Further tidy ups of 2024 day 21.

bin/day2421.ml

@@ -74,51 +74,37 @@ let find_paths (sx, sy) (fx, fy) =
   in
   result
 
+(** [cartesian f initial_acc lst lst'] calls [f acc h h'] for the cross-product
+    of all elements [h], [h'] in [lst] and [lst']. [acc] is updated in each call
+    with the result of all previous calls to [f]. The result is the final [acc].
+*)
+let cartesian f initial_acc lst lst' =
+  let rec impl' acc h = function
+    | [] -> acc
+    | h' :: t' -> impl' (f acc h h') h t'
+  in
+  let rec impl acc = function
+    | [] -> acc
+    | h :: t -> impl (impl' acc h lst') t
+  in
+  impl initial_acc lst
+
 (** [routes pos_of_grid locs] returns a map of [(start, finish)] pairs mapping
     to a list of paths for getting to that route. [locs] are the locations on
     the grid to investiagte. [pos_of_grid] gives the location of each of the
     [locs]. The returned map contains routes from each element in [locs] to
     every element. *)
 let routes pos_of_grid locs =
-  let rec impl acc pos =
-    let start = pos_of_grid pos in
-    function
-    | [] -> acc
-    | h :: t ->
-        impl
-          (CharPairMap.add (pos, h) (find_paths start (pos_of_grid h)) acc)
-          pos t
+  let impl acc h h' =
+    CharPairMap.add (h, h') (find_paths (pos_of_grid h) (pos_of_grid h')) acc
   in
-  let rec impl' acc = function
-    | [] -> acc
-    | h :: t -> impl' (impl acc h locs) t
-  in
-  impl' CharPairMap.empty locs
-
-(** Elements on the number grid *)
-let num_grid = [ '0'; '1'; '2'; '3'; '4'; '5'; '6'; '7'; '8'; '9'; 'A' ]
-
-(** Routes between positions on the number grid *)
-let num_routes = routes pos_of_numeric_grid num_grid
-
-(** Elements on the direction grid *)
-let dir_grid = [ '<'; '>'; 'v'; '^'; 'A' ]
-
-(** Routes between positions on the direction grid. *)
-let dir_routes = routes pos_of_dir_grid dir_grid
+  cartesian impl CharPairMap.empty locs locs
 
 (** [initial_cost_map grid] returns a map for the initial costs (1) of moving
     between different positions on [grid]. *)
 let initial_cost_map grid =
-  let rec impl' acc f = function
-    | [] -> acc
-    | h :: t -> impl' (CharPairMap.add (f, h) 1 acc) f t
-  in
-  let rec impl acc = function
-    | [] -> acc
-    | h :: t -> impl (impl' acc h grid) t
-  in
-  impl CharPairMap.empty grid
+  let update acc h h' = CharPairMap.add (h, h') 1 acc in
+  cartesian update CharPairMap.empty grid grid
 
 (** [calc_cost cost_map steps] calculates the cost of following [steps].
     [cost_map] gives the cost of moving between each position. *)
@@ -142,13 +128,17 @@ let get_next_level_costs route_map cost_map =
 (** [min_code_cost count code] returns the number of buttons a human needs to
     press to get [code] entered when indirected through [count] robots. *)
 let min_code_cost count code =
-  let number_costs =
+  let num_grid = [ '0'; '1'; '2'; '3'; '4'; '5'; '6'; '7'; '8'; '9'; 'A' ] in
+  let num_routes = routes pos_of_numeric_grid num_grid in
+  let dir_grid = [ '<'; '>'; 'v'; '^'; 'A' ] in
+  let dir_routes = routes pos_of_dir_grid dir_grid in
+  let costs =
     Aoc.apply_n count
       (get_next_level_costs dir_routes)
       (initial_cost_map dir_grid)
   in
-  let number_costs = get_next_level_costs num_routes number_costs in
-  calc_cost number_costs code
+  let costs = get_next_level_costs num_routes costs in
+  calc_cost costs code
 
 (** [get_code_complexity count code] returns the complexity of a given code when
     there are [count] robots involved. *)