ocaml: phase 5.1 knapsack.ml baseline (0/1 knapsack, cap=8 -> 36)

Standard 1D 0/1 knapsack DP with reverse inner loop:

  let knapsack values weights cap =
    let n = Array.length values in
    let dp = Array.make (cap + 1) 0 in
    for i = 0 to n - 1 do
      let v = values.(i) and w = weights.(i) in
      for c = cap downto w do
        let take = dp.(c - w) + v in
        if take > dp.(c) then dp.(c) <- take
      done
    done;
    dp.(cap)

  values: [|6; 10; 12; 15; 20|]
  weights: [|1; 2;  3;  4;  5|]
  knapsack v w 8 = 36   (* take items with weights 1, 2, 5 *)

Tests for-downto + array literal access in the same hot loop.

143 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -81,6 +81,7 @@
   "json_pretty.ml": 24,
   "kadane.ml": 6,
   "kmp.ml": 5,
+  "knapsack.ml": 36,
   "lambda_calc.ml": 7,
   "lcs.ml": 4,
   "majority_vote.ml": 4,

lib/ocaml/baseline/knapsack.ml

@@ -0,0 +1,17 @@
+let knapsack values weights cap =
+  let n = Array.length values in
+  let dp = Array.make (cap + 1) 0 in
+  for i = 0 to n - 1 do
+    let v = values.(i) and w = weights.(i) in
+    for c = cap downto w do
+      let take = dp.(c - w) + v in
+      if take > dp.(c) then dp.(c) <- take
+    done
+  done;
+  dp.(cap)
+
+;;
+
+let v = [|6; 10; 12; 15; 20|] in
+let w = [|1; 2; 3; 4; 5|] in
+knapsack v w 8

plans/ocaml-on-sx.md

@@ -407,6 +407,14 @@ _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.
+- 2026-05-10 Phase 5.1 — knapsack.ml baseline (0/1 knapsack DP,
+  cap=8 with values [|6;10;12;15;20|] and weights [|1;2;3;4;5|]
+  → max value 36). 1D rolling DP: outer loop over items, inner
+  for-downto so each item used at most once. Optimal pack {1,2,5}
+  weighing 8 with value 36 (also matches 6+10+20). Tests
+  `for c = cap downto w do … done` reverse iteration plus
+  array literal access in the same hot loop. 143 baseline
+  programs total.
 - 2026-05-10 Phase 5.1 — lcs.ml baseline (longest common subsequence
   of "ABCBDAB" and "BDCAB" = 4). Rolling-array DP in O(mn) time and
   O(min(m,n)) space: keep `prev` and `curr` rows, copy after each