ocaml: phase 5.1 activity_select.ml baseline (greedy non-overlap = 4)

Activity selection by earliest end time. Manual bubble sort over
(start, end) tuple array, then sweep accepting whenever the next
start >= last_end.

  intervals: (1,4) (3,5) (0,6) (5,7) (3,8) (5,9) (6,10) (8,11)
             (8,12) (2,13) (12,14)

  selection: (1,4) -> (5,7) -> (8,11) -> (12,14)  = 4 activities

Tests double-loop bubble sort on tuple array with let-pattern
destructure for swap-key extraction, in-place swap of tuple cells.

192 baseline programs total.

lib/ocaml/baseline/activity_select.ml

@@ -0,0 +1,31 @@
+let max_nonoverlap intervals =
+  let arr = Array.of_list intervals in
+  let n = Array.length arr in
+  let sorted = Array.make n (0, 0) in
+  for i = 0 to n - 1 do
+    sorted.(i) <- arr.(i)
+  done;
+  for i = 0 to n - 1 do
+    for j = 0 to n - 2 - i do
+      let (_, e1) = sorted.(j) in
+      let (_, e2) = sorted.(j + 1) in
+      if e1 > e2 then begin
+        let t = sorted.(j) in
+        sorted.(j) <- sorted.(j + 1);
+        sorted.(j + 1) <- t
+      end
+    done
+  done;
+  let count = ref 0 in
+  let last_end = ref (-1000000) in
+  for i = 0 to n - 1 do
+    let (s, e) = sorted.(i) in
+    if s >= !last_end then begin
+      count := !count + 1;
+      last_end := e
+    end
+  done;
+  !count
+;;
+
+max_nonoverlap [(1, 4); (3, 5); (0, 6); (5, 7); (3, 8); (5, 9); (6, 10); (8, 11); (8, 12); (2, 13); (12, 14)]

lib/ocaml/baseline/expected.json

@@ -1,5 +1,6 @@
 {
   "abundant.ml": 21,
+  "activity_select.ml": 4,
   "ackermann.ml": 125,
   "adler32.ml": 300286872,
   "anagram_check.ml": 2,

plans/ocaml-on-sx.md

@@ -407,6 +407,15 @@ _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 — activity_select.ml baseline (greedy
+  earliest-end-time activity selection on 11 intervals → max
+  non-overlapping 4). Sort intervals by end time (bubble sort to
+  avoid relying on List.sort with tuple comparator), then sweep
+  and accept whenever start ≥ last_end. Optimal selection:
+  (1,4) → (5,7) → (8,11) → (12,14) = 4 activities. Tests double-
+  loop bubble sort on tuple array with let-pattern destructure
+  for swap key extraction, in-place swap of tuple cells via temp.
+  192 baseline programs total.
 - 2026-05-11 Phase 5.1 — count_paths_dag.ml baseline (count
   source-to-sink paths in the same 6-node DAG as topo_sort.ml,
   paths 0→5 = 3). Topological sort via Kahn's (BFS), then relax