From 8d7c14a70751fb1f2fda9259177368661401296c Mon Sep 17 00:00:00 2001
From: Matthew Gretton-Dann <matt@gretton-dann.org.uk>
Date: Fri, 13 Dec 2024 09:16:31 +0000
Subject: [PATCH] 2024 day 13 part 1

---
 bin/day2413.ml | 69 ++++++++++++++++++++++++++++++++++++++++++++++++++
 bin/dune       |  6 +++--
 2 files changed, 73 insertions(+), 2 deletions(-)
 create mode 100644 bin/day2413.ml

diff --git a/bin/day2413.ml b/bin/day2413.ml
new file mode 100644
index 0000000..370696a
--- /dev/null
+++ b/bin/day2413.ml
@@ -0,0 +1,69 @@
+let parse_machine line_a line_b prize_pos =
+  let re_ab = Str.regexp {|Button [AB]: X\+\([0-9]+\), Y\+\([0-9]+\)|} in
+  let re_pos = Str.regexp {|Prize: X=\([0-9]+\), Y=\([0-9]+\)|} in
+  let _ = Str.search_forward re_ab line_a 0 in
+  let a =
+    ( int_of_string (Str.matched_group 1 line_a),
+      int_of_string (Str.matched_group 2 line_a) )
+  in
+  let _ = Str.search_forward re_ab line_b 0 in
+  let b =
+    ( int_of_string (Str.matched_group 1 line_b),
+      int_of_string (Str.matched_group 2 line_b) )
+  in
+  let _ = Str.search_forward re_pos prize_pos 0 in
+  let prize =
+    ( int_of_string (Str.matched_group 1 prize_pos),
+      int_of_string (Str.matched_group 2 prize_pos) )
+  in
+  (a, b, prize)
+
+let parse_machines =
+  let rec impl acc = function
+    | "" :: t -> impl acc t
+    | a :: b :: p :: t -> impl (parse_machine a b p :: acc) t
+    | [] -> acc
+    | _ -> failwith "parse_machines.impl"
+  in
+  impl []
+
+let machines_of_file fname = Aoc.strings_of_file fname |> parse_machines
+
+(*
+  We want to solve A * a.x + B * b.x = X
+  and              A * a.y + B * b.y = Y
+
+  which is
+
+   A * a.x / b.x + B = X / b.x
+   A * a.y / b.y + B = Y / b.y
+   A * (a.x / b.x - a.y / b.y) = X / b.x - Y / b.y
+   A * (a.x * b.y - a.y * b.x) / b.x / b.y = X / b.x - Y / b.y
+   A * (a.x * b.y - a.y * b.x) = X * b.y - Y * b.x
+  
+   A = (X * b.y - Y * b.x) / (a.x * by.y - a.y * b.x)
+   (7870 * 37 - 6450 * 84) / (17 * 37 - 86 * 84)
+   80 - (8400 * 67 - 5400 * 22) / (94 * 67 - 34 * 22)
+   a = (94, 34) b = (22, 67) p = (8400, 5400)
+  [ a.x  b.x ] [ A ]  = [ X ]
+  [ a.y  b.y ] [ B ]    [ Y ]
+*)
+let calc_tokens ((ax, ay), (bx, by), (x, y)) =
+  let a_n = (x * by) - (y * bx) in
+  let a_d = (ax * by) - (ay * bx) in
+  Printf.printf
+    "a = (%d, %d) b = (%d, %d)  p = (%d, %d), a_n / a_d = %d / %d, mod = %d\n"
+    ax ay bx by x y a_n a_d (a_n mod a_d);
+  if a_n mod a_d <> 0 then None
+  else if a_n / a_d <= 0 then None
+  else
+    let a = a_n / a_d in
+    let b = (x - (ax * a)) / bx in
+    Printf.printf "   a = %d b = %d\n" a b;
+    Some ((3 * a) + b)
+
+let part machines =
+  List.map calc_tokens machines
+  |> List.filter_map Fun.id |> List.fold_left ( + ) 0
+
+let _ = Aoc.main machines_of_file [ (string_of_int, part) ]
diff --git a/bin/dune b/bin/dune
index 506ca60..c984710 100644
--- a/bin/dune
+++ b/bin/dune
@@ -11,7 +11,8 @@
   day2409
   day2410
   day2411
-  day2412)
+  day2412
+  day2413)
  (names
   day2401
   day2402
@@ -24,5 +25,6 @@
   day2409
   day2410
   day2411
-  day2412)
+  day2412
+  day2413)
  (libraries str aoc))