From 14b20b12a06abffb37e7ddd7527a0ace64121b4e Mon Sep 17 00:00:00 2001
From: Andreas Grois <andi@grois.info>
Date: Sat, 9 Dec 2023 20:58:59 +0100
Subject: Day 9

---
 Day9.lean | 61 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 Day9.lean

(limited to 'Day9.lean')

diff --git a/Day9.lean b/Day9.lean
new file mode 100644
index 0000000..24cd19d
--- /dev/null
+++ b/Day9.lean
@@ -0,0 +1,61 @@
+import «Common»
+
+namespace Day9
+
+private def parseLine (line : String) : Except String $ List Int :=
+  line.split Char.isWhitespace
+  |> List.map String.trim
+  |> List.filter String.notEmpty
+  |> List.mapM String.toInt?
+  |> Option.toExcept s!"Failed to parse numbers in line \"{line}\""
+
+def parse (input : String) : Except String $ List $ List Int :=
+  let lines := input.splitOn "\n" |> List.map String.trim |> List.filter String.notEmpty
+  lines.mapM parseLine
+
+-------------------------------------------------------------------------------------------
+
+private def differences : List Int → List Int
+| [] => []
+| _ :: [] => []
+| a :: b :: as => (a - b) :: differences (b::as)
+
+private theorem differences_length_independent_arg (a b : Int) (bs : List Int) : (differences (a :: bs)).length = (differences (b :: bs)).length := by
+  induction bs <;> simp[differences]
+
+-- BEWARE: Extrapolate needs the input reversed.
+private def extrapolate : List Int → Int
+| [] => 0
+| a :: as =>
+  if a == 0 && as.all (· == 0) then
+    0
+  else
+    have : List.length (Day9.differences (a :: as)) < Nat.succ (List.length as) := by
+      simp_arith[differences]
+      induction (as) <;> simp_arith[differences]
+      case cons b bs hb => rw[←differences_length_independent_arg]
+                           assumption
+    a + extrapolate (differences (a :: as))
+termination_by extrapolate a => a.length
+
+def part1 : List (List Int) → Int :=
+  List.foldl Int.add 0 ∘ List.map (extrapolate ∘ List.reverse)
+
+-------------------------------------------------------------------------------------------
+
+def part2 : List (List Int) → Int :=
+  List.foldl Int.add 0 ∘ List.map extrapolate
+
+-------------------------------------------------------------------------------------------
+
+open DayPart
+instance : Parse ⟨9, by simp⟩ (ι := List (List Int)) where
+  parse := parse
+
+instance : Part ⟨9,_⟩ Parts.One (ι := List (List Int)) (ρ := Int) where
+  run := some ∘ part1
+
+instance : Part ⟨9,_⟩ Parts.Two (ι := List (List Int)) (ρ := Int) where
+  run := some ∘ part2
+
+-------------------------------------------------------------------------------------------
-- 
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