Multi dimensional array in Data Structures

Multi-dimensional Array: An Overview

In computer programming, data organization plays a crucial role in efficient algorithmic design and execution and Data Structures and Algorithms (DSA) provided it better way, enabling efficient problem-solving and algorithmic design. In this DSA tutorial, we'll explore the concept of multi-dimensional arrays, their characteristics, and their applications in DSA. You might have already come across arrays while learning arrays in C and arrays in C++.

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What is a multi-dimensional array?

The powerful tool that programmers often uses for handling structured data is the multi-dimensional array. Unlike traditional one-dimensional arrays, multi-dimensional arrays provide a way to organize data in multiple dimensions, offering a more versatile and expressive approach to solving complex problems.

A multi-dimensional array is essentially an array of arrays, extending beyond the concept of a one-dimensional array. While a one-dimensional array is a linear collection of elements, a multi-dimensional array can be visualized as a matrix or a grid, where data is arranged in rows and columns. Commonly used dimensions include two-dimensional (2D) arrays, three-dimensional (3D) arrays, and even higher-dimensional arrays.

syntax

               array_name[size1][size2]....[sizeN];

• data_type: The data type that will be stored in the array.
• array_name: The array's name.
• size1, size2,..., sizeN: Dimensional sizes.

Common operations on Multidimensional array

1. Accessing Elements

Retrieving the value stored at a specific position within the multi-dimensional array. This involves providing the indices corresponding to the desired element's location. In a 2D array, for example, access might be performed using array[row][column].

int value = array[2][3];

2. Insertion and Modification

Changing the value of an existing element or inserting a new element at a particular position in the array.

array[1][2] = 42;

3. Initialization

Assigning initial values to the elements of the array during its creation or later in the program.

            int array = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];              

4. Traversal

Iterating through all elements of the multi-dimensional array to perform operations on each element. This is often done using nested loops, one for each dimension.

            for (int i = 0; i < rows; i++) {
    for (int j = 0; j < columns; j++) {
        // Perform operations on array[i][j]
    }
}              

5. Search

Finding the position or value of a specific element within the array.

            index = next((i, j) for i, row in enumerate(array) for j, val in enumerate(row) if val == 42)

6. Deletion

Removing elements from the array. Note that in many programming languages, resizing a multi-dimensional array might involve creating a new array and copying the desired elements.

            array[1][2] = 0;  // Set the value to a default or placeholder value

7. Transpose

Creating a new array where the rows and columns are swapped. This is a common operation in linear algebra.

            for (int i = 0; i < rows; i++) {
    for (int j = 0; j < columns; j++) {
        transposed[j][i] = array[i][j];
    }
}

8. Matrix Multiplication

Specific to 2D arrays, matrix operations such as addition, subtraction, and multiplication are common.

            result = [[sum(a * b for a, b in zip(row, col)) for col in zip(*matrix2)] for row in matrix1]

Read More - Data Structure Interview Questions for Experienced

Examples of Two-dimensional Array

Below is an example of a two-dimensional array in Java, representing a matrix and performing a simple operation on it:

    def main():
    # Declare and initialize a 2D array (3x3 matrix)
    matrix = [
        [1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]
    ]

    # Print the original matrix
    print("Original Matrix:")
    print_matrix(matrix)

    # Example operation: Multiply each element by 2
    multiply_matrix_by_scalar(matrix, 2)

    # Print the modified matrix
    print("\nModified Matrix (multiplied by 2):")
    print_matrix(matrix)

# Function to print a 2D matrix
def print_matrix(matrix):
    for row in matrix:
        for element in row:
            print(element, end=" ")
        print()

# Function to multiply each element of the matrix by a scalar
def multiply_matrix_by_scalar(matrix, scalar):
    for i in range(len(matrix)):
        for j in range(len(matrix[0])):
            matrix[i][j] *= scalar

if __name__ == "__main__":
    main()
        

  public class MultiDimensionalArrayExample {

    public static void main(String[] args) {
        // Declare and initialize a 2D array (3x3 matrix)
        int[][] matrix = {
            {1, 2, 3},
            {4, 5, 6},
            {7, 8, 9}
        };

        // Print the original matrix
        System.out.println("Original Matrix:");
        printMatrix(matrix);

        // Example operation: Multiply each element by 2
        multiplyMatrixByScalar(matrix, 2);

        // Print the modified matrix
        System.out.println("\nModified Matrix (multiplied by 2):");
        printMatrix(matrix);
    }

    // Function to print a 2D matrix
    private static void printMatrix(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                System.out.print(matrix[i][j] + " ");
            }
            System.out.println();
        }
    }

    // Function to multiply each element of the matrix by a scalar
    private static void multiplyMatrixByScalar(int[][] matrix, int scalar) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                matrix[i][j] *= scalar;
            }
        }
    }
}
        

#include 

// Function prototypes
void printMatrix(int matrix[3][3]);
void multiplyMatrixByScalar(int matrix[3][3], int scalar);

int main() {
    // Declare and initialize a 2D array (3x3 matrix)
    int matrix[3][3] = {
        {1, 2, 3},
        {4, 5, 6},
        {7, 8, 9}
    };

    // Print the original matrix
    std::cout << "Original Matrix:" << std::endl;
    printMatrix(matrix);

    // Example operation: Multiply each element by 2
    multiplyMatrixByScalar(matrix, 2);

    // Print the modified matrix
    std::cout << "\nModified Matrix (multiplied by 2):" << std::endl;
    printMatrix(matrix);

    return 0;
}

// Function to print a 2D matrix
void printMatrix(int matrix[3][3]) {
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            std::cout << matrix[i][j] << " ";
        }
        std::cout << std::endl;
    }
}

// Function to multiply each element of the matrix by a scalar
void multiplyMatrixByScalar(int matrix[3][3], int scalar) {
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            matrix[i][j] *= scalar;
        }
    }
}
        

Output

Original Matrix:
1 2 3 
4 5 6 
7 8 9 

Modified Matrix (multiplied by 2):
2 4 6 
8 10 12 
14 16 18 
      

Applications in DSA

Matrix Operations

Multi-dimensional arrays, especially 2D arrays, are extensively used in solving matrix-related problems. Matrix multiplication, addition, inversion, and other operations crucial in linear algebra find straightforward implementation through multi-dimensional arrays.

Dynamic Programming

Dynamic programming, a key paradigm in algorithm design, often involves solving problems by breaking them down into subproblems and storing the results. Multi-dimensional arrays serve as dynamic programming tables, enabling efficient memorization and reducing redundant computations.

Graph Algorithms

Graph-related problems frequently utilize 2D arrays to represent adjacency matrices. Whether traversing graphs, finding shortest paths, or detecting cycles, multi-dimensional arrays provide an organized and efficient means to represent and process graph structures.

Image Processing

In DSA, multi-dimensional arrays are employed for image manipulation and processing. Pixel values in images can be stored in 2D arrays, allowing for efficient application of filters, transformations, and other image-processing algorithms.

Summary

Multi-dimensional arrays evolve as a flexible and efficient tool in the developing environment of Data Structures and Algorithms. This article briefly describes the multi-dimensional array in DSA. We talked about its definition, syntax, declaration, and initialization. We hope this tutorial has helped you understand the one-dimensional array problem in C. You can quickly store and access data in a structurally consistent manner by utilizing an array. This will help make your code more efficient and improve your skills as a programmer.