Levenshtein Distance

 原文地址:http://www.dotnetperls.com/levenshtein

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.

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  in  t-sql

SET QUOTED_IDENTIFIER ON 
GO
SET ANSI_NULLS ON 
GO

CREATE FUNCTION edit_distance_within(@s nvarchar(4000), @t nvarchar(4000), @d int)
RETURNS int
AS
BEGIN
  DECLARE @sl int, @tl int, @i int, @j int, @sc nchar, @c int, @c1 int,
    @cv0 nvarchar(4000), @cv1 nvarchar(4000), @cmin int
  SELECT @sl = LEN(@s), @tl = LEN(@t), @cv1 = '', @j = 1, @i = 1, @c = 0
  WHILE @j <= @tl
    SELECT @cv1 = @cv1 + NCHAR(@j), @j = @j + 1
  WHILE @i <= @sl
  BEGIN
    SELECT @sc = SUBSTRING(@s, @i, 1), @c1 = @i, @c = @i, @cv0 = '', @j = 1, @cmin = 4000
    WHILE @j <= @tl
    BEGIN
      SET @c = @c + 1
      SET @c1 = @c1 - CASE WHEN @sc = SUBSTRING(@t, @j, 1) THEN 1 ELSE 0 END
      IF @c > @c1 SET @c = @c1
      SET @c1 = UNICODE(SUBSTRING(@cv1, @j, 1)) + 1
      IF @c > @c1 SET @c = @c1
      IF @c < @cmin SET @cmin = @c
      SELECT @cv0 = @cv0 + NCHAR(@c), @j = @j + 1
    END
    IF @cmin > @d BREAK
    SELECT @cv1 = @cv0, @i = @i + 1
  END
  RETURN CASE WHEN @cmin <= @d AND @c <= @d THEN @c ELSE -1 END
END
GO

　　

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

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.

Tip: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.

Static Class

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.

Levenshtein Distance [External]

Summary

We saw the famous Levenshtein Distance algorithm, optimized for the C# 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.

Algorithms