@algorithm.ts/lcs

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

This package provide three different implementation of lcs algorithm. To measure the complexity of these algorithms, let the $N_1$ and $N_2$ be the subsequences length of two sequences respectively. And let $L$ be the length of the longest common subsequences, then the $D = 2L - N_1 - N_2$.

1. myers_lcs(N1: number, N2: number, equals: (x: number, y: number) => boolean): [x: number, y: number][]: The vanilla algorithm introduced by this paper An O(ND) Difference Algorithm and Its Variations.

   • Time complexity: $O((N_1 + N_2) \times D)$
   • Memory complexity: $O(N_1 \times N_2)$

2. myers_lcs_linear_space(N1: number, N2: number, equals: (x: number, y: number) => boolean): [x: number, y: number][]: The linear space refinement algorithm from An O(ND) Difference Algorithm and Its Variations.

   • Time complexity: $O((N_1 + N_2) * D)$
   • Memory complexity: $O(N_1 + N_2)$

3. lcs_dp(N1: number, N2: number, equals: (x: number, y: number) => boolean): [x: number, y: number][] This implementation is based on dynamic programming, and can find the minimal lexicographical lcs.

   • Time complexity: $O(N_1 \times N_2)$
   • Memory complexity: $O(N_1 \times N_2)$

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
  

• pnpm

  pnpm add @algorithm.ts/lcs
  

Usage

• Basic

  import { lcs_dp, lcs_myers_size } 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]
  
  lcs_myers_size(s1.length, s2.length, (x, y) => s1[x] === s2[y]) // => 5
  
  lcs_dp(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

• An O(ND) Difference Algorithm and Its Variations.
• 最长公共子序列（LCS） | 光和尘
• Longest common subsequence problem | Wikipedia