ocaml: phase 5.1 distinct_subseq.ml baseline ("rabbit" in "rabbbit" = 3)

Classic distinct-subsequences 2D DP:

  dp[i][j] = dp[i-1][j] + (s[i-1] = t[j-1] ? dp[i-1][j-1] : 0)
  dp[i][0] = 1   (empty t is a subseq of any prefix of s)

  count_subseq "rabbbit" "rabbit" = 3

The three witnesses correspond to which 'b' in "rabbbit" is
dropped (positions 2, 3, or 4 zero-indexed of the run of bs).

Complements subseq_check.ml (just tests presence); this one counts
distinct embeddings.

Tests 2D DP with Array.init n (fun _ -> Array.make m 0), base row
initialization, mixed string + array indexing.

175 baseline programs total.

lib/ocaml/baseline/distinct_subseq.ml

@@ -0,0 +1,20 @@
+let count_subseq s t =
+  let m = String.length s in
+  let n = String.length t in
+  let dp = Array.init (m + 1) (fun _ -> Array.make (n + 1) 0) in
+  for i = 0 to m do
+    dp.(i).(0) <- 1
+  done;
+  for i = 1 to m do
+    for j = 1 to n do
+      if s.[i - 1] = t.[j - 1] then
+        dp.(i).(j) <- dp.(i - 1).(j) + dp.(i - 1).(j - 1)
+      else
+        dp.(i).(j) <- dp.(i - 1).(j)
+    done
+  done;
+  dp.(m).(n)
+
+;;
+
+count_subseq "rabbbit" "rabbit"

lib/ocaml/baseline/expected.json

@@ -34,6 +34,7 @@
   "csv.ml": 10,
   "egg_drop.ml": 8,
   "dijkstra.ml": 7,
+  "distinct_subseq.ml": 3,
   "exception_handle.ml": 4,
   "exception_user.ml": 26,
   "euler1.ml": 233168,

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 — distinct_subseq.ml baseline (count
+  distinct subsequences of "rabbbit" that equal "rabbit" = 3).
+  Classic 2D DP: dp[i][j] = dp[i-1][j] + (s[i-1]=t[j-1] ? dp[i-1][j-1]
+  : 0). Three witnesses correspond to which `b` in "rabbbit" is
+  dropped: positions 2, 3, or 4 (0-indexed of the three b's).
+  Complements existing subseq_check.ml which just tests presence.
+  Tests 2D DP with `Array.init … (fun _ -> Array.make …)`, edge-
+  case base row dp[i][0]=1 (empty t is a subseq of any prefix).
+  175 baseline programs total.
 - 2026-05-11 Phase 5.1 — bracket_match.ml baseline (multi-bracket
   parenthesis matching over 9 test strings, 5 balanced). Stack-
   based scan: push openers `( [ {`, pop and pair-check closers.