ocaml: phase 5.1 manacher.ml baseline (longest palindrome "babadaba" = 7)

Manacher's algorithm: insert # separators (length 2n+1) to unify
odd/even cases, then maintain palindrome radii p[] alongside a
running (center, right) pair to skip work via mirror reflection.
Linear time.

  manacher "babadaba" = 7   (* witness: "abadaba", positions 1..7 *)

Note: requires parenthesizing the if-expression on the rhs of <-:

  p.(i) <- (if pm < v then pm else v)

Real OCaml parses bare `if` at <-rhs since the rhs is at expr
level; our parser places <-rhs at binop level which doesn't include
`if` / `match` / `let`. Workaround until we relax the binop
RHS grammar.

149 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -87,6 +87,7 @@
   "lambda_calc.ml": 7,
   "lcs.ml": 4,
   "majority_vote.ml": 4,
+  "manacher.ml": 7,
   "levenshtein.ml": 11,
   "memo_fib.ml": 75025,
   "mortgage.ml": 1073,

lib/ocaml/baseline/manacher.ml

@@ -0,0 +1,32 @@
+let manacher s =
+  let n = String.length s in
+  let m = 2 * n + 1 in
+  let t = Array.make m '#' in
+  for i = 0 to n - 1 do
+    t.(2 * i + 1) <- s.[i]
+  done;
+  let p = Array.make m 0 in
+  let center = ref 0 and right = ref 0 in
+  let max_p = ref 0 in
+  for i = 0 to m - 1 do
+    let mirror = 2 * !center - i in
+    if i < !right then begin
+      let v = !right - i in
+      let pm = p.(mirror) in
+      p.(i) <- (if pm < v then pm else v)
+    end;
+    while i + p.(i) + 1 < m && i - p.(i) - 1 >= 0
+          && t.(i + p.(i) + 1) = t.(i - p.(i) - 1) do
+      p.(i) <- p.(i) + 1
+    done;
+    if i + p.(i) > !right then begin
+      center := i;
+      right := i + p.(i)
+    end;
+    if p.(i) > !max_p then max_p := p.(i)
+  done;
+  !max_p
+
+;;
+
+manacher "babadaba"