C# Levenshtein Distance

Strings may be different yet very similar. With the Levenshtein distance algorithm, we measure similarity and match approximate strings with fuzzy logic. Many projects need this logic, including programs that manage prescription drugs, spell-checkers, suggestion searches and plagiarism detectors. This implementation uses the C# language.

Levenshtein distance computations

Words:                ant, aunt
Levenshtein distance: 1
Note:                 Only 1 edit is needed.
		      The 'u' must be added at index 2.

Words:                Samantha, Sam
Levenshtein distance: 5
Note:                 The final 5 letters must be removed.

Words:                Flomax, Volmax
Levenshtein distance: 3
Note:                 The first 3 letters must be changed
		      Drug names are commonly confused.

Levenshtein algorithm

First, credit at the conceptual level goes to Vladimir Levenshtein, a Russian scientist. This code uses a two-dimensional array instead of a jagged array because the space required will only have one width and one height. The two-dimensional array requires fewer allocations upon the managed heap and may be faster in this context.

Program that implements the algorithm [C#]

using System;

/// <summary>
/// Contains approximate string matching
/// </summary>
static class LevenshteinDistance
{
    /// <summary>
    /// Compute the distance between two strings.
    /// </summary>
    public static int Compute(string s, string t)
    {
	int n = s.Length;
	int m = t.Length;
	int[,] d = new int[n + 1, m + 1];

	// Step 1
	if (n == 0)
	{
	    return m;
	}

	if (m == 0)
	{
	    return n;
	}

	// Step 2
	for (int i = 0; i <= n; d[i, 0] = i++)
	{
	}

	for (int j = 0; j <= m; d[0, j] = j++)
	{
	}

	// Step 3
	for (int i = 1; i <= n; i++)
	{
	    //Step 4
	    for (int j = 1; j <= m; j++)
	    {
		// Step 5
		int cost = (t[j - 1] == s[i - 1]) ? 0 : 1;

		// Step 6
		d[i, j] = Math.Min(
		    Math.Min(d[i - 1, j] + 1, d[i, j - 1] + 1),
		    d[i - 1, j - 1] + cost);
	    }
	}
	// Step 7
	return d[n, m];
    }
}

class Program
{
    static void Main()
    {
	Console.WriteLine(LevenshteinDistance.Compute("aunt", "ant"));
	Console.WriteLine(LevenshteinDistance.Compute("Sam", "Samantha"));
	Console.WriteLine(LevenshteinDistance.Compute("flomax", "volmax"));
    }
}

Output

1
5
3

Description. The Levenshtein method is static—this Compute method doesn't need to store state or instance data, which means you can declare it as static. This can also improve performance, avoiding callvirt instructions. You can verify that the above implementation is the standard version of Levenshtein by looking at one of the textbooks you were supposed to read.

Static classes. This algorithm is stateless, which means it doesn't store instance data and therefore can be put in a static class. Static classes are easier to add to new projects than separate methods.

Usage

Continuing on, we see how you can call the method in your C# programs. You will often want to compare multiple strings with the Levenshtein algorithm. The example here shows how you can compare strings in a loop; we use a List of string[] arrays.

Program that calls Levenshtein in loop [C#]

static void Main()
{
    List<string[]> l = new List<string[]>
    {
	new string[]{"ant", "aunt"},
	new string[]{"Sam", "Samantha"},
	new string[]{"clozapine", "olanzapine"},
	new string[]{"flomax", "volmax"},
	new string[]{"toradol", "tramadol"},
	new string[]{"kitten", "sitting"}
    };

    foreach (string[] a in l)
    {
	int cost = Compute(a[0], a[1]);
	Console.WriteLine("{0} -> {1} = {2}",
	    a[0],
	    a[1],
	    cost);
    }
}

Output

ant -> aunt = 1
Sam -> Samantha = 5
clozapine -> olanzapine = 3
flomax -> volmax = 3
toradol -> tramadol = 3
kitten -> sitting = 3

Resource

You can visit an excellent page about the Levenshtein distance and many implementations of it. The page and its links provides a more detailed reference.

Summary

We saw the famous Levenshtein Distance algorithm, adapted and optimized for the C# programming language. This code implements approximate string matching: the difference between two strings is not represented as true or false, but as an integer indicating the number of steps needed to get from one to the other. As a reminder, the brilliance of the algorithm comes from Dr. Levenshtein.