retroforth/example/advent-of-code-2020-day-5.retro

# Day 5: Binary Boarding

You board your plane only to discover a new problem: you dropped
your boarding pass! You aren't sure which seat is yours, and all 
of the flight attendants are busy with the flood of people that 
suddenly made it through passport control.

You write a quick program to use your phone's camera to scan all 
of the nearby boarding passes (your puzzle input); perhaps you 
can find your seat through process of elimination.

Instead of zones or groups, this airline uses binary space 
partitioning to seat people. A seat might be specified like 
FBFBBFFRLR, where F means "front", B means "back", L means 
"left", and R means "right".

The first 7 characters will either be F or B; these specify 
exactly one of the 128 rows on the plane (numbered 0 through 
127). Each letter tells you which half of a region the given 
seat is in. Start with the whole list of rows; the first 
letter indicates whether the seat is in the front (0 through 
63) or the back (64 through 127). The next letter indicates 
which half of that region the seat is in, and so on until 
you're left with exactly one row.

For example, consider just the first seven characters of 
FBFBBFFRLR:

    Start by considering the whole range, rows 0 through 127.
    F means to take the lower half, keeping rows 0 through 63.
    B means to take the upper half, keeping rows 32 through 63.
    F means to take the lower half, keeping rows 32 through 47.
    B means to take the upper half, keeping rows 40 through 47.
    B keeps rows 44 through 47.
    F keeps rows 44 through 45.
    The final F keeps the lower of the two, row 44.

	The last three characters will be either L or R; these 
	specify exactly one of the 8 columns of seats on the 
	plane (numbered 0 through 7). The same process as above 
	proceeds again, this time with only three steps. L means 
	to keep the lower half, while R means to keep the upper 
	half.

For example, consider just the last 3 characters of FBFBBFFRLR:

    Start by considering the whole range, columns 0 through 7.
    R means to take the upper half, keeping columns 4 through 7.
    L means to take the lower half, keeping columns 4 through 5.
    The final R keeps the upper of the two, column 5.

	So, decoding FBFBBFFRLR reveals that it is the seat at row
	44, column 5.

Every seat also has a unique seat ID: multiply the row by 8,
then add the column. In this example, the seat has ID 
44 \* 8 + 5 = 357.

Here are some other boarding passes:

    BFFFBBFRRR: row 70, column 7, seat ID 567.
    FFFBBBFRRR: row 14, column 7, seat ID 119.
    BBFFBBFRLL: row 102, column 4, seat ID 820.

As a sanity check, look through your list of boarding passes. 
What is the highest seat ID on a boarding pass?

----

This is actually *really* easy. In this case, the boarding passes
ultimately correspond directly to a binary value for the seat id.
So, all that's needed is to convert the boarding pass to a string
representation of the binary value, then convert that to an actual
number.

Since Retro is decmal only, I started by bringing in some code to
work with other bases.

~~~
'Base var

:binary #2 !Base ;
:decimal #10 !Base ;

{{
  '0123456789ABCDEF 'DIGITS s:const
  'Number var
  'Mod    var
  :convert    (c-)  &DIGITS swap s:index/char 
                    @Number @Base * + !Number ;
  :check-sign (s-s) dup fetch $- eq? 
                    [ #-1 !Mod n:inc ] [ #1 !Mod ] choose ;
---reveal---
  :s:to-number<with-base> (s-n)
    #0 !Number check-sign [ convert ] s:for-each @Number @Mod * ;
}}
~~~

Then the rest was trivial.

~~~
:c:to-binary
  $F [ $0 ] case
  $B [ $1 ] case 
  $L [ $0 ] case 
  $R [ $1 ] case ;
:s:to-binary-rep  [ c:to-binary ] s:map ;
:convert s:to-binary-rep binary s:to-number<with-base> ;

#0 'input-day-5 [ convert n:max ] file:for-each-line
n:put nl
~~~

----

# Part Two ---

Ding! The "fasten seat belt" signs have turned on. Time to find 
your seat.

It's a completely full flight, so your seat should be the only 
missing boarding pass in your list. However, there's a catch: 
some of the seats at the very front and back of the plane don't 
exist on this aircraft, so they'll be missing from your list as 
well.

Your seat wasn't at the very front or back, though; the seats 
with IDs +1 and -1 from yours will be in your list.

What is the ID of your seat?

----

This is also really easy. I just fill in a list of seats to see
which are used, then ignore the empty ones at the start before
returning the first empty one in the middle.

~~~
'Seats d:create #1024 allot
'input-day-5 [ convert &Seats + v:on ] file:for-each-line
&Seats n:inc [ fetch-next n:zero? ] while 
             [ fetch-next n:zero? ] until &Seats - n:put nl
~~~