ocaml: phase 5.1 max_product3.ml baseline (max product of 3, with negatives -> 300)

Sort, then compare two candidates:
  p1 = product of three largest values
  p2 = product of two smallest (potentially negative) values and the largest

For [-10;-10;1;3;2]:
  sorted    = [-10;-10;1;2;3]
  p1        = 3 * 2 * 1                = 6
  p2        = (-10) * (-10) * 3        = 300
  max       = 300

Tests List.sort + Array.of_list + arr.(n-i) end-walk + candidate-pick
via if-then-else.

104 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -51,6 +51,7 @@
   "luhn.ml": 2,
   "mat_mul.ml": 621,
   "max_path_tree.ml": 11,
+  "max_product3.ml": 300,
   "max_run.ml": 5,
   "mod_inverse.ml": 27,
   "json_pretty.ml": 24,

lib/ocaml/baseline/max_product3.ml

@@ -0,0 +1,11 @@
+let max_prod3 xs =
+  let sorted = List.sort compare xs in
+  let arr = Array.of_list sorted in
+  let n = Array.length arr in
+  let p1 = arr.(n - 1) * arr.(n - 2) * arr.(n - 3) in
+  let p2 = arr.(0) * arr.(1) * arr.(n - 1) in
+  if p1 > p2 then p1 else p2
+
+;;
+
+max_prod3 [-10; -10; 1; 3; 2]

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _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 — max_product3.ml baseline (max product of
+  three from a list including negatives = 300). Sort, then compare
+  product of three largest vs product of two smallest negatives and
+  one largest. For [-10;-10;1;3;2]: 3*2*1 = 6 vs (-10)*(-10)*3 = 300.
+  Tests List.sort + Array.of_list + arr.(n-i) end-walk + candidate
+  compare. 104 baseline programs total.
 - 2026-05-09 Phase 5.1 — euler9.ml baseline (Project Euler #9, abc
   product for the unique Pythagorean triple with a+b+c=1000 →
   31875000). Naive triple loop times out under contention (10-min