ocaml: phase 5.1 count_subarrays_k.ml baseline (sum-k subarrays = 7)

Count contiguous subarrays summing to a target k using a prefix
sum table:

  prefix[i+1] = prefix[i] + arr[i]
  count = |{ (i, j) : 0 <= i < j <= n,  prefix[j] - prefix[i] = k }|

For arr = [1; 1; 1; 2; -1; 3; 1; -2; 4] and k = 3, the seven
witnesses are:

  [1, 1, 1]            (0..2)
  [1, 1, 2, -1]        (1..4)
  [1, 2]               (2..3)
  [2, -1, 3, 1, -2]    (3..7)
  [-1, 3, 1]           (4..6)
  [3]                  (5..5)
  [1, -2, 4]           (6..8)

Negative-valued arrays exercise mixed-sign integer arithmetic.

186 baseline programs total.

lib/ocaml/baseline/count_subarrays_k.ml

@@ -0,0 +1,16 @@
+let count_subarr_sum_k arr k =
+  let n = Array.length arr in
+  let prefix = Array.make (n + 1) 0 in
+  for i = 0 to n - 1 do
+    prefix.(i + 1) <- prefix.(i) + arr.(i)
+  done;
+  let count = ref 0 in
+  for i = 0 to n - 1 do
+    for j = i + 1 to n do
+      if prefix.(j) - prefix.(i) = k then count := !count + 1
+    done
+  done;
+  !count
+;;
+
+count_subarr_sum_k [| 1; 1; 1; 2; -1; 3; 1; -2; 4 |] 3

lib/ocaml/baseline/expected.json

@@ -32,6 +32,7 @@
   "coin_min.ml": 6,
   "count_change.ml": 406,
   "count_inversions.ml": 12,
+  "count_subarrays_k.ml": 7,
   "csv.ml": 10,
   "egg_drop.ml": 8,
   "dijkstra.ml": 7,

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.
+- 2026-05-11 Phase 5.1 — count_subarrays_k.ml baseline (count
+  contiguous subarrays of [1;1;1;2;-1;3;1;-2;4] summing to k=3
+  = 7). Prefix-sum brute force in O(n²): build cumulative array,
+  enumerate (i,j) pairs and check prefix[j]−prefix[i]=k. The 7
+  witnesses include [1,1,1], [1,1,2,−1], [1,2], [2,−1,3,1,−2],
+  [−1,3,1], [3], [1,−2,4]. Negative-valued arrays exercise our
+  evaluator's mixed-sign integer arithmetic (no underflow at the
+  JS safe-int boundary). 186 baseline programs total.
 - 2026-05-11 Phase 5.1 — floyd_cycle.ml baseline (Floyd's tortoise
   -and-hare cycle detection on f(x) = (2x+5) mod 17; μ=0 λ=8 →
   encoded 8). Three phases: (1) advance slow/fast until they