ocaml: phase 5.1 task_scheduler.ml baseline ("AAABBC" cooldown 2 -> 7)

Task-scheduler closed-form min total intervals:

  m = max letter frequency
  k = number of letters tied at frequency m
  answer = max((m - 1) * (n + 1) + k, total_tasks)

For "AAABBC" with cooldown n = 2:
  freq A = 3, freq B = 2, freq C = 1 -> m = 3, k = 1
  formula = (3 - 1) * (2 + 1) + 1 = 7
  total tasks = 6
  answer = 7

Witness schedule: A, B, C, A, B, idle, A.

Tests String.iter with side-effecting count update via
Char.code arithmetic, fixed-size 26-bucket histogram.

195 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -173,6 +173,7 @@
   "stock_two.ml": 6,
   "subseq_check.ml": 3,
   "tail_factorial.ml": 479001600,
+  "task_scheduler.ml": 7,
   "tarjan_scc.ml": 4,
   "subset_sum.ml": 8,
   "tic_tac_toe.ml": 1,

lib/ocaml/baseline/task_scheduler.ml

@@ -0,0 +1,18 @@
+let task_intervals tasks n =
+  let counts = Array.make 26 0 in
+  String.iter (fun c -> counts.(Char.code c - Char.code 'A') <- counts.(Char.code c - Char.code 'A') + 1) tasks;
+  let max_c = ref 0 in
+  for i = 0 to 25 do
+    if counts.(i) > !max_c then max_c := counts.(i)
+  done;
+  let max_n = ref 0 in
+  for i = 0 to 25 do
+    if counts.(i) = !max_c then max_n := !max_n + 1
+  done;
+  let intervals = (!max_c - 1) * (n + 1) + !max_n in
+  let total = String.length tasks in
+  if intervals > total then intervals else total
+
+;;
+
+task_intervals "AAABBC" 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 — task_scheduler.ml baseline (task cooldown
+  formula, "AAABBC" with n=2 → 7 intervals). Counts each letter,
+  finds max frequency `m` and the number of letters that hit that
+  max `k`. Formula: `(m-1)·(n+1) + k`, taking the larger of that
+  and the total task count when interleaving fills the schedule.
+  Witness: A,B,C,A,B,idle,A satisfies cooldown 2 between A→A and
+  B→B. Tests String.iter with side-effecting closure (count
+  histogram update via Char.code arithmetic). 195 baseline
+  programs total.
 - 2026-05-11 Phase 5.1 — min_subarr_target.ml baseline (sliding-
   window min subarray with sum ≥ target on [2;3;1;2;4;3] target=7
   = 2). Two-pointer: expand right, then shrink left while sum