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|
import «Common»
namespace Day14
------------------------------------------------------------------------------------
inductive Tile
| Space
| Cube
| Round
deriving Repr, BEq
instance : LawfulBEq Tile where
rfl := λ{a} ↦ by cases a <;> decide
eq_of_beq := by intros a b; cases a <;> cases b <;> simp <;> decide
instance: ToString Tile where
toString := λ
| Tile.Space => "."
| Tile.Cube => "#"
| Tile.Round => "O"
structure ParseCharError where
unexpectedCharacter : Char
instance : ToString ParseCharError where
toString := λc ↦ s!"Unexpected Character '{c.unexpectedCharacter}', expected '.', '#', or 'O'."
private def Tile.ofChar? : Char → Except ParseCharError Tile
| '.' => pure Tile.Space
| '#' => pure Tile.Cube
| 'O' => pure Tile.Round
| c => throw {unexpectedCharacter := c}
abbrev ControlPanel := Parsing.RectangularGrid Tile
abbrev ParseInputError := Parsing.RectangularGrid.ParseError ParseCharError
def parse : String → Except ParseInputError ControlPanel :=
Parsing.RectangularGrid.ofSubstring Tile.ofChar? ∘ String.toSubstring
------------------------------------------------------------------------------------
/-
there's probably a better way, but I'm too lazy, so I'll just move them row-by-row.
pseudocode
for(row)
for(column)
if(tile == Round)
moveTileAsFarNorthAsPossible
-/
/-- Finds the northmost free space reachable from start. Does not look at start. -/
private def findNorthmostFreeTile {controlPanel : ControlPanel} (start : controlPanel.Coordinate) : controlPanel.Coordinate :=
if start.y > ⟨0,controlPanel.not_empty.right⟩ then
let northNeighbour := { start with y := ⟨start.y - 1,Nat.lt_imp_pred_lt start.y.isLt⟩ }
match controlPanel[northNeighbour] with
| Tile.Space => findNorthmostFreeTile northNeighbour
| Tile.Round | Tile.Cube => start
else
start
termination_by start.y
private def moveTileNorth {controlPanel : ControlPanel} (position : controlPanel.Coordinate) : ControlPanel :=
match controlPanel[position] with
| Tile.Space | Tile.Cube => controlPanel
| Tile.Round =>
let intermediate := controlPanel.set position Tile.Space
let positionInIntermediate : intermediate.Coordinate := {x := position.x, y := position.y} -- how? well, I won't complain
let northMost := findNorthmostFreeTile positionInIntermediate
intermediate.set northMost Tile.Round
private theorem moveTileNorth_same_size {controlPanel : ControlPanel} (position : controlPanel.Coordinate) : (moveTileNorth position).width = controlPanel.width ∧ (moveTileNorth position).height = controlPanel.height := by
constructor
all_goals
unfold moveTileNorth
match controlPanel[position] with
| Tile.Space | Tile.Cube => trivial
| Tile.Round =>
simp only[Parsing.RectangularGrid.set_same_size]
/-
-- Old solution, without do-notation. Proven to terminate, but needs a lot more code...
/- had to move this to top level function to be able to prove stuff with it... "Declaration contains metavariables" -/
private def moveAllTilesNorth_handleColumns (cp : ControlPanel) (row : Fin cp.height) (column : Fin cp.width) : ControlPanel :=
let intermediate := moveTileNorth {x := column, y := row : cp.Coordinate}
let nextIndex := column.val + 1
if h : nextIndex < intermediate.width then
have h₁ : intermediate.height = cp.height := (moveTileNorth_same_size {x := column, y := row : cp.Coordinate}).right
moveAllTilesNorth_handleColumns intermediate (h₁▸row) ⟨nextIndex,h⟩
else
intermediate
termination_by cp.width - column
decreasing_by
have h₂ := (moveTileNorth_same_size { x := column, y := row }).left
rw[h₂] at h ⊢
exact Nat.sub_lt_of_gt (Nat.le_of_lt h) (Nat.lt_succ.mpr $ Nat.le_refl _)
private theorem moveAllTilesNorth_handleColumns_same_height (cp : ControlPanel) (row : Fin cp.height) (column : Fin cp.width) : (moveAllTilesNorth_handleColumns cp row column).height = cp.height := by
unfold moveAllTilesNorth_handleColumns
simp
have h₂ := (moveTileNorth_same_size { x := column, y := row }).right
split
case isFalse => exact h₂
case isTrue =>
have := moveAllTilesNorth_handleColumns_same_height (Day14.moveTileNorth { x := column, y := row }) (h₂ ▸ row) ⟨↑column + 1, by assumption⟩
simp[h₂] at this
assumption
termination_by cp.width - column
decreasing_by
have h₂ := (moveTileNorth_same_size { x := column, y := row }).left
rename_i h
rw[h₂] at h ⊢
exact Nat.sub_lt_of_gt (Nat.le_of_lt h) (Nat.lt_succ.mpr $ Nat.le_refl _)
private def moveAllTilesNorth (controlPanel : ControlPanel) : ControlPanel :=
handleRows (controlPanel) ⟨0,controlPanel.not_empty.right⟩
where
handleRows (cp : ControlPanel) (row : Fin cp.height) : ControlPanel :=
let intermediate := moveAllTilesNorth_handleColumns cp row ⟨0,cp.not_empty.left⟩
let nextIndex := row.val + 1
if h : nextIndex < intermediate.height then
handleRows intermediate ⟨nextIndex, h⟩
else
intermediate
termination_by cp.height - row
decreasing_by
have h₁ : intermediate.height = cp.height :=
moveAllTilesNorth_handleColumns_same_height cp row ⟨0,_⟩
rw[h₁] at h ⊢
exact Nat.sub_lt_of_gt (Nat.le_of_lt h) (Nat.lt_succ.mpr $ Nat.le_refl _)
-/
private def moveAllTilesNorth (controlPanel : ControlPanel) : ControlPanel := Id.run do
let mut result : ((c : ControlPanel) ×' (c.width = controlPanel.width ∧ c.height = controlPanel.height)) := ⟨controlPanel, ⟨rfl,rfl⟩⟩
for hr :row in [:controlPanel.height] do
for hc : column in [:controlPanel.width] do
let x : Fin result.fst.width := Fin.cast result.snd.left.symm ⟨column,hc.upper⟩
let y : Fin result.fst.height := Fin.cast result.snd.right.symm ⟨row,hr.upper⟩
let coordinate : result.fst.Coordinate := {x, y}
have : (moveTileNorth coordinate).width = controlPanel.width ∧ (moveTileNorth coordinate).height = controlPanel.height :=
(moveTileNorth_same_size coordinate).right.substr $ (moveTileNorth_same_size coordinate).left.substr result.snd
result := ⟨moveTileNorth coordinate, this⟩
result.fst
private def weightOnNorthSupport (controlPanel : ControlPanel) : Nat := Id.run do
let mut score := 0
for hr :row in [:controlPanel.height] do
for hc : column in [:controlPanel.width] do
let coordinate := {x := ⟨column,hc.upper⟩, y := ⟨row,hr.upper⟩ : controlPanel.Coordinate}
if controlPanel[coordinate] == Tile.Round then
score := score + (controlPanel.height - row)
score
def part1 : (input : ControlPanel) → Nat := weightOnNorthSupport ∘ moveAllTilesNorth
------------------------------------------------------------------------------------
open DayPart
instance : Parse ⟨14, by simp⟩ (ι := ControlPanel) where
parse := Except.mapError toString ∘ parse
instance : Part ⟨14,_⟩ Parts.One (ι := ControlPanel) (ρ := Nat) where
run := some ∘ part1
------------------------------------------------------------------------------------
private def testInput := "O....#....
O.OO#....#
.....##...
OO.#O....O
.O.....O#.
O.#..O.#.#
..O..#O..O
.......O..
#....###..
#OO..#...."
#eval parse testInput
#eval (weightOnNorthSupport ∘ moveAllTilesNorth) <$> parse testInput
|
