# Class LongestCommonSubsequence

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

All Implemented Interfaces:
  `BiFunction<CharSequence, CharSequence, Integer>, ObjectSimilarityScore<CharSequence, Integer>, 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).

As of version 1.10, a more space-efficient of the algorithm is implemented. The new algorithm has linear space complexity instead of quadratic. However, time complexity is still quadratic in the size of input strings.

The implementation is based on Hirschberg's Longest Commons Substring algorithm (cited below).

For further reading see:

- Lothaire, M. Applied combinatorics on words. New York: Cambridge U Press, 2005. 12-13
- D. S. Hirschberg, "A linear space algorithm for computing maximal common subsequences," CACM, 1975, pp. 341--343.

Since:
  1.0

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `LongestCommonSubsequence()`
  Creates a new instance.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `Integer`
  `apply(CharSequence left, CharSequence right)`
  Computes the longest common subsequence similarity score of two `CharSequence`'s passed as input.
  `CharSequence`
  `logestCommonSubsequence(CharSequence left, CharSequence right)`
  Deprecated.
  Deprecated as of 1.2 due to a typo in the method name.
  `CharSequence`
  `longestCommonSubsequence(CharSequence left, CharSequence right)`
  Computes the longest common subsequence between the two `CharSequence`'s passed as input.
  `int[][]`
  `longestCommonSubstringLengthArray(CharSequence left, CharSequence right)`
  Deprecated.
  Deprecated as of 1.10.

  ### Methods inherited from class Object

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

  ### Methods inherited from interface BiFunction

  `andThen`

- ## Constructor Details

  - ### LongestCommonSubsequence

    public LongestCommonSubsequence()
    Creates a new instance.

- ## Method Details

  - ### apply

    public Integer apply(CharSequence left, CharSequence right)
    Computes the longest common subsequence similarity score of two `CharSequence`'s passed as input.

    This method implements a more efficient version of LCS algorithm which has quadratic time and linear space complexity.

    This method is based on newly implemented `algorithmB(CharSequence, CharSequence)`. An evaluation using JMH revealed that this method is almost two times faster than its previous version.

    Specified by:
      `apply` in interface `BiFunction<CharSequence, CharSequence, Integer>`
    Specified by:
      `apply` in interface `ObjectSimilarityScore<CharSequence, Integer>`
    Specified by:
      `apply` in interface `SimilarityScore<Integer>`
    Parameters:
      `left` - first character sequence.
      `right` - second character sequence.
    Returns:
      length of the longest common subsequence of `left` and `right`.
    Throws:
      `IllegalArgumentException` - if either String input `null`.

  - ### logestCommonSubsequence

    @Deprecated public CharSequence logestCommonSubsequence(CharSequence left, CharSequence right)
    Deprecated.
    Deprecated as of 1.2 due to a typo in the method name. Use `longestCommonSubsequence(CharSequence, CharSequence)` instead. This method will be removed in 2.0.
    Computes the longest common subsequence 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:
      the longest common subsequence found.
    Throws:
      `IllegalArgumentException` - if either String input `null`.

  - ### longestCommonSubsequence

    public CharSequence longestCommonSubsequence(CharSequence left, CharSequence right)
    Computes the longest common subsequence between the two `CharSequence`'s passed as input.

    This method implements a more efficient version of LCS algorithm which although has quadratic time, it has linear space complexity.

    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:
      the longest common subsequence found.
    Throws:
      `IllegalArgumentException` - if either String input `null`.
    Since:
      1.2

  - ### longestCommonSubstringLengthArray

    @Deprecated public int[][] longestCommonSubstringLengthArray(CharSequence left, CharSequence right)
    Deprecated.
    Deprecated as of 1.10. A more efficient implementation for calculating LCS is now available. Use `longestCommonSubsequence(CharSequence, CharSequence)` instead to directly calculate the LCS. This method will be removed in 2.0.
    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:
      longest common substring length array.