ocaml: phase 5.1 lps_dp.ml baseline (LPS "BBABCBCAB" = 7)

Standard O(n^2) length-major DP for longest palindromic
subsequence:

  dp[i][j] = dp[i+1][j-1] + 2                if s[i] = s[j]
           = max(dp[i+1][j], dp[i][j-1])     otherwise

  lps "BBABCBCAB" = 7   (witness "BABCBAB" etc.)

Complementary to manacher.ml (longest palindromic *substring*,
also length 7 on that input by coincidence) — this is the
subsequence variant which doesn't require contiguity.

Tests length-major fill order, inline if for the length-2 base
case, double-nested for with derived j = i + len - 1.

177 baseline programs total.

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 — lps_dp.ml baseline (longest palindromic
+  subsequence in "BBABCBCAB" = 7). Classic 2D O(n²) DP over
+  substring lengths: dp[i][j] = dp[i+1][j-1] + 2 when s[i]=s[j],
+  else max(dp[i+1][j], dp[i][j-1]). Witness LPS is "BABCBAB" (or
+  "BACBCAB" etc.) of length 7. Complementary to manacher.ml
+  (substring, length 7) — this is the subsequence variant.
+  Tests length-major fill order, mixed strict/inline if for
+  `len = 2` base case, double-nested for with derived j. 177
+  baseline programs total.
 - 2026-05-11 Phase 5.1 — bs_bounds.ml baseline (lower_bound /
   upper_bound binary search; counts of {3,2,5,9,4} in
   [1;2;2;3;3;3;5;7;9] encoded as 3211). Standard half-open