# C# Levenshtein Distance

Implement the Levenshtein distance algorithm and compute edit distances.**Levenshtein.** In 1965 Vladmir Levenshtein created a distance algorithm. This tells us the number of edits needed to turn one string into another. With Levenshtein distance, we measure similarity and match approximate strings with fuzzy logic.

**Info:** Returns the number of character edits (removals, inserts, replacements) that must occur to get from string A to string B.

**Example.** First, credit at the conceptual level goes to Vladimir Levenshtein. This code uses a two-dimensional array instead of a jagged array because the space required will only have one width and one height.

**Tip:** The two-dimensional array requires fewer allocations upon the managed heap and may be faster in this context.

2D Array**Static:** This Compute method doesn't need to store state or instance data, which means you can declare it as static.

Static**Verify:** You can verify the algorithm's correctness using a computer science textbook.

**C# program that implements the algorithm**
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

**Example 2.** Continuing on, we call the method. You will often want to compare multiple strings with the Levenshtein algorithm. The example here shows how to compare strings in a loop. We use a List of string arrays.

ListArray**C# program that calls Levenshtein in loop**
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

**Notes, edit distance.** Here is a table showing the edit distance of some word pairs. It is important to verify the correctness of all computer code (particularly from websites).

**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.

**Summary.** With the Levenshtein distance algorithm, we implement approximate string matching. The difference between two strings is not represented as true or false, but as the number of steps needed to get from one to the other.

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