Reimplement 2024 day 6 to use a set.

This seems "better" from a functional perspective.  However, it runs
substantially slower for part 2.

bin/day2406.ml

@@ -1,31 +1,59 @@
-(** [find_start map] returns the location [(x, y)] of the starting position. *)
-let find_start map =
-  let rec impl row =
-    if row >= Array.length map then failwith "find_start"
-    else
-      match Array.find_index (fun x -> x = '^') map.(row) with
+(** [IntPair] is a module describing pairs of ints, suitable for using with
+    [Set.Make]. *)
+module IntPair = struct
+  type t = int * int
+
+  let compare (x, y) (x', y') =
+    match compare y y' with 0 -> compare x x' | c -> c
+end
+
+module PosSet = Set.Make (IntPair)
+(** [PosSet] represents a set of positions. *)
+
+type map = { blocks : PosSet.t; width : int; height : int }
+(** [map] represents a map with [blocks] and a [width] and [height]. *)
+
+(** [find_start strs] returns the location [(x, y)] of the starting position. *)
+let find_start strs =
+  let rec impl row = function
+    | [] -> failwith "find_start"
+    | h :: t -> (
+        match String.index_from_opt h 0 '^' with
         | Some i -> (i, row)
-      | None -> impl (row + 1)
+        | None -> impl (row + 1) t)
   in
-  impl 0
+  impl 0 strs
+
+(** [map_of_strings strs] returns the map generated from the input map described
+    by the list of strings [strs] *)
+let map_of_strings strs =
+  let rec row_scan acc y pos s =
+    match String.index_from_opt s pos '#' with
+    | Some x -> row_scan (PosSet.add (x, y) acc) y (x + 1) s
+    | None -> acc
+  in
+  let rec impl acc y = function
+    | h :: t -> impl (row_scan acc y 0 h) (y + 1) t
+    | [] -> (acc, y)
+  in
+  let blocks, height = impl PosSet.empty 0 strs in
+  let width = String.length (List.hd strs) in
+  { blocks; height; width }
 
 (** [read_file fname] reads the input map from [fname]. It returns a
     [(map, pos, vel)] tuple, consisting of the obsticle map, initial position,
     and initial velocity. *)
 let read_file fname =
   let lst = Aoc.strings_of_file fname in
-  let map1 = Array.of_list lst in
-  let map2 =
-    Array.map (fun s -> Array.init (String.length s) (String.get s)) map1
-  in
-  let pos = find_start map2 in
-  (map2, pos, (0, -1))
+  let map = map_of_strings lst in
+  let pos = find_start lst in
+  (map, pos, (0, -1))
 
 (** [is_valid_pos map pos] returns true if the position [pos] is valid for the
     map [map]. *)
 let is_valid_pos map (x, y) =
-  if y < 0 || y >= Array.length map then false
-  else if x < 0 || x >= Array.length map.(y) then false
+  if y < 0 || y >= map.height then false
+  else if x < 0 || x >= map.width then false
   else true
 
 (** [move map (pos, vel)] moves [pos] one step forward on the [map]. [vel] gives
@@ -33,21 +61,9 @@ let is_valid_pos map (x, y) =
     [vel] is rotated right by 90 degrees and we move in that direction. Returns
     the updated [(pos, vel)] pair. *)
 let rec move map ((x, y), (dx, dy)) =
-  if is_valid_pos map (x, y) then
   let x', y' = (x + dx, y + dy) in
-    if is_valid_pos map (x', y') && map.(y').(x') = '#' then
-      move map ((x, y), (-dy, dx))
+  if PosSet.mem (x', y') map.blocks then move map ((x, y), (-dy, dx))
   else ((x', y'), (dx, dy))
-  else ((x, y), (dx, dy))
-
-(** [compare_pos pos pos'] provides a total ordering on the positions [pos] and
-    [pos']. *)
-let compare_pos (x, y) (x', y') =
-  if y < y' then -1
-  else if y > y' then 1
-  else if x < x' then -1
-  else if x > x' then 1
-  else 0
 
 (** [walk_map map (pos, vel)] walks around [map] starting at [pos] moving in the
     direction [vel]. It returns a list of all positions visited before falling
@@ -76,26 +92,21 @@ let has_cycles map (pos, vel) =
      position. *)
   impl (pos, vel) (move map (pos, vel))
 
-(** [map_copy map] returns a deep copy of [map]. *)
-let map_copy = Array.map Array.copy
-
 (** [walk_block map (pos, vel) bpos] adds a block to the map [map] at [bpos] and
     then sees if walking the map starting with [(pos, vel)] has a cycle. *)
-let walk_block map (pos, vel) ((bx, by) as bpos) =
+let walk_block map (pos, vel) bpos =
   if bpos = pos then false
   else
-    let map' = map_copy map in
-    map'.(by).(bx) <- '#';
+    let map' = { map with blocks = PosSet.add bpos map.blocks } in
     has_cycles map' (pos, vel)
 
 let part1 (map, pos, vel) =
-  walk_map map (pos, vel) |> List.sort_uniq compare_pos |> List.length
+  walk_map map (pos, vel) |> List.sort_uniq IntPair.compare |> List.length
 
 let part2 (map, pos, vel) =
-  let map' = Array.copy map in
-  walk_map map' (pos, vel)
-  |> List.sort_uniq compare_pos
-  |> List.filter (walk_block map' (pos, vel))
+  walk_map map (pos, vel)
+  |> List.sort_uniq IntPair.compare
+  |> List.filter (walk_block map (pos, vel))
   |> List.length
 
 let _ = Aoc.main read_file [ (string_of_int, part1); (string_of_int, part2) ]