ocaml: phase 5.1 dp_word_break.ml baseline (4/5 strings segmentable)

Classic word-break DP — for each position i, check whether any
dictionary word ends at i with a prior reachable position:

  dp[i] = exists w in dict with wl <= i and
          dp[i - wl] && s.sub (i - wl) wl = w

Dictionary: apple, pen, pine, pineapple, cats, cat, and, sand, dog
Inputs:
  applepenapple        yes  (apple pen apple)
  pineapplepenapple    yes  (pineapple pen apple)
  catsanddog           yes  (cats and dog)
  catsandog            no   (no segmentation reaches the end)
  applesand            yes  (apple sand)

Tests bool-typed Array, String.sub primitive, nested List.iter
over the dict inside for-loop over end positions, closure capture
of the outer dp.

179 baseline programs total.

lib/ocaml/baseline/dp_word_break.ml

@@ -0,0 +1,27 @@
+let word_break s words =
+  let n = String.length s in
+  let dp = Array.make (n + 1) false in
+  dp.(0) <- true;
+  for i = 1 to n do
+    List.iter (fun w ->
+      let wl = String.length w in
+      if i >= wl && dp.(i - wl) then begin
+        let prefix = String.sub s (i - wl) wl in
+        if prefix = w then dp.(i) <- true
+      end
+    ) words
+  done;
+  if dp.(n) then 1 else 0
+
+let count_ok strings words =
+  let count = ref 0 in
+  List.iter (fun s ->
+    count := !count + word_break s words
+  ) strings;
+  !count
+
+;;
+
+let dict = ["apple"; "pen"; "pine"; "pineapple"; "cats"; "cat"; "and"; "sand"; "dog"] in
+let inputs = ["applepenapple"; "pineapplepenapple"; "catsanddog"; "catsandog"; "applesand"] in
+count_ok inputs dict

lib/ocaml/baseline/expected.json

@@ -35,6 +35,7 @@
   "csv.ml": 10,
   "egg_drop.ml": 8,
   "dijkstra.ml": 7,
+  "dp_word_break.ml": 4,
   "distinct_subseq.ml": 3,
   "exception_handle.ml": 4,
   "exception_user.ml": 26,

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 — 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
+  dp[i−wl]=true. Inputs: applepenapple, pineapplepenapple,
+  catsanddog (yes); catsandog (no — leftover "og"); applesand (yes).
+  Tests bool-typed DP array, `String.sub s start len` substring
+  primitive, nested List.iter over dict inside for-loop over
+  positions, short-circuit + closure. 179 baseline programs total.
 - 2026-05-11 Phase 5.1 — histogram_area.ml baseline (largest
   rectangle in histogram [2;1;5;6;2;3] = 10). Linear-time stack
   algorithm: push indices while heights are non-decreasing; on