Step by Step solution about How to resolve the algorithm Levenshtein distance step by step in the C# programming language

The provided C# code computes the Levenshtein distance between two given strings, s and t. The Levenshtein distance is a metric for measuring the similarity between two strings. It calculates the minimum number of edits (insertions, deletions, or substitutions) required to transform one string into another.

Here's a detailed breakdown of the code:

1. LevenshteinDistance Method:

   • It takes two strings, s and t, as input.
   • It initializes a two-dimensional array d with dimensions (n+1) x (m+1), where n is the length of s and m is the length of t.
   • It initializes the first row and column of d with values 0, 1, 2, ..., n and 0, 1, 2, ..., m, respectively. This populates the borders of the matrix with the edit distances for transforming an empty string into s or t.
   • It iterates through the matrix, starting from the second row and column, to calculate the Levenshtein distance for each pair of characters.
   • If the characters at the current positions in s and t are the same, no operation is needed, so it copies the value from the previous cell.
   • If the characters are different, it calculates the minimum edit distance among the three options:
     • Deleting the character from s (cost: d[i - 1, j] + 1)
     • Inserting the character in t (cost: d[i, j - 1] + 1)
     • Substituting the character in s with the one in t (cost: d[i - 1, j - 1] + 1)
   • It stores the minimum cost in the current cell d[i, j].
   • Finally, it returns the value at d[n, m], which represents the Levenshtein distance between the entire strings s and t.

2. Main Method:

   • It checks if the command-line arguments contain two strings.
   • If yes, it computes and prints the Levenshtein distance between the two strings.
   • If not, it displays usage instructions.

In summary, this code calculates the minimum number of edits needed to transform one string into another. It is commonly used for various applications, including spell checking, natural language processing, and bioinformatics.

using System;

namespace LevenshteinDistance
{
    class Program
    {
        static int LevenshteinDistance(string s, string t)
        {
            int n = s.Length;
            int m = t.Length;
            int[,] d = new int[n + 1, m + 1];
		
	    if (n == 0)
	    {
		return m;
	    }
	
	    if (m == 0)
	    {
		return n;
	    }

            for (int i = 0; i <= n; i++)
                d[i, 0] = i;
            for (int j = 0; j <= m; j++)
                d[0, j] = j;
			
            for (int j = 1; j <= m; j++)
                for (int i = 1; i <= n; i++)
                    if (s[i - 1] == t[j - 1])
                        d[i, j] = d[i - 1, j - 1];  //no operation
                    else
                        d[i, j] = Math.Min(Math.Min(
                            d[i - 1, j] + 1,    //a deletion
                            d[i, j - 1] + 1),   //an insertion
                            d[i - 1, j - 1] + 1 //a substitution
                            );
            return d[n, m];
        }

        static void Main(string[] args)
        {
            if (args.Length == 2)
                Console.WriteLine("{0} -> {1} = {2}",
                    args[0], args[1], LevenshteinDistance(args[0], args[1]));
            else
                Console.WriteLine("Usage:-\n\nLevenshteinDistance <string1> <string2>");
        }
    }
}