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.

lib/ocaml/baseline/expected.json

@@ -85,6 +85,7 @@
   "floyd_warshall.ml": 9,
   "lis.ml": 6,
   "list_ops.ml": 30,
+  "lps_dp.ml": 7,
   "lru_cache.ml": 499,
   "luhn.ml": 2,
   "magic_square.ml": 65,

lib/ocaml/baseline/lps_dp.ml

@@ -0,0 +1,21 @@
+let lps s =
+  let n = String.length s in
+  let dp = Array.init n (fun _ -> Array.make n 0) in
+  for i = 0 to n - 1 do dp.(i).(i) <- 1 done;
+  for len = 2 to n do
+    for i = 0 to n - len do
+      let j = i + len - 1 in
+      if s.[i] = s.[j] then
+        dp.(i).(j) <- (if len = 2 then 2 else dp.(i + 1).(j - 1) + 2)
+      else begin
+        let a = dp.(i + 1).(j) in
+        let b = dp.(i).(j - 1) in
+        dp.(i).(j) <- if a > b then a else b
+      end
+    done
+  done;
+  dp.(0).(n - 1)
+
+;;
+
+lps "BBABCBCAB"