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import «Common»
import Std.Data.HashMap
namespace Day12
------------------------------------------------------------------------------------
inductive SpringState
| operational
| damaged
| unknown
deriving Repr, BEq, Hashable
instance : ToString (List SpringState) where
toString := λl ↦
let rec w := λ
| .operational :: as => "." ++ (w as)
| .damaged :: as => "#" ++ (w as)
| .unknown :: as => "?" ++ (w as)
| [] => ""
w l
structure SpringArrangement where
mask : List SpringState
damagedGroups : List Nat
instance : ToString SpringArrangement where
toString := λ
| {mask, damagedGroups} => (inferInstance : ToString (List SpringState)).toString mask ++ " " ++ damagedGroups.toString
inductive ParsingError
| unknownSymbolInLeftBlock : Char → ParsingError
| nonNumericSymbolInRightBlock : Substring → ParsingError
| invalidNumberOfBlockSeparators : Nat → ParsingError
| noInput : ParsingError
| missingLeftBlock : ParsingError
| missingRightBlock : ParsingError
instance : ToString ParsingError where
toString := λ
| .unknownSymbolInLeftBlock c => s!"Unkown character in left part of input: '{c}'. Expected '#', '.' or '?'."
| .nonNumericSymbolInRightBlock s => s!"The right block contained an unknown symbol. Expected ',' or numeric digits. Found {s}"
| .invalidNumberOfBlockSeparators n => s!"An input line has an unexpected number of whitespace characters. Expected 1, found {n}."
| .noInput => "The input file is empty."
| .missingLeftBlock => "The left block, which should contain a map of operational ('.') or damaged ('#') springs, or the question mark ('?') is empty."
| .missingRightBlock => "The right block, which should contain a comma-separted list of numbers, is empty."
def parse (input : String) : Except ParsingError (List SpringArrangement) :=
let input := input.toSubstring.trim
let lines := input.splitOn "\n"
let lines := lines.filterMap λx ↦
let r : Substring := x.trim
(Function.const Unit r) <$> Option.ofBool !r.isEmpty
if lines.isEmpty then
Except.error ParsingError.noInput
else
lines.mapM λl ↦
match l.splitOn " " with
| l :: r :: [] => parseLeftBlock l [] >>= λmask↦ parseRightBlock r <&> λdamagedGroups ↦ {mask, damagedGroups}
| _ :: [] => .error $ ParsingError.invalidNumberOfBlockSeparators 0
| l => .error $ ParsingError.invalidNumberOfBlockSeparators (l.length - 1)
where
parseLeftBlock : Substring → List SpringState → Except ParsingError (List SpringState) := λs p ↦
if s.isEmpty then
Except.ok p.reverse
else
match parseMaskChar s.front with
| .error e => .error e
| .ok v => parseLeftBlock (s.drop 1) $ v :: p
termination_by s => s.bsize
decreasing_by
simp_wf
rename_i h₁
apply Substring.drop_bsize_dec _ _ h₁ Nat.one_ne_zero
parseMaskChar : Char → Except ParsingError SpringState := λ
| '#' => .ok .damaged
| '?' => .ok .unknown
| '.' => .ok .operational
| c => Except.error $ .unknownSymbolInLeftBlock c
parseRightBlock : Substring → Except ParsingError (List Nat) := λs ↦
s.splitOn ","
|> List.mapM λs ↦ (Substring.toNat? s).toExcept (ParsingError.nonNumericSymbolInRightBlock s)
----------------------------------------------------------------------------------------------------
-- There is probably some nice closed form, but I don't have the brain for that right now.
-- Brute force, it is.
inductive DefiniteSpringState
| operational
| damaged
def canFirstNBeDamaged (states : List SpringState) (n : Nat) : Bool :=
match n, states with
| 0, _ => true
| (_ + 1), [] => false
| (_ + 1), .operational :: _ => false
| (nn + 1), _ :: ss => canFirstNBeDamaged ss nn
def canFirstBeOperational : (states : List SpringState) → Bool
| .operational :: _ => true
| .unknown :: _ => true
| _ => false
def mustFirstBeDamaged : (states : List SpringState) → Bool
| .damaged :: _ => true
| _ => false
abbrev PossiblePositionsMemo := Std.HashMap (List SpringState × List Nat) Nat
def countPossiblePositionsWithDamagedMemoized (memo : PossiblePositionsMemo) (remainingSpace : List SpringState) (remainingDamagedGroups : List Nat) (h₁ : remainingDamagedGroups ≠ []) : (PossiblePositionsMemo × Nat) :=
if h₂ : remainingSpace.isEmpty then
(memo,0)
else
match remainingDamagedGroups with
| g :: gs =>
let (memo, fromCurrentPosition) :=
if canFirstNBeDamaged remainingSpace g then
if h₃ : gs.isEmpty then
if (remainingSpace.drop g).any (· == .damaged) then
(memo, 0)
else
(memo, 1)
else
let d := (remainingSpace.drop g)
if canFirstBeOperational d then
let d := (d.drop 1)
if let some r := memo.get? (d, gs) then
(memo,r)
else
let (memo, r) :=countPossiblePositionsWithDamagedMemoized memo d gs (List.ne_nil_of_not_empty.mp $ (Bool.not_eq_true _).mp h₃)
(memo.insert (d, gs) r, r)
else
(memo, 0)
else
(memo, 0)
have : remainingSpace.length > 0 := List.not_empty_iff_size_gt_zero.mp $ (Bool.not_eq_true _).mp h₂
let (memo, fromOtherPositions) :=
if mustFirstBeDamaged remainingSpace then
(memo, 0)
else
let remainingSpace := (remainingSpace.drop 1)
if let some r := memo.get? (remainingSpace, g :: gs) then
(memo,r)
else
let (memo, r) := countPossiblePositionsWithDamagedMemoized memo remainingSpace (g :: gs) h₁
(memo.insert (remainingSpace, g :: gs) r, r)
(memo, fromCurrentPosition + fromOtherPositions)
termination_by remainingSpace.length + remainingDamagedGroups.length
def countPossiblePositions (remainingSpace : List SpringState) (remainingDamagedGroups : List Nat) : Nat :=
if h : remainingDamagedGroups.isEmpty then
let canAllBeOperational := remainingSpace.all λ
| .operational | .unknown => true
| _ => false
if canAllBeOperational then
1
else
0
else
Prod.snd $ countPossiblePositionsWithDamagedMemoized Std.HashMap.empty remainingSpace remainingDamagedGroups (List.ne_nil_of_not_empty.mp $ (Bool.not_eq_true _).mp h)
def part1 (springs : List SpringArrangement) : Nat :=
let possiblePositions := springs.map λ{mask, damagedGroups} ↦ Task.spawn λ_ ↦ countPossiblePositions mask damagedGroups
let possiblePositions := possiblePositions.map Task.get
possiblePositions.foldl (· + ·) 0
----------------------------------------------------------------------------------------------------
def convertInputToDay2 (l : List SpringArrangement) : List SpringArrangement :=
l.map λ{mask, damagedGroups} ↦ {
mask := mask ++ [.unknown] ++ mask ++ [.unknown] ++ mask ++ [.unknown] ++ mask ++ [.unknown] ++ mask
damagedGroups := damagedGroups ++ damagedGroups ++ damagedGroups ++ damagedGroups ++ damagedGroups
}
def part2 : (springs : List SpringArrangement) → Nat := part1 ∘ convertInputToDay2
----------------------------------------------------------------------------------------------------
open DayPart
instance : Parse ⟨12, by simp⟩ (ι := List SpringArrangement) where
parse := Except.mapError toString ∘ parse
instance : Part ⟨12,_⟩ Parts.One (ι := List SpringArrangement) (ρ := Nat) where
run := some ∘ part1
instance : Part ⟨12,_⟩ Parts.Two (ι := List SpringArrangement) (ρ := Nat) where
run := some ∘ part2
----------------------------------------------------------------------------------------------------
def testData := "???.### 1,1,3
.??..??...?##. 1,1,3
?#?#?#?#?#?#?#? 1,3,1,6
????.#...#... 4,1,1
????.######..#####. 1,6,5
?###???????? 3,2,1"
#eval parse testData <&> part2
def testData2 := "?##?.##???????#??#.. 2,10,1"
#eval parse testData2 <&> part1
|
