LevenshteinDistance.js

/* The Levenshtein distance (a.k.a edit distance) is a
measure of similarity between two strings. It is
defined as the minimum number of changes required to
convert string a into string b (this is done by
inserting, deleting or replacing a character in
string a).
The smaller the Levenshtein distance,
the more similar the strings are. This is a very
common problem in the application of Dynamic Programming.
*/

const levenshteinDistance = (a, b) => {
 // Declaring array 'D' with rows = len(a) + 1 and columns = len(b) + 1:
 const distanceMatrix = Array(b.length + 1)
 .fill(null)
 .map(() => Array(a.length + 1).fill(null))

 // Initializing first column:
 for (let i = 0; i <= a.length; i += 1) {
 distanceMatrix[0][i] = i
 }

 // Initializing first row:
 for (let j = 0; j <= b.length; j += 1) {
 distanceMatrix[j][0] = j
 }

 for (let j = 1; j <= b.length; j += 1) {
 for (let i = 1; i <= a.length; i += 1) {
 const indicator = a[i - 1] === b[j - 1] ? 0 : 1
 // choosing the minimum of all three, vis-a-vis:
 distanceMatrix[j][i] = Math.min(
 distanceMatrix[j][i - 1] + 1, // deletion
 distanceMatrix[j - 1][i] + 1, // insertion
 distanceMatrix[j - 1][i - 1] + indicator // substitution
 )
 }
 }

 return distanceMatrix[b.length][a.length]
}

export { levenshteinDistance }