org.apache.commons.text.similarity

## Class LongestCommonSubsequence

- java.lang.Object
- - org.apache.commons.text.similarity.LongestCommonSubsequence

- All Implemented Interfaces:
    SimilarityScore<Integer>

      public class LongestCommonSubsequence
      extends Object
      implements SimilarityScore<Integer>

  A similarity algorithm indicating the length of the longest common subsequence between two strings.

  The Longest common subsequence algorithm returns the length of the longest subsequence that two strings have in common. Two strings that are entirely different, return a value of 0, and two strings that return a value of the commonly shared length implies that the strings are completely the same in value and position. Note. Generally this algorithm is fairly inefficient, as for length m, n of the input `CharSequence`'s `left` and `right` respectively, the runtime of the algorithm is O(m*n).

  This implementation is based on the Longest Commons Substring algorithm from https://en.wikipedia.org/wiki/Longest_common_subsequence_problem.

  For further reading see:

  Lothaire, M. Applied combinatorics on words. New York: Cambridge U Press, 2005. 12-13

  Since:
    1.0

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `LongestCommonSubsequence()`

  - ### Method Summary

    All Methods Instance Methods Concrete Methods
    Modifier and Type | Method and Description
    --- | ---
    `Integer` | `apply(CharSequence left, CharSequence right)` Calculates longestCommonSubsequence similarity score of two `CharSequence`'s passed as input.
    `CharSequence` | `logestCommonSubsequence(CharSequence left, CharSequence right)` Computes the longestCommonSubsequence between the two `CharSequence`'s passed as input.
    `int[][]` | `longestCommonSubstringLengthArray(CharSequence left, CharSequence right)` Computes the lcsLengthArray for the sake of doing the actual lcs calculation.

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### LongestCommonSubsequence

          public LongestCommonSubsequence()

  - ### Method Detail

    - #### apply

          public Integer apply(CharSequence left,
                               CharSequence right)

      Calculates longestCommonSubsequence similarity score of two `CharSequence`'s passed as input.
      Specified by:
        `apply` in interface `SimilarityScore<Integer>`
      Parameters:
        `left` - first character sequence
        `right` - second character sequence
      Returns:
        longestCommonSubsequenceLength
      Throws:
        `IllegalArgumentException` - if either String input `null`

    - #### logestCommonSubsequence

          public CharSequence logestCommonSubsequence(CharSequence left,
                                                      CharSequence right)

      Computes the longestCommonSubsequence between the two `CharSequence`'s passed as input.

      Note, a substring and subsequence are not necessarily the same thing. Indeed, `abcxyzqrs` and `xyzghfm` have both the same common substring and subsequence, namely `xyz`. However, `axbyczqrs` and `abcxyzqtv` have the longest common subsequence `xyzq` because a subsequence need not have adjacent characters.

      For reference, we give the definition of a subsequence for the reader: a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

      Parameters:
        `left` - first character sequence
        `right` - second character sequence
      Returns:
        lcsLengthArray
      Throws:
        `IllegalArgumentException` - if either String input `null`

    - #### longestCommonSubstringLengthArray

          public int[][] longestCommonSubstringLengthArray(CharSequence left,
                                                           CharSequence right)

      Computes the lcsLengthArray for the sake of doing the actual lcs calculation. This is the dynamic programming portion of the algorithm, and is the reason for the runtime complexity being O(m*n), where m=left.length() and n=right.length().
      Parameters:
        `left` - first character sequence
        `right` - second character sequence
      Returns:
        lcsLengthArray

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