ocaml: phase 5.1 convex_hull.ml baseline (Andrew monotone chain, 5 vertices)

Andrew's monotone chain hull over 8 integer points:

  pts = [(0,0); (1,1); (2,0); (2,2); (0,2); (1,0); (3,3); (5,1)]

Sort lex, build lower hull L->R then upper R->L, popping while
the cross product is non-positive (collinear included on hull).

Hull traverse: (0,0) -> (2,0) -> (5,1) -> (3,3) -> (0,2) = 5
((2,0) lies on the lower edge from (0,0) to (5,1)).

Tests List.sort with 2-tuple comparator using nested pair
destructure, repeated `let (x, y) = arr.(i) in` array tuple
destructure across both passes, while + cont-flag pattern.

170 baseline programs total.

lib/ocaml/baseline/convex_hull.ml

@@ -0,0 +1,43 @@
+let cross ox oy ax ay bx by =
+  (ax - ox) * (by - oy) - (ay - oy) * (bx - ox)
+
+let hull_size pts =
+  let n = List.length pts in
+  if n < 3 then n
+  else begin
+    let sorted = List.sort (fun (a, b) (c, d) ->
+      if a <> c then compare a c else compare b d) pts in
+    let arr = Array.of_list sorted in
+    let h = Array.make (2 * n) (0, 0) in
+    let k = ref 0 in
+    for i = 0 to n - 1 do
+      let (xi, yi) = arr.(i) in
+      let cont = ref true in
+      while !cont && !k >= 2 do
+        let (ox, oy) = h.(!k - 2) in
+        let (ax, ay) = h.(!k - 1) in
+        if cross ox oy ax ay xi yi <= 0 then k := !k - 1
+        else cont := false
+      done;
+      h.(!k) <- (xi, yi);
+      k := !k + 1
+    done;
+    let lo = !k + 1 in
+    for i = n - 2 downto 0 do
+      let (xi, yi) = arr.(i) in
+      let cont = ref true in
+      while !cont && !k >= lo do
+        let (ox, oy) = h.(!k - 2) in
+        let (ax, ay) = h.(!k - 1) in
+        if cross ox oy ax ay xi yi <= 0 then k := !k - 1
+        else cont := false
+      done;
+      h.(!k) <- (xi, yi);
+      k := !k + 1
+    done;
+    !k - 1
+  end
+
+;;
+
+hull_size [(0, 0); (1, 1); (2, 0); (2, 2); (0, 2); (1, 0); (3, 3); (5, 1)]

lib/ocaml/baseline/expected.json

@@ -25,6 +25,7 @@
   "calc.ml": 13,
   "catalan.ml": 42,
   "closures.ml": 315,
+  "convex_hull.ml": 5,
   "coin_change.ml": 6,
   "coin_min.ml": 6,
   "count_change.ml": 406,

plans/ocaml-on-sx.md

@@ -407,6 +407,17 @@ _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.
+- 2026-05-11 Phase 5.1 — convex_hull.ml baseline (Andrew's monotone
+  chain over 8 points → 5-vertex convex hull). Sorts points
+  lexicographically, then builds lower hull left-to-right and upper
+  hull right-to-left, popping back when the cross product turns the
+  wrong way. Points: (0,0), (1,1), (2,0), (2,2), (0,2), (1,0),
+  (3,3), (5,1). Hull = (0,0) → (2,0) → (5,1) → (3,3) → (0,2) = 5
+  vertices ((2,0) lies on lower edge, included by the ≤ test).
+  Tests List.sort with a 2-tuple comparator using nested pair
+  destructure, repeated `let (x, y) = arr.(i) in` array tuple
+  destructure across both passes, while + cont-flag pattern instead
+  of break. 170 baseline programs total.
 - 2026-05-10 Phase 5.1 — next_greater.ml baseline (monotonic stack
   for next-greater-element over [4;5;2;25;7;8;1;30;12], sum of
   successors = 153). Right-to-left scan with a stack that pops