A typescript implementation to find the lcs (Longest Common Subsequence).

The following definition is quoted from Wikipedia (https://en.wikipedia.org/wiki/Longest_common_subsequence_problem):

The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring problem: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The longest common subsequence problem is a classic computer science problem, the basis of data comparison programs such as the diff utility, and has applications in computational linguistics and bioinformatics. It is also widely used by revision control systems such as Git for reconciling multiple changes made to a revision-controlled collection of files.

Install

• npm

  npm install --save @algorithm.ts/lcs

• yarn

  yarn add @algorithm.ts/lcs

Usage

• Basic

  import { findLengthOfLCS, findMinLexicographicalLCS } from '@algorithm.ts/lcs'
  
  const s1: number[] = [1, 2, 3, 4, 6, 6, 7, 8, 6]
  const s2: number[] = [2, 3, 4, 7, 9, 8, 2, 3, 5, 2]
  
  findLengthOfLCS(s1.length, s2.length, (x, y) => s1[x] === s2[y]) // => 5
  
  findMinLexicographicalLCS(s1.length, s2.length, (x, y) => s1[x] === s2[y])
  // => [ [1, 0], [2, 1], [3, 2], [6, 3], [7, 5] ]
  //
  //    Here is why:
  //
  //          0 1 2 3 4 5 6 7 8 9
  //      s1: 1 2 3 4 6 6 7 8 6
  //      s2: 2 3 4 7 9 8 2 3 5 2
  //
  //      s1[1] <----> s2[0]
  //      s1[2] <----> s2[1]
  //      s1[3] <----> s2[2]
  //      s1[6] <----> s2[3]
  //      null  <----> s2[4]
  //      s1[7] <----> s2[5]
  //      null  <----> s2[6]
  //      null  <----> s2[7]
  //      null  <----> s2[8]
  //      null  <----> s2[9]

Related

• 最长公共子序列（LCS） | 光和尘
• Longest common subsequence problem | Wikipedia