cmpstr/src/algorithms/needlemanWunsch.js

lightweight npm package to calculate string similarity

/**
 * Needleman-Wunsch Algorithm
 * CmpStr module
 * 
 * The Needleman-Wunsch algorithm performs global alignment,
 * aligning two strings entirely, including gaps. It is commonly
 * used in bioinformatics.
 * 
 * @author Paul Köhler
 * @license MIT
 */


'use strict';

/**
 * module exports
 * @public
 * 
 * @param {String} a string a
 * @param {String} b string b
 * @param {Object} options having {
 *   @param {Number} [match=1] score for a match
 *   @param {Number} [mismatch=-1] penalty for a mismatch
 *   @param {Number} [gap=-1] penalty for a gap
 * }
 * @returns {Number} similarity score (0..1)
 */

module.exports = ( a, b, {
    match = 1, mismatch = -1, gap = -1
} = {} ) => {

    let rows = a.length + 1,
        cols = b.length + 1;

    /* step 1: initialize scoring matrix */

    let matrix = Array.from(
        { length: rows },
        ( _, i ) => Array.from(
            { length: cols },
            ( _, j ) => ( i === 0 ? j * gap : j === 0 ? i * gap : 0 )
        )
    );

    /* step 2: fill the scoring matrix */

    for ( let i = 1; i < rows; i++ ) {

        for ( let j = 1; j < cols; j++ ) {

            let matchScore = a[ i - 1 ] === b[ j - 1 ] ? match : mismatch;

            matrix[ i ][ j ] = Math.max(
                matrix[ i - 1 ][ j - 1 ] + matchScore,
                matrix[ i - 1 ][ j ] + gap,
                matrix[ i ][ j - 1 ] + gap
            );

        }

    }

    /* step 3: normalize the score to a value between 0..1 */

    return Math.max( 0, Math.min( 1,
        matrix[ a.length ][ b.length ] / (
            Math.max( a.length, b.length ) * match
        )
    ) );

};