Develop Reference

Function for computing percentage of how similar an array of text strings are to each other in javascript

Lets say I have the following array of strings, var = array_of_strings["abc","abcd"]
My goal is to run a function and have this return roughly 75% (0.75). Implying that the results are roughly 75% in common. Roughly being defined as within a certain error range, let us say 5% or some settable number.
I'm currently using the the Levenshtein algorithm to compute differences in the strings, however, this is extremely slow and taxing on the CPU in my situation as the strings I'm using are thousands and thousands of lines long.
Levenshtein gives me what the differences are; and while useful in certain situations, my particular use case is simply looking to see what percentage the strings are roughly different from each other and not what each difference actually is necessarily.
The current levenshtein algorithm I'm using is below (which I borrowed from another answer here on stackoverflow). It will return how many differences it found which I can then use to calculate a percentage difference, but it's very slow! Sometimes taking a couple of seconds to run and freezes up the computer as well.
async function levenshtein(s, t) {
return new Promise((resolve, reject) => {
console.log("levenshtein active");
if (s === t) {
return 0;
}
var n = s.length, m = t.length;
if (n === 0 || m === 0) {
return n + m;
}
var x = 0, y, a, b, c, d, g, h, k;
var p = new Array(n);
for (y = 0; y < n;) {
p[y] = ++y;
}
for (; (x + 3) < m; x += 4) {
var e1 = t.charCodeAt(x);
var e2 = t.charCodeAt(x + 1);
var e3 = t.charCodeAt(x + 2);
var e4 = t.charCodeAt(x + 3);
c = x;
b = x + 1;
d = x + 2;
g = x + 3;
h = x + 4;
for (y = 0; y < n; y++) {
k = s.charCodeAt(y);
a = p[y];
if (a < c || b < c) {
c = (a > b ? b + 1 : a + 1);
}
else {
if (e1 !== k) {
c++;
}
}
if (c < b || d < b) {
b = (c > d ? d + 1 : c + 1);
}
else {
if (e2 !== k) {
b++;
}
}
if (b < d || g < d) {
d = (b > g ? g + 1 : b + 1);
}
else {
if (e3 !== k) {
d++;
}
}
if (d < g || h < g) {
g = (d > h ? h + 1 : d + 1);
}
else {
if (e4 !== k) {
g++;
}
}
p[y] = h = g;
g = d;
d = b;
b = c;
c = a;
}
}
for (; x < m;) {
var e = t.charCodeAt(x);
c = x;
d = ++x;
for (y = 0; y < n; y++) {
a = p[y];
if (a < c || d < c) {
d = (a > d ? d + 1 : a + 1);
}
else {
if (e !== s.charCodeAt(y)) {
d = c + 1;
}
else {
d = c;
}
}
p[y] = d;
c = a;
}
h = d;
}
resolve(h);
})
}
My question is, is there a way to calculate the difference faster when large string sets are used? In my case accuracy is not too important just as long as a rough difference is known of a certain percentage.
For example, if a research paper was published and I have the original paper and the students paper I want to know if roughly 10% of the students paper is plagiarized.
Maybe if I cut a random parts out of the strings this can help to save on time but this feels very dirty/inefficient.

How to optimize levenshtein distance for checking for a distance of 1?

I'm working on a game where I only need to check if there's a distance of 0 or 1 between two words and return true if that's the case. I found a general purpose levenshtein distance algorithm:
function levenshtein(s, t) {
if (s === t) { return 0; }
var n = s.length, m = t.length;
if (n === 0 || m === 0) { return n + m; }
var x = 0, y, a, b, c, d, g, h, k;
var p = new Array(n);
for (y = 0; y < n;) { p[y] = ++y; }
for (;
(x + 3) < m; x += 4) {
var e1 = t.charCodeAt(x);
var e2 = t.charCodeAt(x + 1);
var e3 = t.charCodeAt(x + 2);
var e4 = t.charCodeAt(x + 3);
c = x; b = x + 1; d = x + 2; g = x + 3; h = x + 4;
for (y = 0; y < n; y++) {
k = s.charCodeAt(y);
a = p[y];
if (a < c || b < c) { c = (a > b ? b + 1 : a + 1); }
else { if (e1 !== k) { c++; } }
if (c < b || d < b) { b = (c > d ? d + 1 : c + 1); }
else { if (e2 !== k) { b++; } }
if (b < d || g < d) { d = (b > g ? g + 1 : b + 1); }
else { if (e3 !== k) { d++; } }
if (d < g || h < g) { g = (d > h ? h + 1 : d + 1); }
else { if (e4 !== k) { g++; } }
p[y] = h = g; g = d; d = b; b = c; c = a;
}
}
for (; x < m;) {
var e = t.charCodeAt(x);
c = x;
d = ++x;
for (y = 0; y < n; y++) {
a = p[y];
if (a < c || d < c) { d = (a > d ? d + 1 : a + 1); }
else {
if (e !== s.charCodeAt(y)) { d = c + 1; }
else { d = c; }
}
p[y] = d;
c = a;
}
h = d;
}
return h;
}
Which works, but this spot is going to be a hotspot and be run potentially hundreds of thousands of times a second and I want to optimize it because I don't need a general purpose algorithm, just one that checks if there's a distance of 0 or 1.
I tried writing it and came up with this:
function closeGuess(guess, word) {
if (Math.abs(word.length - guess.length) > 1) { return false; }
var errors = 0, guessIndex = 0, wordIndex = 0;
while (guessIndex < guess.length || wordIndex < word.length) {
if (errors > 1) { return false; }
if (guess[guessIndex] !== word[wordIndex]) {
if (guess.length < word.length) { wordIndex++; }
else { guessIndex++; }
errors++;
} else {
wordIndex++;
guessIndex++;
}
}
return true;
}
But after profiling it I found that my code was twice as slow, which surprised me because I think the general purpose algorithm is O(n*m) and I think mine is O(n).
I've been testing the performance difference on this fiddle: https://jsfiddle.net/aubtze2L/3/
Are there any better algorithms I can use or any way I can optimize my code to be faster?

I don't see a more elegant way which is at the same time faster than the good old for-loop:
function lev01(a, b) {
let la = a.length;
let lb = b.length;
let d = 0;
switch (la - lb) {
case 0: // mutation
for (let i = 0; i < la; ++i) {
if (a.charAt(i) != b.charAt(i) && ++d > 1) {
return false;
}
}
return true;
case -1: // insertion
for (let i = 0; i < la + d; ++i) {
if (a.charAt(i - d) != b.charAt(i) && ++d > 1) {
return false;
}
}
return true;
case +1: // deletion
for (let i = 0; i < lb + d; ++i) {
if (a.charAt(i) != b.charAt(i - d) && ++d > 1) {
return false;
}
}
return true;
}
return false;
}
console.log(lev01("abc", "abc"));
console.log(lev01("abc", "abd"));
console.log(lev01("abc", "ab"));
console.log(lev01("abc", "abcd"));
console.log(lev01("abc", "cba"));
Performance comparison (Chrome):
80.33ms - lev01 (this answer)
234.84ms - lev
708.12ms - close

Consider the following cases:
If the difference in lengths of the terms is greater than 1, then
the Levenshtein distance between them will be greater than 1.
If the difference in lengths is exactly 1, then the shortest string must be equal to the longest string, with a single deletion (or insertion).
If the strings are the same length then you should
consider a modified version of Hamming distance which returns false
if two, different characters are found:
Here is a sample implementation:
var areSimilar;
areSimilar = function(guess, word) {
var charIndex, foundDiff, guessLength, lengthDiff, substring, wordLength, shortest, longest, shortestLength, offset;
guessLength = guess.length;
wordLength = word.length;
lengthDiff = guessLength - wordLength;
if (lengthDiff < -1 || lengthDiff > 1) {
return false;
}
if (lengthDiff !== 0) {
if (guessLength < wordLength) {
shortest = guess;
longest = word;
shortestLength = guessLength;
} else {
shortest = word;
longest = guess;
shortestLength = wordLength;
}
offset = 0;
for (charIndex = 0; charIndex < shortestLength; charIndex += 1) {
if (shortest[charIndex] !== longest[offset + charIndex]) {
if (offset > 0) {
return false; // second error
}
offset = 1;
if (shortest[charIndex] !== longest[offset + charIndex]) {
return false; // second error
}
}
}
return true; // only one error
}
foundDiff = false;
for (charIndex = 0; charIndex < guessLength; charIndex += 1) {
if (guess[charIndex] !== word[charIndex]) {
if (foundDiff) {
return false;
}
foundDiff = true;
}
}
return true;
};
I've updated your fiddle to include this method. Here are the results on my machine:
close: 154.61
lev: 176.72500000000002
sim: 32.48000000000013
Fiddle: https://jsfiddle.net/dylon/aubtze2L/11/

If you know that you are looking for distance 0 and 1, then the general purpose DP algorithm does not make sense (and by the way the algorithm you showed looks convoluted, take a look at a better explanation here).
To check that the distance is 0, all you need is to check whether 2 strings are the same. Now if the distance is one, it means that either insertion, deletion or substitution should have happened. So generate all possible deletion from the original string and check whether it is equal to second string. So you will get something like this:
for (var i = 0; i < s_1.length; i++) {
if s_2 == s_1.slice(0, i) + s_1.slice(i + 1) {
return true
}
}
For insertions and substitution you will need to know the alphabet of all characters. You can define it as a big string var alphabet = "abcde....". Now you do a similar thing, but when you introduce substitution or insertion, you also iterate over all elements in your alphabet. I am not planning to write the whole code here.
A couple of additional things. You can make a lot of micro-optimizations here. For example if the length of two strings are different by more than 1, they clearly can't have a distance 1. Another one relates to the frequencies of underlying characters in the string.

Function to solve cubic equation analytically

I need to solve a cubic equation (ax^3 + bx^2 + c*x + d = 0) analytically and in real numbers, preferably in pure javascript (no libs). As there could be 1 to 3 roots, I think an array of numbers is a reasonable result type.
P.S. Provided my own solution below, hope it'll be useful.

Here you go. Includes handling degenerate cases. Main algorithm is mostly from wikipedia article.
function cuberoot(x) {
var y = Math.pow(Math.abs(x), 1/3);
return x < 0 ? -y : y;
}
function solveCubic(a, b, c, d) {
if (Math.abs(a) < 1e-8) { // Quadratic case, ax^2+bx+c=0
a = b; b = c; c = d;
if (Math.abs(a) < 1e-8) { // Linear case, ax+b=0
a = b; b = c;
if (Math.abs(a) < 1e-8) // Degenerate case
return [];
return [-b/a];
}
var D = b*b - 4*a*c;
if (Math.abs(D) < 1e-8)
return [-b/(2*a)];
else if (D > 0)
return [(-b+Math.sqrt(D))/(2*a), (-b-Math.sqrt(D))/(2*a)];
return [];
}
// Convert to depressed cubic t^3+pt+q = 0 (subst x = t - b/3a)
var p = (3*a*c - b*b)/(3*a*a);
var q = (2*b*b*b - 9*a*b*c + 27*a*a*d)/(27*a*a*a);
var roots;
if (Math.abs(p) < 1e-8) { // p = 0 -> t^3 = -q -> t = -q^1/3
roots = [cuberoot(-q)];
} else if (Math.abs(q) < 1e-8) { // q = 0 -> t^3 + pt = 0 -> t(t^2+p)=0
roots = [0].concat(p < 0 ? [Math.sqrt(-p), -Math.sqrt(-p)] : []);
} else {
var D = q*q/4 + p*p*p/27;
if (Math.abs(D) < 1e-8) { // D = 0 -> two roots
roots = [-1.5*q/p, 3*q/p];
} else if (D > 0) { // Only one real root
var u = cuberoot(-q/2 - Math.sqrt(D));
roots = [u - p/(3*u)];
} else { // D < 0, three roots, but needs to use complex numbers/trigonometric solution
var u = 2*Math.sqrt(-p/3);
var t = Math.acos(3*q/p/u)/3; // D < 0 implies p < 0 and acos argument in [-1..1]
var k = 2*Math.PI/3;
roots = [u*Math.cos(t), u*Math.cos(t-k), u*Math.cos(t-2*k)];
}
}
// Convert back from depressed cubic
for (var i = 0; i < roots.length; i++)
roots[i] -= b/(3*a);
return roots;
}

Compare strings with 'similar' letters [duplicate]

So I have a random javascript array of names...
[#larry,#nicholas,#notch] etc.
They all start with the # symbol. I'd like to sort them by the Levenshtein Distance so that the the ones at the top of the list are closest to the search term. At the moment, I have some javascript that uses jQuery's .grep() on it using javascript .match() method around the entered search term on key press:
(code edited since first publish)
limitArr = $.grep(imTheCallback, function(n){
return n.match(searchy.toLowerCase())
});
modArr = limitArr.sort(levenshtein(searchy.toLowerCase(), 50))
if (modArr[0].substr(0, 1) == '#') {
if (atRes.childred('div').length < 6) {
modArr.forEach(function(i){
atRes.append('<div class="oneResult">' + i + '</div>');
});
}
} else if (modArr[0].substr(0, 1) == '#') {
if (tagRes.children('div').length < 6) {
modArr.forEach(function(i){
tagRes.append('<div class="oneResult">' + i + '</div>');
});
}
}
$('.oneResult:first-child').addClass('active');
$('.oneResult').click(function(){
window.location.href = 'http://hashtag.ly/' + $(this).html();
});
It also has some if statements detecting if the array contains hashtags (#) or mentions (#). Ignore that. The imTheCallback is the array of names, either hashtags or mentions, then modArr is the array sorted. Then the .atResults and .tagResults elements are the elements that it appends each time in the array to, this forms a list of names based on the entered search terms.
I also have the Levenshtein Distance algorithm:
var levenshtein = function(min, split) {
// Levenshtein Algorithm Revisited - WebReflection
try {
split = !("0")[0]
} catch(i) {
split = true
};
return function(a, b) {
if (a == b)
return 0;
if (!a.length || !b.length)
return b.length || a.length;
if (split) {
a = a.split("");
b = b.split("")
};
var len1 = a.length + 1,
len2 = b.length + 1,
I = 0,
i = 0,
d = [[0]],
c, j, J;
while (++i < len2)
d[0][i] = i;
i = 0;
while (++i < len1) {
J = j = 0;
c = a[I];
d[i] = [i];
while(++j < len2) {
d[i][j] = min(d[I][j] + 1, d[i][J] + 1, d[I][J] + (c != b[J]));
++J;
};
++I;
};
return d[len1 - 1][len2 - 1];
}
}(Math.min, false);
How can I work with algorithm (or a similar one) into my current code to sort it without bad performance?
UPDATE:
So I'm now using James Westgate's Lev Dist function. Works WAYYYY fast. So performance is solved, the issue now is using it with source...
modArr = limitArr.sort(function(a, b){
levDist(a, searchy)
levDist(b, searchy)
});
My problem now is general understanding on using the .sort() method. Help is appreciated, thanks.
Thanks!

I wrote an inline spell checker a few years ago and implemented a Levenshtein algorithm - since it was inline and for IE8 I did quite a lot of performance optimisation.
var levDist = function(s, t) {
var d = []; //2d matrix
// Step 1
var n = s.length;
var m = t.length;
if (n == 0) return m;
if (m == 0) return n;
//Create an array of arrays in javascript (a descending loop is quicker)
for (var i = n; i >= 0; i--) d[i] = [];
// Step 2
for (var i = n; i >= 0; i--) d[i][0] = i;
for (var j = m; j >= 0; j--) d[0][j] = j;
// Step 3
for (var i = 1; i <= n; i++) {
var s_i = s.charAt(i - 1);
// Step 4
for (var j = 1; j <= m; j++) {
//Check the jagged ld total so far
if (i == j && d[i][j] > 4) return n;
var t_j = t.charAt(j - 1);
var cost = (s_i == t_j) ? 0 : 1; // Step 5
//Calculate the minimum
var mi = d[i - 1][j] + 1;
var b = d[i][j - 1] + 1;
var c = d[i - 1][j - 1] + cost;
if (b < mi) mi = b;
if (c < mi) mi = c;
d[i][j] = mi; // Step 6
//Damerau transposition
if (i > 1 && j > 1 && s_i == t.charAt(j - 2) && s.charAt(i - 2) == t_j) {
d[i][j] = Math.min(d[i][j], d[i - 2][j - 2] + cost);
}
}
}
// Step 7
return d[n][m];
}

I came to this solution:
var levenshtein = (function() {
var row2 = [];
return function(s1, s2) {
if (s1 === s2) {
return 0;
} else {
var s1_len = s1.length, s2_len = s2.length;
if (s1_len && s2_len) {
var i1 = 0, i2 = 0, a, b, c, c2, row = row2;
while (i1 < s1_len)
row[i1] = ++i1;
while (i2 < s2_len) {
c2 = s2.charCodeAt(i2);
a = i2;
++i2;
b = i2;
for (i1 = 0; i1 < s1_len; ++i1) {
c = a + (s1.charCodeAt(i1) === c2 ? 0 : 1);
a = row[i1];
b = b < a ? (b < c ? b + 1 : c) : (a < c ? a + 1 : c);
row[i1] = b;
}
}
return b;
} else {
return s1_len + s2_len;
}
}
};
})();
See also http://jsperf.com/levenshtein-distance/12
Most speed was gained by eliminating some array usages.

Updated: http://jsperf.com/levenshtein-distance/5
The new Revision annihilates all other benchmarks. I was specifically chasing Chromium/Firefox performance as I don't have an IE8/9/10 test environment, but the optimisations made should apply in general to most browsers.
Levenshtein Distance
The matrix to perform Levenshtein Distance can be reused again and again. This was an obvious target for optimisation (but be careful, this now imposes a limit on string length (unless you were to resize the matrix dynamically)).
The only option for optimisation not pursued in jsPerf Revision 5 is memoisation. Depending on your use of Levenshtein Distance, this could help drastically but was omitted due to its implementation specific nature.
// Cache the matrix. Note this implementation is limited to
// strings of 64 char or less. This could be altered to update
// dynamically, or a larger value could be used.
var matrix = [];
for (var i = 0; i < 64; i++) {
matrix[i] = [i];
matrix[i].length = 64;
}
for (var i = 0; i < 64; i++) {
matrix[0][i] = i;
}
// Functional implementation of Levenshtein Distance.
String.levenshteinDistance = function(__this, that, limit) {
var thisLength = __this.length, thatLength = that.length;
if (Math.abs(thisLength - thatLength) > (limit || 32)) return limit || 32;
if (thisLength === 0) return thatLength;
if (thatLength === 0) return thisLength;
// Calculate matrix.
var this_i, that_j, cost, min, t;
for (i = 1; i <= thisLength; ++i) {
this_i = __this[i-1];
for (j = 1; j <= thatLength; ++j) {
// Check the jagged ld total so far
if (i === j && matrix[i][j] > 4) return thisLength;
that_j = that[j-1];
cost = (this_i === that_j) ? 0 : 1; // Chars already match, no ++op to count.
// Calculate the minimum (much faster than Math.min(...)).
min = matrix[i - 1][j ] + 1; // Deletion.
if ((t = matrix[i ][j - 1] + 1 ) < min) min = t; // Insertion.
if ((t = matrix[i - 1][j - 1] + cost) < min) min = t; // Substitution.
matrix[i][j] = min; // Update matrix.
}
}
return matrix[thisLength][thatLength];
};
Damerau-Levenshtein Distance
jsperf.com/damerau-levenshtein-distance
Damerau-Levenshtein Distance is a small modification to Levenshtein Distance to include transpositions. There is very little to optimise.
// Damerau transposition.
if (i > 1 && j > 1 && this_i === that[j-2] && this[i-2] === that_j
&& (t = matrix[i-2][j-2]+cost) < matrix[i][j]) matrix[i][j] = t;
Sorting Algorithm
The second part of this answer is to choose an appropriate sort function. I will upload optimised sort functions to http://jsperf.com/sort soon.

I implemented a very performant implementation of levenshtein distance calculation if you still need this.
function levenshtein(s, t) {
if (s === t) {
return 0;
}
var n = s.length, m = t.length;
if (n === 0 || m === 0) {
return n + m;
}
var x = 0, y, a, b, c, d, g, h, k;
var p = new Array(n);
for (y = 0; y < n;) {
p[y] = ++y;
}
for (; (x + 3) < m; x += 4) {
var e1 = t.charCodeAt(x);
var e2 = t.charCodeAt(x + 1);
var e3 = t.charCodeAt(x + 2);
var e4 = t.charCodeAt(x + 3);
c = x;
b = x + 1;
d = x + 2;
g = x + 3;
h = x + 4;
for (y = 0; y < n; y++) {
k = s.charCodeAt(y);
a = p[y];
if (a < c || b < c) {
c = (a > b ? b + 1 : a + 1);
}
else {
if (e1 !== k) {
c++;
}
}
if (c < b || d < b) {
b = (c > d ? d + 1 : c + 1);
}
else {
if (e2 !== k) {
b++;
}
}
if (b < d || g < d) {
d = (b > g ? g + 1 : b + 1);
}
else {
if (e3 !== k) {
d++;
}
}
if (d < g || h < g) {
g = (d > h ? h + 1 : d + 1);
}
else {
if (e4 !== k) {
g++;
}
}
p[y] = h = g;
g = d;
d = b;
b = c;
c = a;
}
}
for (; x < m;) {
var e = t.charCodeAt(x);
c = x;
d = ++x;
for (y = 0; y < n; y++) {
a = p[y];
if (a < c || d < c) {
d = (a > d ? d + 1 : a + 1);
}
else {
if (e !== s.charCodeAt(y)) {
d = c + 1;
}
else {
d = c;
}
}
p[y] = d;
c = a;
}
h = d;
}
return h;
}
It was my answer to a similar SO question
Fastest general purpose Levenshtein Javascript implementation
Update
A improved version of the above is now on github/npm see
https://github.com/gustf/js-levenshtein

The obvious way of doing this is to map each string to a (distance, string) pair, then sort this list, then drop the distances again. This way you ensure the levenstein distance only has to be computed once. Maybe merge duplicates first, too.

I would definitely suggest using a better Levenshtein method like the one in #James Westgate's answer.
That said, DOM manipulations are often a great expense. You can certainly improve your jQuery usage.
Your loops are rather small in the example above, but concatenating the generated html for each oneResult into a single string and doing one append at the end of the loop will be much more efficient.
Your selectors are slow. $('.oneResult') will search all elements in the DOM and test their className in older IE browsers. You may want to consider something like atRes.find('.oneResult') to scope the search.
In the case of adding the click handlers, we may want to do one better avoid setting handlers on every keyup. You could leverage event delegation by setting a single handler on atRest for all results in the same block you are setting the keyup handler:
atRest.on('click', '.oneResult', function(){
window.location.href = 'http://hashtag.ly/' + $(this).html();
});
See http://api.jquery.com/on/ for more info.

I just wrote an new revision: http://jsperf.com/levenshtein-algorithms/16
function levenshtein(a, b) {
if (a === b) return 0;
var aLen = a.length;
var bLen = b.length;
if (0 === aLen) return bLen;
if (0 === bLen) return aLen;
var len = aLen + 1;
var v0 = new Array(len);
var v1 = new Array(len);
var i = 0;
var j = 0;
var c2, min, tmp;
while (i < len) v0[i] = i++;
while (j < bLen) {
c2 = b.charAt(j++);
v1[0] = j;
i = 0;
while (i < aLen) {
min = v0[i] - (a.charAt(i) === c2 ? 1 : 0);
if (v1[i] < min) min = v1[i];
if (v0[++i] < min) min = v0[i];
v1[i] = min + 1;
}
tmp = v0;
v0 = v1;
v1 = tmp;
}
return v0[aLen];
}
This revision is faster than the other ones. Works even on IE =)

Fastest general purpose Levenshtein Javascript implementation

I am looking for a good general purpose Levenshtein implementation in Javascript. It must be fast and be useful for short and long strings. It should also be used many times (hence the caching). The most important thing is that it calculates a plain simple Levenshtein distance. I came up with this:
var levenshtein = (function() {
var row2 = [];
return function(s1, s2) {
if (s1 === s2) {
return 0;
} else {
var s1_len = s1.length, s2_len = s2.length;
if (s1_len && s2_len) {
var i1 = 0, i2 = 0, a, b, c, c2, row = row2;
while (i1 < s1_len)
row[i1] = ++i1;
while (i2 < s2_len) {
c2 = s2.charCodeAt(i2);
a = i2;
++i2;
b = i2;
for (i1 = 0; i1 < s1_len; ++i1) {
c = a + (s1.charCodeAt(i1) === c2 ? 0 : 1);
a = row[i1];
b = b < a ? (b < c ? b + 1 : c) : (a < c ? a + 1 : c);
row[i1] = b;
}
}
return b;
} else {
return s1_len + s2_len;
}
}
};
})();
Now I have two questions:
Can this be faster? I know by writing out the first iteration of each loop one can gain about 20%.
Is this code well written to serve as general purpose code, to be used in a library for instance?

We had a competition for fun at work about making the fastest levenshtein implementation and I came up with a faster one. First of all, I must say that it was not easy to beat your solution which was the fastest to find "out there". :)
This is tested with node.js and it my benchmarks results indicates that this implementation is ~15% faster on small texts (random words size 2-10 characters) and over twice as fast on longer texts (with lengths 30+ containing random characters)
Note: I removed array caching of all implementations
function levenshtein(s, t) {
if (s === t) {
return 0;
}
var n = s.length, m = t.length;
if (n === 0 || m === 0) {
return n + m;
}
var x = 0, y, a, b, c, d, g, h, k;
var p = new Array(n);
for (y = 0; y < n;) {
p[y] = ++y;
}
for (; (x + 3) < m; x += 4) {
var e1 = t.charCodeAt(x);
var e2 = t.charCodeAt(x + 1);
var e3 = t.charCodeAt(x + 2);
var e4 = t.charCodeAt(x + 3);
c = x;
b = x + 1;
d = x + 2;
g = x + 3;
h = x + 4;
for (y = 0; y < n; y++) {
k = s.charCodeAt(y);
a = p[y];
if (a < c || b < c) {
c = (a > b ? b + 1 : a + 1);
}
else {
if (e1 !== k) {
c++;
}
}
if (c < b || d < b) {
b = (c > d ? d + 1 : c + 1);
}
else {
if (e2 !== k) {
b++;
}
}
if (b < d || g < d) {
d = (b > g ? g + 1 : b + 1);
}
else {
if (e3 !== k) {
d++;
}
}
if (d < g || h < g) {
g = (d > h ? h + 1 : d + 1);
}
else {
if (e4 !== k) {
g++;
}
}
p[y] = h = g;
g = d;
d = b;
b = c;
c = a;
}
}
for (; x < m;) {
var e = t.charCodeAt(x);
c = x;
d = ++x;
for (y = 0; y < n; y++) {
a = p[y];
if (a < c || d < c) {
d = (a > d ? d + 1 : a + 1);
}
else {
if (e !== s.charCodeAt(y)) {
d = c + 1;
}
else {
d = c;
}
}
p[y] = d;
c = a;
}
h = d;
}
return h;
}
On longer texts it will get almost up to 3 times the speed of your implementation if it initially cache the inner loop's s.charCodeAt(y) in an Uint32Array. Longer texts also seemed to benefit from using a Uint16Array as a the distance cost array. Here is the code for that solution
function levenshtein(s, t) {
if (s === t) {
return 0;
}
var n = s.length, m = t.length;
if (n === 0 || m === 0) {
return n + m;
}
var x = 0, y, a, b, c, d, g, h;
var p = new Uint16Array(n);
var u = new Uint32Array(n);
for (y = 0; y < n;) {
u[y] = s.charCodeAt(y);
p[y] = ++y;
}
for (; (x + 3) < m; x += 4) {
var e1 = t.charCodeAt(x);
var e2 = t.charCodeAt(x + 1);
var e3 = t.charCodeAt(x + 2);
var e4 = t.charCodeAt(x + 3);
c = x;
b = x + 1;
d = x + 2;
g = x + 3;
h = x + 4;
for (y = 0; y < n; y++) {
a = p[y];
if (a < c || b < c) {
c = (a > b ? b + 1 : a + 1);
}
else {
if (e1 !== u[y]) {
c++;
}
}
if (c < b || d < b) {
b = (c > d ? d + 1 : c + 1);
}
else {
if (e2 !== u[y]) {
b++;
}
}
if (b < d || g < d) {
d = (b > g ? g + 1 : b + 1);
}
else {
if (e3 !== u[y]) {
d++;
}
}
if (d < g || h < g) {
g = (d > h ? h + 1 : d + 1);
}
else {
if (e4 !== u[y]) {
g++;
}
}
p[y] = h = g;
g = d;
d = b;
b = c;
c = a;
}
}
for (; x < m;) {
var e = t.charCodeAt(x);
c = x;
d = ++x;
for (y = 0; y < n; y++) {
a = p[y];
if (a < c || d < c) {
d = (a > d ? d + 1 : a + 1);
}
else {
if (e !== u[y]) {
d = c + 1;
}
else {
d = c;
}
}
p[y] = d;
c = a;
}
h = d;
}
return h;
}
All benchmark results is from my tests and test-data might be different with your test-data.
The main 2 difference in this solution than to yours (and some other fast ones) I think is
Not always do compare of the characters in the inner loop if not necessary.
Sort of "Loop unrolling" in the outer loop doing 4 rows at a time in the levenshtein "matrix". This was a major performance win.
http://jsperf.com/levenshtein-distance/24
I will put this solution on github when I find the time :)
Update:
Finally, I put the solution on github
https://github.com/gustf/js-levenshtein. Its a bit modified/optimized but it is the same base algorithm.