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## Big O Forum

# Figuring out the logic behind 2.1 *spoiler

So, I think I have it figured out...but please feel free to comment on my logic:

This exercise basically returns an array containing all the possible combinations using 1 and 0 in a string of length (n).

The answer is O(2^n) because the amount of possible combinations is

2^n. That is why you get 4 elements (2^2) with 2 digits, 8 elements (2^3) with 3 digits and so on. Therefore the function is exponentially proportionate to the amount of digits.

How the code works:

```
var binary = function(n){
var helper = function(i, s){
// If there are no characters left to print, then stop printing
//THIS MEANS THAT AN ARRAY WITH VALUE S WILL BE CREATED WHEN i = 0 OR LOWER.
if(i < 1) return [s];
// array1.concat(array2) is a new array containing the elements of array1 followed by those of array2
return helper(i-1, "1"+s).concat(helper(i-1, "0"+s));
// Forget about all the concats below, it was just a way to follow logic. Remember
//concat "attaches" two strings. By putting "1" + s, basically we are saying that "1" is a string, not a number. This way it will attach and not add.
//`with binary (3)
//helper(2,1).concat(helper(2,0))
//helper(1,11).concat(helper(1,01).concat(helper(1,10),concat(helper(1,00))))
//helper()
//helper((0,111).concat(0,011)).concat(0,101)(0,001)......etc,etc
// Since i < 1 here, we start printing, the first helper will make [s] = 111, second one will make [s] = [111] .concat[011] which is [111,011] this logic follows until giving the ending array: [ "111", "011", "101", "001", "110", "010", "100", "000"]
return helper(n, "");
}
console.log(binary(0));
console.log("O(2^n)")
```

## 2 Comments

Hun over 4 years ago

seconded!

Sofia Perwallius over 3 years ago

Thanks