ocaml: phase 5.1 count_change.ml baseline (ways to make 50c from [1;2;5;10;25] = 406)

Companion to coin_change.ml (min coins). Counts distinct multisets
via the unbounded-knapsack DP:

  let count_ways coins target =
    let dp = Array.make (target + 1) 0 in
    dp.(0) <- 1;
    List.iter (fun c ->
      for i = c to target do
        dp.(i) <- dp.(i) + dp.(i - c)
      done
    ) coins;
    dp.(target)

Outer loop over coins, inner DP relaxes dp.(i) += dp.(i - c). The
order matters — coin in outer, amount in inner — to count multisets
rather than ordered sequences.

count_ways [1; 2; 5; 10; 25] 50 = 406.

79 baseline programs total.

lib/ocaml/baseline/count_change.ml

@@ -0,0 +1,13 @@
+let count_ways coins target =
+  let dp = Array.make (target + 1) 0 in
+  dp.(0) <- 1;
+  List.iter (fun c ->
+    for i = c to target do
+      dp.(i) <- dp.(i) + dp.(i - c)
+    done
+  ) coins;
+  dp.(target)
+
+;;
+
+count_ways [1; 2; 5; 10; 25] 50

lib/ocaml/baseline/expected.json

@@ -18,6 +18,7 @@
   "calc.ml": 13,
   "closures.ml": 315,
   "coin_change.ml": 6,
+  "count_change.ml": 406,
   "csv.ml": 10,
   "exception_handle.ml": 4,
   "exception_user.ml": 26,