diff --git a/bin/day2419.ml b/bin/day2419.ml
index f5b73fb..543d520 100644
--- a/bin/day2419.ml
+++ b/bin/day2419.ml
@@ -7,59 +7,50 @@ let towels_of_strings = function
       (h, t)
   | _ -> failwith "towels_of_strings"
 
+(** [towels_of_file fname] returns the list of towels and patterns from the file
+    [fname]. *)
 let towels_of_file fname = Aoc.strings_of_file fname |> towels_of_strings
+
+(** Memoizing hash table shared between parts 1 and 2. *)
 let memo = Hashtbl.create 1000
 
-let rec memoize_has_pattern pattern towels =
-  let pattern_len = String.length pattern in
-  let rec has_pattern = function
-    | [] -> false
-    | h :: t ->
-        let towel_len = String.length h in
-        if String.starts_with ~prefix:h pattern then
-          memoize_has_pattern
-            (String.sub pattern towel_len (pattern_len - towel_len))
-            towels
-          || has_pattern t
-        else has_pattern t
-  in
-  match Hashtbl.find_opt memo pattern with
+(** [memoize memo f value] returns the result of [f value]. The hashtable [memo]
+    is used to cache results, so repeated calls with the same [value] will not
+    call [f] again. *)
+let memoize memo f value =
+  match Hashtbl.find_opt memo value with
   | Some x -> x
   | None ->
-      let x = if pattern_len = 0 then true else has_pattern towels in
-      Hashtbl.add memo pattern x;
+      let x = f value in
+      Hashtbl.add memo value x;
       x
 
-let has_match towels pattern = memoize_has_pattern pattern towels
-let memo2 = Hashtbl.create 1000
-
-let rec memoize_count_matches pattern towels =
+(** [count_hashes memo towels pattern] counts the number of ways of matching
+    [pattern] using [towels]. [memo] is a hashtable used for memoizing results.
+*)
+let rec count_matches memo towels pattern =
   let pattern_len = String.length pattern in
-  let rec has_pattern = function
+  let rec count_matched = function
     | [] -> 0
     | h :: t ->
         let towel_len = String.length h in
         if String.starts_with ~prefix:h pattern then
-          memoize_count_matches
+          memoize memo
+            (count_matches memo towels)
             (String.sub pattern towel_len (pattern_len - towel_len))
-            towels
-          + has_pattern t
-        else has_pattern t
+          + count_matched t
+        else count_matched t
   in
-  match Hashtbl.find_opt memo2 pattern with
-  | Some x -> x
-  | None ->
-      let x = if pattern_len = 0 then 1 else has_pattern towels in
-      Hashtbl.add memo2 pattern x;
-      x
-
-let count_matches towels pattern = memoize_count_matches pattern towels
+  if pattern_len = 0 then 1 else count_matched towels
 
 let part1 (towels, patterns) =
-  List.filter (has_match towels) patterns |> List.length
+  List.map (count_matches memo towels) patterns
+  |> List.filter (( > ) 0)
+  |> List.length
 
 let part2 (towels, patterns) =
-  List.map (count_matches towels) patterns |> List.fold_left ( + ) 0
+  List.map (memoize memo (count_matches memo towels)) patterns
+  |> List.fold_left ( + ) 0
 
 let _ =
   Aoc.main towels_of_file [ (string_of_int, part1); (string_of_int, part2) ]