/2Dimensional_Arrays

Experiment 8

Primary LanguageC++

2 Dimensional Arrays

Experiment 8

AIM

To study and implement 2 Dimensional arrays in C++

Software Used

VS Code

Theory

A 2D array is a data structure that with a grid, where each element is identified by two indices: a row index and a column index.

int matrix[3][4] = {
    {1, 2, 3, 4},
    {5, 6, 7, 8},
    {9, 10, 11, 12}
};

Features of 2D array:

  • Structure: A 2D array is essentially an array of arrays, where each element of the outer array is another array representing a row in the matrix.
  • Indexing: Elements in a 2D array are accessed using two indices.
  • Contiguous Memory: In C++, a 2D array is stored in memory as a continuous block of memory.
  • Operations: Various operations can be performed on 2D arrays, including addition, subtraction, and multiplication (in the case of matrices).

Uses of 2D Arrays:

  • Used in applications including computer graphics, image processing.
  • Used in scientific simulations, spreadsheets.
  • Used in mathematical representation of matrix. eg-
1 2 3
4 5 6
7 8 9

Algorithm

Input and Display a 2D Array.

  1. Start

  2. Input:

    • Ask user to enter the number of rows (r).
    • Prompt user to enter the number of columns (c).

  3. Initialize:

    • Create a 2D array arr[r][c].

  4. Input Elements:

    • For each row i from 0 to r-1:
      • For each column j from 0 to c-1:
        • Ask user to enter the element at position (i+1, j+1).
        • Store the entered value in arr[i][j].

  5. Display Matrix:

    • For each row i from 0 to r-1:
      • For each column j from 0 to c-1:
        • Print arr[i][j] followed by a space.
      • Print a newline after each row.

  6. End

Sum of Diagonal Elements in a Square Matrix

  1. Start

  2. Initialize:

    • Define r (number of rows) to 3.
    • Define c (number of columns) to 3.
    • Define a 2D array a with the following elements: 
      1 2 3
5 7 4
5 9 1
    • Set sum to 0.

  3. Check matrix:

    • If r is equal to c (i.e., the matrix is square):

      1. Display Matrix:

        • For each row i from 0 to r-1:
          • For each column j from 0 to c-1:
            • Print the element a[i][j] followed by a space.
          • Print a newline after each row.

      2. Sum of Diagonals:

        • For each row i from 0 to r-1:
          • For each column j from 0 to c-1:
            • If i is equal to j (i.e., the element is on the main diagonal):
              • Add a[i][j] to sum.

      3. Display Result:

        • Print "The sum of diagonals is: " followed by the value of sum.

    • Else if r is not equal to c:

      • Print "Input should be square matrix."

  4. End

Sum of Antidiagonals of a 3x3 Matrix

  1. Start

  2. Initialize:

    • Define a matrix a with the following values: 
      1 2 3
5 7 4
5 9 1
    • Set sum to 0.
    • Set r (number of rows) to 3.

  3. Compute Sum of Antidiagonals:

    • For each row i from 0 to 2:
      • For each column j from 0 to 2:
        • If the i + j == r - 1 is true:
          • Add the value of a[i][j] to sum.

  4. Display Result:

    • Print "The sum of antidiagonals is: " followed by the value of sum.

  5. End

Conclusion

We learnt about the use cases of 2 dimensional matrices in C++.