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import «Common»
import Lean.Data.HashMap
import Lean.Data.HashSet
namespace Day8
inductive Instruction
| left
| right
deriving Repr
abbrev WaypointId := String
structure Waypoint where
id : WaypointId
left : WaypointId
right : WaypointId
deriving Repr
-- Okay, the need for different representations in both parts has burnt me once too often.
-- This time it's going to be really dumb.
private def parseInstructions (input : String) : Except String $ List Instruction := do
let mut result := []
for character in input.toList do
match character with
| 'L' => result := Instruction.left :: result
| 'R' => result := Instruction.right :: result
| _ => throw s!"Invalid instruction {character}. Only 'L' and 'R' are valid instructions."
pure result.reverse
private def parseWaypoint (input : String) : Except String Waypoint :=
if let [id, targets] := input.splitOn " = " |> List.map String.trim then
if targets.startsWith "(" && targets.endsWith ")" then
let withoutBraces := targets.drop 1 |> flip String.dropRight 1
match withoutBraces.splitOn "," |> List.map String.trim with
| [a,b] => pure {id := id, left := a, right := b : Waypoint}
| _ => throw s!"Targets need to have 2 entries, separated by ',', but were {targets}"
else
throw s!"Targets for waypoint need to be enclosed in (), but were {targets}"
else
throw s!"Waypoint could not be split in ID and targets: {input}"
private def parseWaypoints (input : List String) : Except String $ List Waypoint :=
input.mapM parseWaypoint
open Lean in
private def validateWaypointLinks (waypoints : List Waypoint) : Bool :=
let validLinks := HashSet.insertMany HashSet.empty $ waypoints.map Waypoint.id
waypoints.all λw ↦ validLinks.contains w.left && validLinks.contains w.right
def target : WaypointId := "ZZZ"
def start : WaypointId := "AAA"
def parse (input : String) : Except String $ List Instruction × List Waypoint := do
let lines := input.splitOn "\n" |> List.map String.trim |> List.filter String.notEmpty
match lines with
| instructions :: waypoints =>
let instructions ← parseInstructions instructions
let waypoints ← parseWaypoints waypoints
if let none := waypoints.find? λx ↦ x.id == start then
throw s!"Input must contain the waypoint \"{start}\"."
if let none := waypoints.find? λx ↦ x.id == target then
throw s!"Input must contain the waypoint \"{target}\""
if not $ validateWaypointLinks waypoints then
throw "Input contained a waypoint that is not properly linked."
return (instructions, waypoints)
| [] => throw "Input was empty (or only contained whitespace)."
--------------------------------------------------------------------------------------------------------
-- One of my goals for this Advent of Code is to show that the code terminates whenever that's
-- possible. In this case, it's not directly possible from the riddle input, but it's possible
-- by adding circle detection. So, instead of making the instructions just an infinite list
-- I'll treat the case that we run out of instruction in a special way, such that we detect
-- if we are lost in the desert.
private structure ConnectedWaypoints where
left : WaypointId
right : WaypointId
private def ConnectedWaypoints.get : ConnectedWaypoints → Instruction → WaypointId
| {left, right := _}, Instruction.left => left
| {left := _, right}, Instruction.right => right
-- does a single pass over all instructions. Returns err if no result has been found and another pass is needed.
-- error is optional - if none, then there is an inconsistency in the input and we are stuck.
private def pass (waypoints : Lean.HashMap WaypointId ConnectedWaypoints) (alreadyDoneSteps : Nat) (currentPosition : WaypointId) (instructions : List Instruction) : Except (Option (Nat × WaypointId)) Nat := do
if currentPosition == "ZZZ" then
return alreadyDoneSteps
match instructions with
| [] => throw $ some (alreadyDoneSteps, currentPosition)
| a :: as =>
let currentWaypoint := waypoints.find? currentPosition
match currentWaypoint with
| none => throw none -- should not happen
| some currentWaypoint => pass waypoints (alreadyDoneSteps + 1) (currentWaypoint.get a) as
private def part1_impl (waypoints : Lean.HashMap WaypointId ConnectedWaypoints) (instructions : List Instruction) (possibleStarts : List WaypointId) (alreadyDoneSteps : Nat) (currentPosition : WaypointId) : Option Nat :=
let remainingStarts := possibleStarts.filter λs ↦ s != currentPosition
if remainingStarts.length < possibleStarts.length then -- written this way to make termination_by easy
let passResult := pass waypoints alreadyDoneSteps currentPosition instructions
match passResult with
| Except.ok n => some n
| Except.error none => none -- dead end on map. Should not be possible.
| Except.error $ some n => part1_impl waypoints instructions remainingStarts n.fst n.snd
else
none -- walking in circles
termination_by part1_impl a b c d e => c.length
open Lean in
def part1 (input : List Instruction × List Waypoint) : Option Nat :=
let possibleStarts := input.snd.map Waypoint.id
let waypoints : HashMap WaypointId ConnectedWaypoints := HashMap.ofList $ input.snd.map λw ↦ (w.id, {left := w.left, right := w.right : ConnectedWaypoints})
let instructions := input.fst
part1_impl waypoints instructions possibleStarts 0 start
--------------------------------------------------------------------------------------------------------
-- okay, part 2 is nasty.
-- what do we know?
-- o) All paths we follow simultaneously have the same path length, as they have common instructions.
-- x) This means that once we walk in circles on all of them, we are lost.
-- -> That's the way to convince the compiler this program terminates.
-- o) We could use the cycle detection to rule out short, cycled paths.
-- x) Once a path is in a cycle, the targets repeat at cycle-lenght interval.
-- x) I doubt that this would be much faster than brute-force though.
-- let's try brute force first. Maybe it's fast enough?
private def parallelPass (waypoints : Lean.HashMap WaypointId ConnectedWaypoints) (alreadyDoneSteps : Nat) (currentPositions : List WaypointId) (instructions : List Instruction) : Except (Option (Nat × (List WaypointId))) Nat := do
if currentPositions.all λw ↦ w.endsWith "Z" then
return alreadyDoneSteps
match instructions with
| [] => throw $ some (alreadyDoneSteps, currentPositions)
| a :: as =>
let currentWaypoint := currentPositions.mapM waypoints.find?
match currentWaypoint with
| none => throw none -- should not happen
| some currentWaypoints =>
let nextWaypoints := currentWaypoints.map $ flip ConnectedWaypoints.get a
parallelPass waypoints (alreadyDoneSteps + 1) nextWaypoints as
private def totalRemainingStarts (s : List (List WaypointId)) : Nat :=
s.foldl (·+·.length) 0
private def part2_impl (waypoints : Lean.HashMap WaypointId ConnectedWaypoints) (instructions : List Instruction) (alreadyDoneSteps : Nat) (possibleStarts : List (List WaypointId)) (currentPositions : List WaypointId) : Option Nat :=
let remainingStarts := (possibleStarts.zip currentPositions).map λs ↦ s.fst.filter λt ↦ t != s.snd
-- I _really_ don't want to prove stuff by hand... Luckily this works.
if totalRemainingStarts remainingStarts < totalRemainingStarts possibleStarts then
let passResult := parallelPass waypoints alreadyDoneSteps currentPositions instructions
match passResult with
| Except.ok n => some n
| Except.error none => none -- dead end on map. Should not be possible.
| Except.error $ some n => part2_impl waypoints instructions n.fst remainingStarts n.snd
else
none -- walking in circles
termination_by part2_impl a b c d e => totalRemainingStarts d
open Lean in
def part2 (input : List Instruction × List Waypoint) : Option Nat :=
let possibleStarts := input.snd.map Waypoint.id
let waypoints : HashMap WaypointId ConnectedWaypoints := HashMap.ofList $ input.snd.map λw ↦ (w.id, {left := w.left, right := w.right : ConnectedWaypoints})
let instructions := input.fst
let positions : List WaypointId := (input.snd.filter λ(w : Waypoint) ↦ w.id.endsWith "A").map Waypoint.id
part2_impl waypoints instructions 0 (positions.map λ_ ↦ possibleStarts) positions
--------------------------------------------------------------------------------------------------------
open DayPart
instance : Parse ⟨8, by simp⟩ (ι := List Instruction × List Waypoint) where
parse := parse
instance : Part ⟨8,_⟩ Parts.One (ι := List Instruction × List Waypoint) (ρ := Nat) where
run := part1
instance : Part ⟨8,_⟩ Parts.Two (ι := List Instruction × List Waypoint) (ρ := Nat) where
run := part2
--------------------------------------------------------------------------------------------------------
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