How to use recursion in a power loop with growing number of parameters?

Question

This is a typical Power Loop problem, and I only need a simple and elegant (compact) solution... I will show fist the sample of problem/solution with nested for loops. Suppose that I need to transform this piece of code into a recursion:

console.log("bits","Binary")
for (let i=0; i<2; i++) {
    show(i)
    for (let j=0; j<2; j++) {
      show(i,j)
      for (let k=0; k<2; k++)
        show(i,j,k) // ... l,m,n,o,p
  } // j
} // i

function show(...args) {
   let code = String( args.reduce( (ac,cur) => ''+ac+cur ) )
   console.log( code.length, code )
}

The 14-unique-lines output of this 3-level sample is

bits Binary
1 '0'
2 '00'
3 '000'
3 '001'
2 '01'
3 '010'
3 '011'
1 '1'
2 '10'
3 '100'
3 '101'
2 '11'
3 '110'
3 '111'

---

Ugly and partial solution

I am trying to solve using as reference this solution:

callManyTimes([2,2,2], show);

function callManyTimes(maxIndices, func) {
    doCallManyTimes(maxIndices, func, [], 0);
}

function doCallManyTimes(maxIndices, func, args, index) {
    if (maxIndices.length == 0) {
        let x = args.slice(0); // cloning
        while(x.length>0) {
          func(x); // why send array[array]?
          x.shift();
        }
    } else {
        var rest = maxIndices.slice(1);
        for (args[index] = 0; args[index] < maxIndices[0]; ++args[index]) {
            doCallManyTimes(rest, func, args, index + 1);
        }
    }
}

function show(...args) {
   if (typeof args[0] == 'object') args=args[0] // workaround... can optimize?
   let code = String( args.reduce( (ac,cur) => ''+ac+cur ) )
   console.log( code.length, code )
}

The output have duplicated lines, but there are a subset of lines that are the solution... So, seems near, but is ugly (no elegant use of the recurrence stack, etc.)

3 '000'
2 '00'
1 '0'
3 '001'
2 '01'
1 '1'
3 '010'
2 '10'
1 '0'
3 '011'
2 '11'
1 '1'
...

Answer 1

You could take a function which takes a temporary array for the generated values.

function show(...args) {
    let code = args.join('');
    console.log(code.length, code);
}

function callManyTimes(max, cb, items = []) {
    var i, temp;
    if (items.length === max.length) return;
    for (i = 0; i < max[items.length]; i++) {
        temp = items.concat(i);
        cb(...temp);
        callManyTimes(max, cb, temp);
    }
}

callManyTimes([2, 2, 2], show);

Answer 2

A simple backtracking recursive function will visit these in the order of the first example with something like:

function iter(maxlength, cur = ''){
  if (cur.length >= maxlength) return
  for (let i = 0; i < 2; i++){
    console.log(cur.length + 1 + ":",   cur + i)
    iter(maxlength, cur + i)
  }
}

iter(3)

You can also generate an array with the same idea and a generator function (here it's returning an array of arrays to join later, but the same principle):

function* iter(maxlength, prefix = []){
  if (prefix.length >= maxlength) return
   for (let i = 0; i < 2; i++){
     yield [i, ...prefix]
     yield * iter(maxlength, [i, ...prefix])
   }
}
  
console.log([...iter(3)].map(a => a.join(',')))