ocaml: phase 5.1 island_count.ml baseline (6x7 grid, 5 components)

Count 4-connected components of 1-cells via DFS flood from every
unvisited 1-cell.

Grid (1s shown as #):
  # # . . . # #
  # . . . # # .
  . . # # . . .
  . # # # . # #
  # . . . . # .
  # # . # # # .

Components:
  {(0,0),(0,1),(1,0)}
  {(0,5),(0,6),(1,4),(1,5)}
  {(2,2),(2,3),(3,1),(3,2),(3,3)}
  {(3,5),(3,6),(4,5),(5,3),(5,4),(5,5)}
  {(4,0),(5,0),(5,1)}
                              -> 5 islands

Complementary to flood_fill.ml (largest component); this counts
total components.

Tests recursive function returning () at early-exit branches,
ordered double-for entry pass triggering one fill per island root.

180 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -80,6 +80,7 @@
   "huffman.ml": 224,
   "int_sqrt.ml": 1027,
   "is_prime.ml": 25,
+  "island_count.ml": 5,
   "fizz_classifier.ml": 540,
   "fizzbuzz.ml": 57,
   "flatten_tree.ml": 28,

lib/ocaml/baseline/island_count.ml

@@ -0,0 +1,37 @@
+let h = 6
+let w = 7
+let grid = [|
+  [| 1; 1; 0; 0; 0; 1; 1 |];
+  [| 1; 0; 0; 0; 1; 1; 0 |];
+  [| 0; 0; 1; 1; 0; 0; 0 |];
+  [| 0; 1; 1; 1; 0; 1; 1 |];
+  [| 1; 0; 0; 0; 0; 1; 0 |];
+  [| 1; 1; 0; 1; 1; 1; 0 |]
+|]
+
+let rec fill visited r c =
+  if r < 0 || r >= h || c < 0 || c >= w then ()
+  else if visited.(r).(c) || grid.(r).(c) = 0 then ()
+  else begin
+    visited.(r).(c) <- true;
+    fill visited (r - 1) c;
+    fill visited (r + 1) c;
+    fill visited r (c - 1);
+    fill visited r (c + 1)
+  end
+
+let count_islands () =
+  let visited = Array.init h (fun _ -> Array.make w false) in
+  let count = ref 0 in
+  for r = 0 to h - 1 do
+    for c = 0 to w - 1 do
+      if grid.(r).(c) = 1 && not visited.(r).(c) then begin
+        count := !count + 1;
+        fill visited r c
+      end
+    done
+  done;
+  !count
+;;
+
+count_islands ()

plans/ocaml-on-sx.md

@@ -407,6 +407,18 @@ _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 — island_count.ml baseline (count 4-connected
+  components of 1-cells in a 6×7 grid = 5). DFS flood from every
+  unvisited 1-cell. Counted islands:
+    {(0,0),(0,1),(1,0)}
+    {(0,5),(0,6),(1,4),(1,5)}
+    {(2,2),(2,3),(3,1),(3,2),(3,3)}
+    {(3,5),(3,6),(4,5),(5,3),(5,4),(5,5)}
+    {(4,0),(5,0),(5,1)}
+  Complementary to flood_fill.ml which measures largest component;
+  this counts them. Tests recursive returning `()` (unit) at
+  early-exit branches, ordered double-for entry pass that triggers
+  one fill per island root. 180 baseline programs total.
 - 2026-05-11 Phase 5.1 — dp_word_break.ml baseline (word-break DP
   over 5 strings with 9-word dictionary; 4 strings segmentable).
   dp[i] = ∃ word w of length wl ≤ i with prefix s[i−wl..i]=w and