Dynamic Programming Approach

When it comes to calculating edit distance between two strings, the dynamic programming algorithm is a commonly used approach. This algorithm takes advantage of overlapping subproblems and optimal substructure properties to efficiently calculate the edit distance.

The dynamic programming approach uses a bottom-up strategy to build a matrix that represents the edit distance between substrings of the two input strings. Each cell in the matrix represents the minimum number of operations required to transform one substring into another.

The algorithm starts by initializing the first row and first column of the matrix with incremental values representing the number of deletions or insertions required.

Then, it iterates over each cell of the matrix, comparing the characters of the substrings. If the characters match, the value in the current cell is set to the diagonal cell's value. If the characters don't match, the value in the current cell is set to the minimum value among the adjacent cells plus 1 (representing the cost of substitution).

Finally, the bottom-right cell of the matrix represents the edit distance between the two input strings.

Here's an example implementation of the dynamic programming algorithm in C#:

1{code}

In this example, we have two strings: "kitten" and "sitting". We calculate the edit distance between them using the EditDistanceCalculator class. The result is printed to the console.

The dynamic programming approach is a powerful technique for efficiently solving problems related to string manipulation and is widely used in various applications, such as spell checking, DNA sequence alignment, and text comparison.

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class EditDistanceCalculator {

  public static int CalculateEditDistance(string s1, string s2) {

    int[,] dp = new int[s1.Length + 1, s2.Length + 1];

​

    for (int i = 0; i <= s1.Length; i++) {

      for (int j = 0; j <= s2.Length; j++) {

        if (i == 0) {

          dp[i, j] = j;

        } else if (j == 0) {

          dp[i, j] = i;

        } else if (s1[i - 1] == s2[j - 1]) {

          dp[i, j] = dp[i - 1, j - 1];

        } else {

          dp[i, j] = 1 + Math.Min(dp[i, j - 1], Math.Min(dp[i - 1, j], dp[i - 1, j - 1]));

        }

      }

    }

​

    return dp[s1.Length, s2.Length];

  }

}

​

string s1 = "kitten";

string s2 = "sitting";

int editDistance = EditDistanceCalculator.CalculateEditDistance(s1, s2);

Console.WriteLine("The edit distance between '" + s1 + "' and '" + s2 + "' is: " + editDistance);