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 $D = 2L - N1 - N2$.
-
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((N1 + N2) * D)
- Memory complexity:
O(N1 * N2)
-
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((N1 + N2) * D)
- Memory complexity:
O(N1 + N2)
-
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(N1 * N2)
- Memory complexity:
O(N1 * N2)
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
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])
lcs_dp(s1.length, s2.length, (x, y) => s1[x] === s2[y])
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