Matrix Sort

Create a C# console application that generates a square matrix with random integers and sorts its main diagonal elements in ascending order.

Solution

This program demonstrates 2D array manipulation and selective sorting. It creates an N×N matrix filled with random integers, displays the original matrix, sorts only the main diagonal elements using Selection Sort, and then displays the modified matrix with the sorted diagonal.

namespace MatrixSort
{
    internal class Program
    {
        // Printing the matrix to the console
        static void Print(int[,] matrix)
        {
            for (int i = 0; i < matrix.GetLength(0); i++)
            {
                for (int j = 0; j < matrix.GetLength(1); j++)
                {
                    Console.Write($"{matrix[i, j]}\t");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
        }


        static void Main(string[] args)
        {
            Console.Write("N = ");
            var str = Console.ReadLine();
            var N = int.Parse(str!);
            var M = new int[N, N];
            var rnd = new Random();

            // Generating the matrix
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N; j++)
                {
                    M[i, j] = rnd.Next(-10, 10);
                }
            }

            // Initial matrix print
            Print(M);

            // Sorting the diagonal elements
            for (int i = 0; i < N; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    if (M[i, i] > M[j, j])
                    {
                        var tmp = M[i, i];
                        M[i, i] = M[j, j];
                        M[j, j] = tmp;
                    }
                }
            }

            // Final matrix print
            Print(M);
        }
    }
}

Features

• User-defined matrix size (N×N)
• Generates random integers in the range [-10, 9]
• Displays the matrix in a formatted table layout
• Sorts only the main diagonal elements (M[0,0], M[1,1], M[2,2], ...)
• Non-diagonal elements remain unchanged
• Uses Selection Sort algorithm for diagonal sorting
• Clean, tab-separated matrix output

Usage

1. Run the application
2. Enter the desired matrix size (N) when prompted
3. The program will display:
   • The original matrix with random values
   • The matrix after sorting the diagonal elements

Example Output

N = 4
-5      3       7       -2
8       9       1       4
-3      6       -8      0
2       -1      5       3

-8      3       7       -2
8       -5      1       4
-3      6       3       0
2       -1      5       9

Note: In this example, the diagonal values were [-5, 9, -8, 3] and became [-8, -5, 3, 9] after sorting.

How It Works

Matrix Generation

for (int i = 0; i < N; i++)
{
    for (int j = 0; j < N; j++)
    {
        M[i, j] = rnd.Next(-10, 10);
    }
}

Creates an N×N matrix with random integers from -10 to 9.

Diagonal Sorting (Selection Sort)

for (int i = 0; i < N; i++)
{
    for (int j = i + 1; j < N; j++)
    {
        if (M[i, i] > M[j, j])
        {
            var tmp = M[i, i];
            M[i, i] = M[j, j];
            M[j, j] = tmp;
        }
    }
}

This algorithm:

1. Only accesses diagonal elements where row index equals column index (i == j)
2. Compares M[i,i] with all subsequent diagonal elements M[j,j]
3. Swaps elements if they're out of order
4. Leaves all non-diagonal elements unchanged

Matrix Display

The Print() method formats the matrix with tab-separated values for better readability.

Algorithm Details

Selection Sort on Diagonal

• Time Complexity: O(N²) where N is the matrix dimension
• Space Complexity: O(1) - sorts in-place
• Elements sorted: N diagonal elements
• Elements unchanged: N² - N non-diagonal elements

Main Diagonal

In an N×N matrix, the main diagonal consists of elements where the row index equals the column index:

• M[0,0], M[1,1], M[2,2], ..., M[N-1,N-1]

Building and Running

Using Visual Studio

1. Open the project in Visual Studio
2. Press F5 or click "Start" to build and run

Using .NET CLI

dotnet run

Educational Value

This project is excellent for learning:

• 2D arrays (matrices): Creating and manipulating multidimensional arrays
• Matrix concepts: Understanding rows, columns, and diagonals
• Selective sorting: Sorting specific elements without affecting others
• Nested loops: Working with double-nested iterations
• Method extraction: Using helper methods like Print()
• Array indexing: Using GetLength(0) and GetLength(1) for dimensions
• Sorting algorithms: Applying Selection Sort to a subset of data

Technical Notes

• Uses int.Parse() for string-to-integer conversion
• Null-forgiving operator (!) used for ReadLine() result
• Random number range: [-10, 10) (includes -10, excludes 10)
• Matrix elements are tab-separated (\t) for aligned output
• Works with any positive integer matrix size

Possible Extensions

Consider these enhancements:

• Sort secondary diagonal (anti-diagonal)
• Sort specific rows or columns
• Sort in descending order
• Support rectangular matrices (N×M)
• Add matrix operations (transpose, sum, product)

Source Code

Please refer to the GitHub repository.