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,

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — count_change.ml baseline (number of ways to
+  make 50c from [1;2;5;10;25] = 406). Companion to coin_change.ml
+  (min coins): instead of minimising, this counts distinct
+  multisets. Outer loop over coins, inner DP `dp.(i) += dp.(i - c)`
+  (the standard "unbounded knapsack" count). Tests Array.make +
+  arr.(i) accumulation through nested List.iter / for. 79 baseline
+  programs total.
 - 2026-05-09 Phase 5.1 — paren_depth.ml baseline (max paren nesting
   depth, 3+3+1 = 7). One-pass walk tracking current depth and a
   high-water mark. Tests three inputs: