# ETOOBUSY đźš€ minimal blogging for the impatient

# PWC193 - Binary String

**TL;DR**

Here we are with TASK #1 from The Weekly Challenge #193. Enjoy!

# The challenge

You are given an integer,

`$n > 0`

.Write a script to find all possible binary numbers of size

`$n`

.

Example 1`Input: $n = 2 Output: 00, 11, 01, 10`

Example 2`Input: $n = 3 Output: 000, 001, 010, 100, 111, 110, 101, 011`

# The questions

I think that by â€śall possible binary numbersâ€ť we mean â€śall possible
strings of length `$n`

that can be build over an alphabet comprising `0`

and `1`

onlyâ€ť. This is because Iâ€™m not sure I would consider `0123`

a
decimal number of size 4, to be honest.

Alsoâ€¦ Iâ€™m not sure how weâ€™re supposed to produce the strings. I guess any order will do.

# The solution

Each challenge lives on its own little monad, and has its own rules. But
(you knew there was a *but*) I canâ€™t help observing that the binary
strings *here* can happily start with a string of `0`

characters, while
no later than the last week they had to definitely start with a `1`

, or
bad things would have happened.

So shouldnâ€™t this go in the *questions* sections somehow? Well, no. The
challenge is subtly worded as to find all possible binary numbers of
size `$n`

, which means that we donâ€™t get to do any conversion if we
donâ€™t want to.

OK, as usual letâ€™s start with Raku:

```
#!/usr/bin/env raku
use v6;
sub MAIN (Int:D $n where * > 0 = 2) { .put for binary-strings($n) }
sub binary-strings (Int:D $n where * > 0) {
my $prefix = '0' x ($n - 1);
my $i = 0;
return gather loop {
my $raw = ($i++).base(2).Str;
my $len = $raw.chars;
last if $len > $n;
take ('0' x ($n - $len)) ~ $raw;
};
}
```

Weâ€™re just counting from 0 upwards, stopping when the binary
representation gets too long. To cope with the length requirement, we
just pre-pend each produced string with a suitable number of `0`

characters.

I know, this solution is neither efficient nor scalable. Raku has
built-in big integers, but weâ€™re computing/accumulating all strings
up-front and weâ€™re also using `gather`

/`take`

, which is not the best
efficiency-wise. I like it too much though.

For the Perl alternative we move on to good old iterators - they
play nicer for bigger values of the input `$n`

, as we start seeing stuff
immediately and we keep memory consumption to a minimum.

```
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
use Math::BigInt;
my $it = binary_strings_iterator(shift // 2);
while (defined(my $binary_string = $it->())) {
say $binary_string;
}
sub binary_strings_iterator ($n) {
my $i = Math::BigInt->bzero;
return sub {
return unless defined $i;
my $raw = ($i++)->to_bin;
my $len = length $raw;
return $i = undef if $len > $n;
return ('0' x ($n - $len)) . $raw;
};
}
```

So go ahead, feed it with 1000 as input and stop it when youâ€™ve got enough!

Stay safe!

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