Damerau Leveneshtein Distance algorithm in C# (idea from https://www.youtube.com/watch?v=MiqoA-yF-0M)

DamerauLeveneshteinDistanceCalculator.cs

using System;

namespace DamerauLeveneshteinDistanceCalculator
{
    static class Program
    {
        public static int ComputeDamerauLeveneshteinDistance(string a, string b)
        {
            if (string.IsNullOrEmpty(a) && string.IsNullOrEmpty(b))
                return 0;

            if (!string.IsNullOrEmpty(a) && string.IsNullOrEmpty(b))
                return a.Length;

            if (string.IsNullOrEmpty(a) && !string.IsNullOrEmpty(b))
                return b.Length;

            var rows = a.Length + 1;
            var columns = b.Length + 1;

            var matrix = new int[rows, columns];
            for (var r = 0; r < rows; r++) matrix[r, 0] = r;
            for (var c = 0; c < columns; c++) matrix[0, c] = c;

            for (int c = 1; c < columns; c++)
            {
                for (int r = 1; r < rows; r++)
                {
                    if (a[r - 1] == b[c - 1])
                    {
                        matrix[r, c] = matrix[r - 1, c - 1];
                    }
                    else
                    {
                        var replace = matrix[r - 1, c - 1];
                        var insertion = matrix[r - 1, c];
                        var deletion = matrix[r, c - 1];

                        matrix[r, c] = Math.Min(replace, Math.Min(insertion, deletion)) + 1;
                    }
                }
            }

            return matrix[rows - 1, columns - 1];
        }
        
        static void Main()
        {
            Console.WriteLine($"ali, alireza: {ComputeDamerauLeveneshteinDistance("ali", "alireza")}");
            Console.WriteLine($"jalal, kamal: {ComputeDamerauLeveneshteinDistance("jalal", "kamal")}");
            Console.WriteLine($"mohammad, mammad: {ComputeDamerauLeveneshteinDistance("mohammad", "mammad")}");
            Console.WriteLine($"jalal, jalal: {ComputeDamerauLeveneshteinDistance("jalal", "jalal")}");
            Console.ReadKey();
        }
    }
}