ocaml: phase 5.1 palindrome_part.ml baseline (min cuts "aabba" = 1)

Two-phase palindrome-partition DP for the minimum-cuts variant:

  Phase 1: is_pal[i][j] palindrome table via length-major fill
           (single chars, then pairs, then expand inward).

  Phase 2: cuts[i] = 0 if s[0..i] is itself a palindrome,
                  = min over j of (cuts[j-1] + 1)
                    where s[j..i] is a palindrome.

  min_cut "aabba" = 1   ("a" | "abba")

Tests two sequential 2D DPs sharing the same is_pal matrix,
inline begin/end branches inside the length-major fill, mixed
bool and int 2D arrays.

181 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -125,6 +125,7 @@
   "mutable_record.ml": 10,
   "option_match.ml": 5,
   "palindrome.ml": 4,
+  "palindrome_part.ml": 1,
   "palindrome_sum.ml": 49500,
   "paren_depth.ml": 7,
   "partition.ml": 3025,

lib/ocaml/baseline/palindrome_part.ml

@@ -0,0 +1,35 @@
+let min_cut s =
+  let n = String.length s in
+  if n <= 1 then 0
+  else begin
+    let is_pal = Array.init n (fun _ -> Array.make n false) in
+    for i = 0 to n - 1 do is_pal.(i).(i) <- true 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 begin
+          if len = 2 then is_pal.(i).(j) <- true
+          else is_pal.(i).(j) <- is_pal.(i + 1).(j - 1)
+        end
+      done
+    done;
+    let cuts = Array.make n 0 in
+    for i = 0 to n - 1 do
+      if is_pal.(0).(i) then cuts.(i) <- 0
+      else begin
+        let best = ref i in
+        for j = 1 to i do
+          if is_pal.(j).(i) then begin
+            let c = cuts.(j - 1) + 1 in
+            if c < !best then best := c
+          end
+        done;
+        cuts.(i) <- !best
+      end
+    done;
+    cuts.(n - 1)
+  end
+
+;;
+
+min_cut "aabba"