day19

aoc-racket.scrbl

@@ -38,4 +38,5 @@ You can install this package (if you haven't already) with
 @include-section[(submod "day15.rkt" doc)]
 @include-section[(submod "day16.rkt" doc)]
 @include-section[(submod "day17.rkt" doc)]
-@include-section[(submod "day18.rkt" doc)]
+@include-section[(submod "day18.rkt" doc)]
+@include-section[(submod "day19.rkt" doc)]

day19-input.txt

@@ -0,0 +1,45 @@
+Al => ThF
+Al => ThRnFAr
+B => BCa
+B => TiB
+B => TiRnFAr
+Ca => CaCa
+Ca => PB
+Ca => PRnFAr
+Ca => SiRnFYFAr
+Ca => SiRnMgAr
+Ca => SiTh
+F => CaF
+F => PMg
+F => SiAl
+H => CRnAlAr
+H => CRnFYFYFAr
+H => CRnFYMgAr
+H => CRnMgYFAr
+H => HCa
+H => NRnFYFAr
+H => NRnMgAr
+H => NTh
+H => OB
+H => ORnFAr
+Mg => BF
+Mg => TiMg
+N => CRnFAr
+N => HSi
+O => CRnFYFAr
+O => CRnMgAr
+O => HP
+O => NRnFAr
+O => OTi
+P => CaP
+P => PTi
+P => SiRnFAr
+Si => CaSi
+Th => ThCa
+Ti => BP
+Ti => TiTi
+e => HF
+e => NAl
+e => OMg
+
+ORnPBPMgArCaCaCaSiThCaCaSiThCaCaPBSiRnFArRnFArCaCaSiThCaCaSiThCaCaCaCaCaCaSiRnFYFArSiRnMgArCaSiRnPTiTiBFYPBFArSiRnCaSiRnTiRnFArSiAlArPTiBPTiRnCaSiAlArCaPTiTiBPMgYFArPTiRnFArSiRnCaCaFArRnCaFArCaSiRnSiRnMgArFYCaSiRnMgArCaCaSiThPRnFArPBCaSiRnMgArCaCaSiThCaSiRnTiMgArFArSiThSiThCaCaSiRnMgArCaCaSiRnFArTiBPTiRnCaSiAlArCaPTiRnFArPBPBCaCaSiThCaPBSiThPRnFArSiThCaSiThCaSiThCaPTiBSiRnFYFArCaCaPRnFArPBCaCaPBSiRnTiRnFArCaPRnFArSiRnCaCaCaSiThCaRnCaFArYCaSiRnFArBCaCaCaSiThFArPBFArCaSiRnFArRnCaCaCaFArSiRnFArTiRnPMgArF

day19.rkt

@@ -0,0 +1,95 @@
+#lang scribble/lp2
+@(require scribble/manual aoc-racket/helper)
+
+@aoc-title[19]
+
+@defmodule[aoc-racket/day19]
+
+@link["http://adventofcode.com/day/19"]{The puzzle}. Our @link-rp["day19-input.txt"]{input} is list of ``molecule'' transformations that look like @tt{B => TiRnFAr}, and then a longer test molecule.
+
+
+@chunk[<day19>
+       <day19-setup>
+       <day19-q1>
+       <day19-q2>
+       <day19-test>]
+
+@section{How many distinct molecules can be created after one transformation?}
+
+Starting with our test molecule, we are asked to try every molecule transformation at every possible position, and count up the distinct molecules that are created.
+
+Each molecule transformation defines a string replacement. We'll parse our input  into a test molecule, and a list of transformations (= each transformation is a list of a before and after string). Because we want to perform each transformation at every possible point in the test molecule, we can't use @racket[regexp-replace] (because it only replaces the first match) or @racket[regexp-replace*] (because it replaces all matches). Instead we'll use @racket[regexp-match-positions*] to generate a list of match positions, and then perform the substitutions at each location to generate our list of molecules. After doing this for every transformation, we can @racket[remove-duplicates] and see how many are left.
+
+
+@chunk[<day19-setup>
+       (require racket rackunit)
+       (provide (all-defined-out))
+       
+       (define (parse-input-str input-str)
+         (match-define (cons molecule transformation-strings)
+           (reverse (string-split input-str "\n")))
+         (define transformations
+           (filter-not empty?
+                       (map (curryr string-split " => ")  transformation-strings)))
+         (values molecule transformations))
+                                           
+                                           
+       ]
+
+@chunk[<day19-q1>
+       (define (transform-molecule* molecule target-atom replacement-atom)
+         (for/list ([pos (in-list (regexp-match-positions* (regexp target-atom) molecule))])
+                   (match-define (cons start finish) pos)
+                   (string-append (substring molecule 0 start)
+                                  replacement-atom
+                                  (substring molecule finish (string-length molecule)))))
+       
+       (define (q1 input-str)
+         (define-values (molecule transformations) (parse-input-str input-str))
+         (length
+          (remove-duplicates
+           (append-map (λ(target replacement)
+                         (transform-molecule* molecule target replacement))
+                       (map first transformations) (map second transformations)))))]
+
+
+
+@section{What's the fewest number of transformations that will generate the test module?}
+
+Unlike some of the puzzles, this second part is a lot harder. The idea is that the test molecule was made from a series of transformations, starting with the single atom @racket{e}. So not only do we have to reverse-engineer this process, but we have to find the most efficient path.
+
+There were three questions in Advent of Code that I couldn't figure out. This was the first. The answer to the first question seems to provide a clue: we could reverse the transformations, perform the same replacement process, and we'd have a list of precursor molecules that could've existed one step before the test molecule. Then you repeat this process with all the possible precursors, until you get back to @racket{e}. This will work in theory, but not in practice, because it requires checking too many possibilities.
+
+So I cheated. I adapted a @link["https://github.com/ChrisPenner/Advent-Of-Code-Polyglot/blob/master/python/19/part2.py"]{Python algorithm} for Racket. I can tell you how it works, though I'm still figuring out @italic{why} it does. This function loops through the transformations and applies them everywhere they will fit. When it reaches a dead end — meaning, the molecule hasn't changed during the loop — it randomly reorders the transformations with @racket[shuffle] and tries again. It is strange to me that this process would converge to an answer at all, let alone the best answer, let alone so quickly.
+
+@chunk[<day19-q2>
+       
+       (define (q2 input-str)
+         (define-values (starting-molecule xforms) (parse-input-str input-str))
+         (let loop ([current-mol starting-molecule][transform-count 0]
+                                                   [shuffles 0][xforms xforms])
+           (cond
+             [(equal? current-mol "e") transform-count]
+             [else
+              (define-values (xformed-mol last-count)
+                (for/fold ([mol current-mol][count-so-far transform-count])
+                          ([(from to) (in-parallel (map first xforms) (map second xforms))])
+                  (values (string-replace mol to from)
+                          (+ count-so-far (length (regexp-match* to mol))))))
+              (if (not (equal? current-mol xformed-mol))
+                  (loop xformed-mol last-count shuffles xforms)
+                  (loop starting-molecule 0 (add1 shuffles) (shuffle xforms)))])))
+                                                                                  
+       ]
+
+
+
+@section{Testing Day 18}
+
+@chunk[<day19-test>
+       (module+ test
+         (define input-str (file->string "day19-input.txt"))
+         (check-equal? (q1 input-str) 576)
+         (check-equal? (q2 input-str) 207))]
+
+