I was up when the day turned to the 16th, but with the wordy spec and what I suspected would be a pile of code to write, I saved the puzzle for the daylight hours.

(ns aoc.2021.day.16
  (:require [hyperfiddle.rcf :as rcf]))


Day 16 is this year’s first tedious-spec-following puzzle; it might be a multi-day project like a previous year’s ‘intcode’ interpreter. These puzzles are nice, if a little monotonous, because there usually aren’t walls of confusion to be hit, and they feel sort of real-worldy.

This one took some time from a busy day to implement, so minimal cleanup was done.

The input is a hexadecimal string which we’re told to convert immediately to binary.

(def input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

(defn to-bit-seq [hex-str]
  ;; Courtesy https://stackoverflow.com/questions/4421400/how-to-get-0-padded-binary-representation-of-an-integer-in-java
  (mapcat (fn [char]
            (as-> (Character/digit ^char char 16) $
                  (Long/toBinaryString $)
                  (format "%4s" $)
                  (.replace $ \space \0)
                  (seq $)))

The string is a packet, like one sent over a wire; a packet is a recursive tree-like structure, i.e., a packet has sub-packets.

A packet has a version (not totally sure what this represents) and a type; a packet may be of type ‘literal number,’ ‘plus,’ ‘minimum,’ or one of several other mathematical operators.

Our task is to decode the packets (part 1) and then evaluate the mathematical expression it represents (part 2).

First, an annoying var declaration for a function which will feed the following multimethod.

(declare parse-packets)

This multi-method switches on the packet type and does the required parsing work for that packet. Parsing is recursive for those packets that contain sub-packets; decode-packets is mutually recursive with parse-packets.

We dispatch on the packet type, but only switch on literal- or non-literal-, i.e. operator-, packet, since the work to be done ends up being about the same. (Kind of inconsistent, but gets the job done.)

(defmulti decode-packets (fn [version type bits] (#{4} type)))

Literal packet decoder:

(defmethod decode-packets 4 [version type bits]
  (let [[literal bits] (loop [literal-acc []
                              bits bits]
                         (let [[[indicator & chunk] bits] (split-at 5 bits)
                               literal-acc (concat literal-acc chunk)]
                           (if (= \0 indicator)
                             [(Long/parseLong (apply str literal-acc) 2) bits]
                             (recur literal-acc bits))))]
    [bits [{:version version :type type :literal literal}]]))

(def bool->int {true 1 false 0})
(defn bool-int [f] (comp bool->int f))

Operator packet decoder and helpers:

(defn decode-length-type-packet [version type bits op]
  (let [[length-str init-bits] (split-at 15 bits)
        length (Long/parseLong (apply str length-str) 2)
        [bits sub-packets] (loop [sub-packets []
                                  bits init-bits]
                             (if (= length (- (count init-bits) (count bits)))
                               [bits sub-packets]
                               (let [[bits packets] (parse-packets bits)]
                                 (recur (into sub-packets packets) bits))))]
    [bits [{:version version :op op :type type :sub-packets sub-packets}]]))

(defn decode-count-type-packet [version type bits op]
  (let [[count-str bits] (split-at 11 bits)
        sub-packet-count (Long/parseLong (apply str count-str) 2)
        [bits sub-packets] (loop [bits bits
                                  sub-packets []]
                             (if (= (count sub-packets) sub-packet-count)
                               [bits sub-packets]
                               (let [[bits packets] (parse-packets bits)]
                                 (recur bits (into sub-packets packets)))))]
    [bits [{:version version :op op :type type :sub-packets sub-packets}]]))

(defmethod decode-packets nil [version type bits]
  (let [[length-type-id & bits] bits
        op ({0 + 1 * 2 min 3 max 5 (bool-int >) 6 (bool-int <) 7 (bool-int =)}
    (if (= length-type-id \0)
      (decode-length-type-packet version type bits op)
      (decode-count-type-packet version type bits op))))

Instead of stuffing logic into the multimethod dispatch function, I left it here in this helper:

(defn parse-packets [bits]
  (let [[version bits] (split-at 3 bits)
        version (Long/parseLong (apply str version) 2)
        [type bits] (split-at 3 bits)
        type (Long/parseLong (apply str type) 2)]
    (decode-packets version type bits)))

Part 1 asks us to sum the versions parsed from the packets:

(defn version-sum [packets]
  (->> packets
       (mapcat #(tree-seq :sub-packets :sub-packets %))
       (map :version)
       (reduce +)))

(defn part-1 [hex]
  (let [[leftover-bits packets] (parse-packets (to-bit-seq hex))]
    (version-sum packets)))

  (part-1 input) := 951)

Part 2 asks us to evaluate the tree. Initially I had a separate multimethod here but there was a lot of duplication in its methods; it seemed at least more succinct to give each packet an operator earlier on.

(defn eval-packet [{:keys [type literal op sub-packets]}]
  (or literal (apply op (map eval-packet sub-packets))))

(defn part-2 [hex]
  (let [[leftover-bits packets] (parse-packets (to-bit-seq hex))]
    (eval-packet (first packets))))

  (time (part-2 input)) := 902198718880)  ; => 14.68375 ms

Satisfying, if not super clean. I hope this is a multi-day-er so that I can revisit it.