // Student-0's marks
 [86, 94, 79], // Student-1's marks
 [84, 90, 75], // Student-2's marks
 [79, 75, 89]  // Student-3's marks
]

Now let’s look at different ways to traversing or visiting all the elements in the 2 dimensional array.

Traversing a 2D Array in Row Major Order

In row-major order, we visit the elements of a 2D array row by row. Starting with the first row, we access all elements from left to right. Then, we move to the next row and repeat the process until all rows have been traversed. This is a natural way to traverse the array if the focus is on operations performed for each student (like calculating overall scores for each student).

Algorithm:

Use two nested loops: the outer loop to iterate through rows, and the inner loop to iterate through columns within each row.
The outer loop which iterates through each row starts from 0 (index of the first row) and ends at the index of the last row (number of rows - 1)
The inner loop which iterates through each column starts from 0 (index of the first column) and ends at the index of the last column (number of columns - 1)
Process Element: Inside the nested loops, access the current element using the current row and current column indices.

Code:


# Initialize a 2D array containing student marks
students_marks = [
    [81, 75, 92],  # Student-0's marks
    [86, 94, 79],  # Student-1's marks
    [84, 90, 75],  # Student-2's marks
    [79, 75, 89]   # Student-3's marks
]

# Iterate through each row (student)
for row_index in range(len(students_marks)):
  # Print that the following marks are for the current student
  print(f"The following marks are for student-{row_index}:")
  
  # Iterate through each column (subject)
  for col_index in range(len(students_marks[row_index])):
    # Get the score for the current subject
    score = students_marks[row_index][col_index]
    
    # Print the score for the current subject
    print(f"The score for subject-{col_index} is {score}")


#include <stdio.h>
#include <stdlib.h>

int main() {
  // Initialize a 2D array containing student marks
  int students_marks[4][3] = {
    {81, 75, 92},  // Student-0's marks
    {86, 94, 79},  // Student-1's marks
    {84, 90, 75},  // Student-2's marks
    {79, 75, 89}   // Student-3's marks
  };

  // Iterate through each row (student)
  for (int row_index = 0; row_index < 4; row_index++) {
    // Print that the following marks are for the current student
    printf("The following marks are for student-%d:\n", row_index);

    // Iterate through each column (subject)
    for (int col_index = 0; col_index < 3; col_index++) {
      // Get the score for the current subject
      int score = students_marks[row_index][col_index];

      // Print the score for the current subject
      printf("The score for subject-%d is %d\n", col_index, score);
    }
  }

  return 0;
}


#include <iostream>
#include <vector>

int main() {
  // Initialize a 2D vector containing student marks
  std::vector<std::vector<int>> students_marks = {
    {81, 75, 92},  // Student-0's marks
    {86, 94, 79},  // Student-1's marks
    {84, 90, 75},  // Student-2's marks
    {79, 75, 89}   // Student-3's marks
  };

  // Iterate through each row (student)
  for (size_t row_index = 0; row_index < students_marks.size(); row_index++) {
    // Print that the following marks are for the current student
    std::cout << "The following marks are for student-" << row_index << ":" << std::endl;

    // Iterate through each column (subject)
    for (size_t col_index = 0; col_index < students_marks[row_index].size(); col_index++) {
      // Get the score for the current subject
      int score = students_marks[row_index][col_index];

      // Print the score for the current subject
      std::cout << "The score for subject-" << col_index << " is " << score << std::endl;
    }
  }

  return 0;
}


// Initialize a 2D array containing student marks
const students_marks = [
  [81, 75, 92],  // Student-0's marks
  [86, 94, 79],  // Student-1's marks
  [84, 90, 75],  // Student-2's marks
  [79, 75, 89]   // Student-3's marks
];

// Iterate through each row (student)
for (let row_index = 0; row_index < students_marks.length; row_index++) {
  // Print that the following marks are for the current student
  console.log(`The following marks are for student-${row_index}:`);
  
  // Iterate through each column (subject)
  for (let col_index = 0; col_index < students_marks[row_index].length; col_index++) {
    // Get the score for the current subject
    const score = students_marks[row_index][col_index];
    
    // Print the score for the current subject
    console.log(`The score for subject-${col_index} is ${score}`);
  }
}


// Initialize a 2D array containing student marks
int[][] students_marks = {
    {81, 75, 92},  // Student-0's marks
    {86, 94, 79},  // Student-1's marks
    {84, 90, 75},  // Student-2's marks
    {79, 75, 89}   // Student-3's marks
};

// Iterate through each row (student)
for (int row_index = 0; row_index < students_marks.length; row_index++) {
  // Print that the following marks are for the current student
  System.out.println("The following marks are for student-" + row_index + ":");
  
  // Iterate through each column (subject)
  for (int col_index = 0; col_index < students_marks[row_index].length; col_index++) {
    // Get the score for the current subject
    int score = students_marks[row_index][col_index];
    
    // Print the score for the current subject
    System.out.println("The score for subject-" + col_index + " is " + score);
  }
}

Traversing a 2D Array in Column Major Order

In column-major order, we traverse the 2D array by visiting elements column by column. Within each column, we move from the top element down to the bottom element. Once a column is traversed, we move to the next column and repeat the process. This method is helpful if your focus is on operations performed for each subject (like calculating the average score for a subject).

Algorithm:

Use two nested loops: the outer loop to iterate through columns, and the inner loop to iterate through all rows for each column.
The outer loop which iterates through each column starts from 0 (index of the first column) and ends at the index of the last column (number of columns - 1)
The inner loop which iterates through each row starts from 0 (index of the first row) and ends at the index of the last row (number of rows - 1)
Process Element: Inside the nested loops, access the current element using the current row and current column indices.

code:


# Initialize a 2D array to store student marks
students_marks = [
    [81, 75, 92],  # Student-0's marks
    [86, 94, 79],  # Student-1's marks
    [84, 90, 75],  # Student-2's marks
    [79, 75, 89]   # Student-3's marks
]

# Iterate through the columns (subjects)
for col_index in range(len(students_marks[0])):
  # Print the subject index
  print(f"The following marks are for subject-{col_index}")
  
  # Iterate through the rows (students)
  for row_index in range(len(students_marks)):
    # Get the score for the current student and subject
    score = students_marks[row_index][col_index]
    
    # Print the score for the current student
    print(f"The score for student-{row_index} is {score}")


#include <stdio.h>
#include <stdlib.h>

int main() {
  // Initialize a 2D array to store student marks
  int students_marks[4][3] = {
    {81, 75, 92},  // Student-0's marks
    {86, 94, 79},  // Student-1's marks
    {84, 90, 75},  // Student-2's marks
    {79, 75, 89}   // Student-3's marks
  };

  // Iterate through the columns (subjects)
  for (int col_index = 0; col_index < 3; col_index++) {
    // Print the subject index
    printf("The following marks are for subject-%d\n", col_index);

    // Iterate through the rows (students)
    for (int row_index = 0; row_index < 4; row_index++) {
      // Get the score for the current student and subject
      int score = students_marks[row_index][col_index];

      // Print the score for the current student
      printf("The score for student-%d is %d\n", row_index, score);
    }
  }

  return 0;
}


#include <iostream>
#include <vector>

int main() {
  // Initialize a 2D vector to store student marks
  std::vector<std::vector<int>> students_marks = {
    {81, 75, 92},  // Student-0's marks
    {86, 94, 79},  // Student-1's marks
    {84, 90, 75},  // Student-2's marks
    {79, 75, 89}   // Student-3's marks
  };

  // Iterate through the columns (subjects)
  for (int col_index = 0; col_index < students_marks[0].size(); col_index++) {
    // Print the subject index
    std::cout << "The following marks are for subject-" << col_index << std::endl;

    // Iterate through the rows (students)
    for (int row_index = 0; row_index < students_marks.size(); row_index++) {
      // Get the score for the current student and subject
      int score = students_marks[row_index][col_index];

      // Print the score for the current student
      std::cout << "The score for student-" << row_index << " is " << score << std::endl;
    }
  }

  return 0;
}


// Initialize a 2D array to store student marks
const students_marks = [
  [81, 75, 92],  // Student-0's marks
  [86, 94, 79],  // Student-1's marks
  [84, 90, 75],  // Student-2's marks
  [79, 75, 89]   // Student-3's marks
];

// Iterate through the columns (subjects)
for (let col_index = 0; col_index < students_marks[0].length; col_index++) {
  // Print the subject index
  console.log(`The following marks are for subject-${col_index}`);
  
  // Iterate through the rows (students)
  for (let row_index = 0; row_index < students_marks.length; row_index++) {
    // Get the score for the current student and subject
    const score = students_marks[row_index][col_index];
    
    // Print the score for the current student
    console.log(`The score for student-${row_index} is ${score}`);
  }
}


public class Main {
  public static void main(String[] args) {
    // Initialize a 2D array to store student marks
    int[][] students_marks = {
        {81, 75, 92},  // Student-0's marks
        {86, 94, 79},  // Student-1's marks
        {84, 90, 75},  // Student-2's marks
        {79, 75, 89}   // Student-3's marks
    };

    // Iterate through the columns (subjects)
    for (int col_index = 0; col_index < students_marks[0].length; col_index++) {
      // Print the subject index
      System.out.println("The following marks are for subject-" + col_index);

      // Iterate through the rows (students)
      for (int row_index = 0; row_index < students_marks.length; row_index++) {
        // Get the score for the current student and subject
        int score = students_marks[row_index][col_index];

        // Print the score for the current student
        System.out.println("The score for student-" + row_index + " is " + score);
      }
    }
  }
}