Question

There are other questions about this in other languages, and other non-lazy JavaScript versions, but no lazy JavaScript versions that I have found.

Given an array of an arbitrary number of arbitrary-sized arrays:

var sets = [ [2,3,4,5], ['sweet','ugly'], ['cats','dogs','hogs'] ];

and a callback function:

function holla( n, adj, noun ){
  console.log( [n,adj,noun].join(' ') );
}

what’s an elegant way to iterate the entire product space without creating a huge array of all possible combinations first?

lazyProduct( sets, holla );
// 2 sweet cats
// 2 sweet dogs
// 2 sweet hogs
// 2 ugly cats
// 2 ugly dogs
// 2 ugly hogs
// 3 sweet cats
// 3 sweet dogs
// 3 sweet hogs
// 3 ugly cats
// 3 ugly dogs
// 3 ugly hogs
// 4 sweet cats
// 4 sweet dogs
// 4 sweet hogs
// 4 ugly cats
// 4 ugly dogs
// 4 ugly hogs
// 5 sweet cats
// 5 sweet dogs
// 5 sweet hogs
// 5 ugly cats
// 5 ugly dogs
// 5 ugly hogs

---

Note that these combinations are the same as the results you would get if you had nested loops:

var counts     = [2,3,4,5];
var adjectives = ['sweet','ugly'];
var animals    = ['cats','dogs','hogs'];
for (var i=0;i<counts.length;++i){
  for (var j=0;j<adjectives.length;++j){
    for (var k=0;k<animals.length;++k){
      console.log( [ counts[i], adjectives[j], animals[k] ].join(' ') );
    }
  }
}

The benefits of the Cartesian product are:

1. It lets you nest an arbitrary number of loops (perhaps you don’t know how many items you’ll iterate)
2. It lets you change the order of looping (e.g. loop by adjectives first) without having to edit your code or write out all possible combinations of looping order.

---

Benchmarks

You can see the benchmarks for the answers below here:
http://jsperf.com/lazy-cartesian-product/26

Answer 1

Coincidentally working on the same thing over the weekend. I was looking to find alternative implementations to my [].every-based algo which turned out to have abyssmal performance in Firefox (but screams in Chrome — more than twice as fast as the next).

The end result is http://jsperf.com/lazy-cartesian-product/19 . It’s similar to Tomalak’s approach but there is only one arguments array which is mutated as the carets move instead of being generated each time.

I’m sure it could be improved further by using the clever maths in the other algos. I don’t quite understand them though, so I leave it to others to try.

EDIT: the actual code, same interface as Tomalak’s. I like this interface because it could be breaked anytime. It’s only slightly slower than if the loop is inlined in the function itself.

var xp = crossProduct([
  [2,3,4,5],['angry','happy'], 
  ['monkeys','anteaters','manatees']]);
while (xp.next()) xp.do(console.log, console);

function crossProduct(sets) {
  var n = sets.length, carets = [], args = [];

  function init() {
    for (var i = 0; i < n; i++) {
      carets[i] = 0;
      args[i] = sets[i][0];
    }
  }

  function next() {
    if (!args.length) {
      init();
      return true;
    }
    var i = n - 1;
    carets[i]++;
    if (carets[i] < sets[i].length) {
      args[i] = sets[i][carets[i]];
      return true;
    }
    while (carets[i] >= sets[i].length) {
      if (i == 0) {
        return false;
      }
      carets[i] = 0;
      args[i] = sets[i][0];
      carets[--i]++;
    }
    args[i] = sets[i][carets[i]];
    return true;
  }

  return {
    next: next,
    do: function (block, _context) {
      return block.apply(_context, args);
    }
  }
}