June 2018 Update

Task/Catalan-numbers/OCaml/catalan-numbers.ocaml

@@ -1,12 +1,54 @@
-let catalan : int ref = ref 0 in
-Printf.printf "%d ," 1 ;
-for i = 2 to 9  do
-let nm : int ref = ref 1 in
-let den : int ref = ref 1 in
-for k = 2 to i do
-nm := (!nm)*(i+k);
-den := (!den)*k;
-catalan := (!nm)/(!den) ;
-done;
-print_int (!catalan); print_string "," ;
-done;;
+let imp_catalan n =
+  let return = ref 1 in
+  for i = 1 to n do
+    return := !return * 2 * (2 * i - 1) / (i + 1)
+  done;
+  !return
+
+let rec catalan = function
+  | 0 -> 1
+  | n -> catalan (n - 1) * 2 * (2 * n - 1) / (n + 1)
+
+let memoize f =
+  let cache = Hashtbl.create 20 in
+  fun n ->
+    match Hashtbl.find_opt cache n with
+    | None ->
+      let x = f n in
+      Hashtbl.replace cache n x;
+      x
+    | Some x -> x
+
+let catalan_cache = Hashtbl.create 20
+
+let rec memo_catalan n =
+  if n = 0 then 1 else
+    match Hashtbl.find_opt catalan_cache n with
+    | None ->
+      let x = memo_catalan (n - 1) * 2 * (2 * n - 1) / (n + 1) in
+      Hashtbl.replace catalan_cache n x;
+      x
+    | Some x -> x
+
+let () =
+  if not !Sys.interactive then
+    let bench label f n times =
+      let start = Unix.gettimeofday () in
+      begin
+        for i = 1 to times do f n done;
+        let stop = Unix.gettimeofday () in
+        Printf.printf "%s (%d runs) : %.3f\n"
+          label times (stop -. start)
+      end in
+    let show f g h f' n =
+      for i = 0 to n do
+        Printf.printf "%2d %7d %7d %7d %7d\n"
+          i (f i) (g i) (h i) (f' i)
+      done
+    in
+    List.iter (fun (l, f) -> bench l f 15 10_000_000)
+      ["imperative", imp_catalan;
+       "recursive", catalan;
+       "hand-memoized", memo_catalan;
+       "memoized", (memoize catalan)];
+    show imp_catalan catalan memo_catalan (memoize catalan) 15