EditDistance.java

/**
 * An implementation of the edit distance algorithm
 *
 * <p>Time Complexity: O(nm)
 *
 * @author Micah Stairs
*/

public class EditDistance {

  // Computes the cost to convert a string 'a' into a string 'b' using dynamic
  // programming given the insertionCost, deletionCost and substitutionCost, O(nm)
  public static int editDistance(
      String a, String b, int insertionCost, int deletionCost, int substitutionCost) {

    final int AL = a.length(), BL = b.length();
    int[][] arr = new int[AL + 1][BL + 1];

    for (int i = 0; i <= AL; i++) {
      for (int j = (i == 0 ? 1 : 0); j <= BL; j++) {

        int min = Integer.MAX_VALUE;

        // Substitution
        if (i > 0 && j > 0)
          min = arr[i - 1][j - 1] + (a.charAt(i - 1) == b.charAt(j - 1) ? 0 : substitutionCost);

        // Deletion
        if (i > 0) min = Math.min(min, arr[i - 1][j] + deletionCost);

        // Insertion
        if (j > 0) min = Math.min(min, arr[i][j - 1] + insertionCost);

        arr[i][j] = min;
      }
    }

    return arr[AL][BL];
  }

  public static void main(String[] args) {

    String a = "abcdefg";
    String b = "abcdefg";

    // The strings are the same so the cost is zero
    System.out.println(editDistance(a, b, 10, 10, 10));

    a = "aaa";
    b = "aaabbb";

    // 10*3 = 30 because of three insertions
    System.out.println(editDistance(a, b, 10, 2, 3));

    a = "1023";
    b = "10101010";

    // Outputs 2*2 + 4*5 = 24 for 2 substitutions and 4 insertions
    System.out.println(editDistance(a, b, 5, 7, 2));

    a = "923456789";
    b = "12345";

    // Outputs 4*4 + 1 = 16 because we need to delete 4
    // characters and perform one substitution
    System.out.println(editDistance(a, b, 2, 4, 1));
  }
}