adventofcode/2023/day19/problem

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   br0xen [7](AoC++) 38*

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--- Day 19: Aplenty ---

   The Elves of Gear Island are thankful for your help and send you on your
   way. They even have a hang glider that someone [16]stole from Desert
   Island; since you're already going that direction, it would help them a
   lot if you would use it to get down there and return it to them.

   As you reach the bottom of the relentless avalanche of machine parts, you
   discover that they're already forming a formidable heap. Don't worry,
   though - a group of Elves is already here organizing the parts, and they
   have a system.

   To start, each part is rated in each of four categories:

     • x: Extremely cool looking
     • m: Musical (it makes a noise when you hit it)
     • a: Aerodynamic
     • s: Shiny

   Then, each part is sent through a series of workflows that will ultimately
   accept or reject the part. Each workflow has a name and contains a list of
   rules; each rule specifies a condition and where to send the part if the
   condition is true. The first rule that matches the part being considered
   is applied immediately, and the part moves on to the destination described
   by the rule. (The last rule in each workflow has no condition and always
   applies if reached.)

   Consider the workflow ex{x>10:one,m<20:two,a>30:R,A}. This workflow is
   named ex and contains four rules. If workflow ex were considering a
   specific part, it would perform the following steps in order:

     • Rule "x>10:one": If the part's x is more than 10, send the part to the
       workflow named one.
     • Rule "m<20:two": Otherwise, if the part's m is less than 20, send the
       part to the workflow named two.
     • Rule "a>30:R": Otherwise, if the part's a is more than 30, the part is
       immediately rejected (R).
     • Rule "A": Otherwise, because no other rules matched the part, the part
       is immediately accepted (A).

   If a part is sent to another workflow, it immediately switches to the
   start of that workflow instead and never returns. If a part is accepted
   (sent to A) or rejected (sent to R), the part immediately stops any
   further processing.

   The system works, but it's not keeping up with the torrent of weird metal
   shapes. The Elves ask if you can help sort a few parts and give you the
   list of workflows and some part ratings (your puzzle input). For example:

 px{a2090:A,rfg}
 pv{a>1716:R,A}
 lnx{m>1548:A,A}
 rfg{s2440:R,A}
 qs{s>3448:A,lnx}
 qkq{x2662:A,R}
 in{s2770:qs,m3333:R,R}
 hdj{m>838:A,pv}

 {x=787,m=2655,a=1222,s=2876}
 {x=1679,m=44,a=2067,s=496}
 {x=2036,m=264,a=79,s=2244}
 {x=2461,m=1339,a=466,s=291}
 {x=2127,m=1623,a=2188,s=1013}

   The workflows are listed first, followed by a blank line, then the ratings
   of the parts the Elves would like you to sort. All parts begin in the
   workflow named in. In this example, the five listed parts go through the
   following workflows:

     • {x=787,m=2655,a=1222,s=2876}: in -> qqz -> qs -> lnx -> A
     • {x=1679,m=44,a=2067,s=496}: in -> px -> rfg -> gd -> R
     • {x=2036,m=264,a=79,s=2244}: in -> qqz -> hdj -> pv -> A
     • {x=2461,m=1339,a=466,s=291}: in -> px -> qkq -> crn -> R
     • {x=2127,m=1623,a=2188,s=1013}: in -> px -> rfg -> A

   Ultimately, three parts are accepted. Adding up the x, m, a, and s rating
   for each of the accepted parts gives 7540 for the part with x=787, 4623
   for the part with x=2036, and 6951 for the part with x=2127. Adding all of
   the ratings for all of the accepted parts gives the sum total of 19114.

   Sort through all of the parts you've been given; what do you get if you
   add together all of the rating numbers for all of the parts that
   ultimately get accepted?

   Your puzzle answer was 409898.

--- Part Two ---

   Even with your help, the sorting process still isn't fast enough.

   One of the Elves comes up with a new plan: rather than sort parts
   individually through all of these workflows, maybe you can figure out in
   advance which combinations of ratings will be accepted or rejected.

   Each of the four ratings (x, m, a, s) can have an integer value ranging
   from a minimum of 1 to a maximum of 4000. Of all possible distinct
   combinations of ratings, your job is to figure out which ones will be
   accepted.

   In the above example, there are 167409079868000 distinct combinations of
   ratings that will be accepted.

   Consider only your list of workflows; the list of part ratings that the
   Elves wanted you to sort is no longer relevant. How many distinct
   combinations of ratings will be accepted by the Elves' workflows?

   Your puzzle answer was 113057405770956.

   Both parts of this puzzle are complete! They provide two gold stars: **

   At this point, you should [17]return to your Advent calendar and try
   another puzzle.

   If you still want to see it, you can [18]get your puzzle input.

   You can also [Shareon [19]Twitter [20]Mastodon] this puzzle.

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