ocaml: phase 5.1 count_palindromes.ml baseline ("aabaa" -> 9 palindromes)

Expand-around-center linear-time palindrome counting:

  for c = 0 to 2*n - 2 do
    let l = ref (c / 2) in
    let r = ref ((c + 1) / 2) in
    while !l >= 0 && !r < n && s.[!l] = s.[!r] do
      count := !count + 1; l := !l - 1; r := !r + 1
    done
  done

The 2n-1 centers cover both odd (c even -> l = r) and even
(c odd -> l = r - 1) palindromes.

For "aabaa":
  5 singletons + 2 "aa" + 1 "aba" + 1 "aabaa" = 9

Complements lps_dp.ml (longest subsequence) and manacher.ml
(longest substring); this one *counts* all palindromic substrings.

187 baseline programs total.

lib/ocaml/baseline/count_palindromes.ml

@@ -0,0 +1,17 @@
+let count_pal s =
+  let n = String.length s in
+  let count = ref 0 in
+  for c = 0 to 2 * n - 2 do
+    let l = ref (c / 2) in
+    let r = ref ((c + 1) / 2) in
+    while !l >= 0 && !r < n && s.[!l] = s.[!r] do
+      count := !count + 1;
+      l := !l - 1;
+      r := !r + 1
+    done
+  done;
+  !count
+
+;;
+
+count_pal "aabaa"

lib/ocaml/baseline/expected.json

@@ -32,6 +32,7 @@
   "coin_min.ml": 6,
   "count_change.ml": 406,
   "count_inversions.ml": 12,
+  "count_palindromes.ml": 9,
   "count_subarrays_k.ml": 7,
   "csv.ml": 10,
   "egg_drop.ml": 8,