I was recently browsing twitter when I found an interesting tweet claiming that "Any JS integer can be represented using only [, ] and +". The tweet also showed the number 10 encoded as ++[+[]][+[]]+[+[]]:
console.log( ++[+[]][+[]]+[+[]] ); // Logs '10'This tweet intrigued me. Can really any javascript integer be represented in this way? I had to find out.
First, I tried to deconstruct the example value. The expression can be split into two main parts: ++[+[]][+[]] and [+[]], connected by a + addition operator. Running each individual expression in a javascript REPL showed that the first expression encodes the number 1 and the second the number 0. For some strange reason that is beyond me, javascript decides that because of the way the expression is written, the two numbers should be treated as strings and concatenated instead of being added (Why, javascript, why!?).
The second part of the term is quite simple. +[] is the same as 0+[] (javascript implicitly creates the 0), the empty array is implicitly converted to 0 (the value at the first index or 0 otherwise), and hence the result is 0. This is wrapped in brackets again ([+[]]), which, because of the + operator in front of them (the same one connecting the two terms), is again converted to 0. (Try it out: +[+[]] is the same as 0)
The other side of the expression (++[+[]][+[]]) is a bit more complex. It contains the same +[] expression mutiple times, so let's replace that with 0, since they're the same: ++[0][0]. That's simpler. It's now easily visible that the second pair of brackets is an accessor that reads the element at index 0 from the array [0], and that the result of the read is incremented using ++. We need the increment operator because it's the only way to get any value higher than 0 without using regular digits and thus breaking the constraint of using only +, [ and ]. However, we can't just apply an increment to an array (++[+[]] wouldn't work), so we access a property, and for some reason that allows us to increment it. Again, why this works isn't really important, just as long as it does work.
The following function can convert any integer (yes, any integer) to its "array" representation:
function numberToArrays(n) {
return (
n
.toString()
.split('')
.map((d) =>
((x) => (x === 0 ? '+[]' : `++[${numberToArrays(x - 1)}][+[]]`))(
parseInt(d)
)
)
.join('+[') + ']'.repeat(n.toString().length - 1)
);
}Basically, we first convert the number into a string, then split it into its indivdual digits. E.g. "12" => ["1", "2"]. Now, we convert each digit to its array representation and then join them like this: digit_1_encoded + '[' + (digit_2_encoded + '[' + digit_3_encoded + ']') + ']' (and so on). Each digit is encoded using a recursive algorithm, but if you want to do it by hand, here's a quick lookup table for you:
| Digit | Representation |
|---|---|
| 0 | +[] |
| 1 | ++[+[]][+[]] |
| 2 | ++[++[+[]][+[]]][+[]] |
| 3 | ++[++[++[+[]][+[]]][+[]]][+[]] |
| 4 | ++[++[++[++[+[]][+[]]][+[]]][+[]]][+[]] |
| 5 | ++[++[++[++[++[+[]][+[]]][+[]]][+[]]][+[]]][+[]] |
| 6 | ++[++[++[++[++[++[+[]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]] |
| 7 | ++[++[++[++[++[++[++[+[]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]] |
| 8 | ++[++[++[++[++[++[++[++[+[]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]] |
| 9 | ++[++[++[++[++[++[++[++[++[+[]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]]][+[]] |
This function is rather naïve and by no means creates an efficient encoding of the number, but it works well enough for a simple demo like this...
Apparently, there's been some innovation in this space since I posted this gist. Someone seems to have figured out a way to encode not only any JS number, but, in fact, any JS program at all using only +, [, ], (, ) and !. That's three characters more than my old number encoder, but nonetheless way more impressive.
So, just for fun, I decided to run my encoder through a jsfuck compiler:
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To use it, simply call the value this expression returns with the number you want converted. Basically, you can just tag on, say, (12) onto the snippet to get the number 12 represented with only square brackets and pluses.
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