BruteForceMethod.cs

void Main()
{
	// Example cost matrix
	int[,] matrix = {{7, 0, 8},
					{15, 2, 7},
					{5, 3, 5}};

	int n = matrix.GetLength(0);
	int[] permutation = new int[n];
	for (int i = 0; i < n; i++)
	{
		permutation[i] = i;
	}

	int[] minPermutation = new int[n];
	int minCost = int.MaxValue;
	BruteForceMethod bruteForce = new BruteForceMethod();
	// Generate all permutations and find the minimum cost permutation
	bruteForce.Permute(permutation, 0, n, matrix, ref minCost, ref minPermutation);

	// Output the minimum cost and the corresponding permutation
	Console.WriteLine("Minimum Cost: " + minCost);
	Console.Write("Permutation: ");
	for (int i = 0; i < n; i++)
	{
		Console.Write(minPermutation[i] + " ");
	}
}

public class BruteForceMethod
{

	// Function to calculate the total cost of a permutation
	static int CalculateCost(int[,] matrix, int[] permutation)
	{
		int cost = 0;
		int n = matrix.GetLength(0);

		for (int i = 0; i < n; i++)
		{
			cost += matrix[i, permutation[i]];
		}

		return cost;
	}

	// Function to generate all possible permutations
	public void Permute(int[] permutation, int start, int n, int[,] matrix, ref int minCost, ref int[] minPermutation)
	{
		if (start == n - 1)
		{
			int cost = CalculateCost(matrix, permutation);
			if (cost < minCost)
			{
				minCost = cost;
				Array.Copy(permutation, minPermutation, n);
			}
		}
		else
		{
			for (int i = start; i < n; i++)
			{
				int temp = permutation[start];
				permutation[start] = permutation[i];
				permutation[i] = temp;

				Permute(permutation, start + 1, n, matrix, ref minCost, ref minPermutation);

				temp = permutation[start];
				permutation[start] = permutation[i];
				permutation[i] = temp;
			}
		}
	}
}