ocaml: phase 5.1 kmp.ml baseline (5 occurrences of "abab" in haystack)

Knuth-Morris-Pratt linear-time string search:
  - kmp_table builds failure function in O(|pattern|)
  - kmp_search scans text once in O(|text|), counting matches
  - After a hit, k := t.(n-1) so overlapping matches still count

  kmp_search "abababcabababcababcc" "abab" = 5

Hits at positions 0, 2, 7, 9, 14 (overlapping at 0/2 and 7/9).

Tests: nested while-inside-for, char inequality (.<>), pat.[i]
string indexing, Array.make 0, combined string + array indexing.

140 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -79,6 +79,7 @@
   "josephus.ml": 11,
   "json_pretty.ml": 24,
   "kadane.ml": 6,
+  "kmp.ml": 5,
   "lambda_calc.ml": 7,
   "majority_vote.ml": 4,
   "levenshtein.ml": 11,

lib/ocaml/baseline/kmp.ml

@@ -0,0 +1,37 @@
+let kmp_table pat =
+  let n = String.length pat in
+  let t = Array.make n 0 in
+  let k = ref 0 in
+  for i = 1 to n - 1 do
+    while !k > 0 && pat.[!k] <> pat.[i] do
+      k := t.(!k - 1)
+    done;
+    if pat.[!k] = pat.[i] then k := !k + 1;
+    t.(i) <- !k
+  done;
+  t
+
+let kmp_search text pat =
+  let m = String.length text in
+  let n = String.length pat in
+  if n = 0 then 0
+  else begin
+    let t = kmp_table pat in
+    let count = ref 0 in
+    let k = ref 0 in
+    for i = 0 to m - 1 do
+      while !k > 0 && pat.[!k] <> text.[i] do
+        k := t.(!k - 1)
+      done;
+      if pat.[!k] = text.[i] then k := !k + 1;
+      if !k = n then begin
+        count := !count + 1;
+        k := t.(n - 1)
+      end
+    done;
+    !count
+  end
+
+;;
+
+kmp_search "abababcabababcababcc" "abab"

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _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.
+- 2026-05-10 Phase 5.1 — kmp.ml baseline (KMP string search, count
+  occurrences of "abab" in "abababcabababcababcc" = 5). Two-phase
+  classic: build failure table in O(m), then linear scan in O(n).
+  After a full match, set k := t.(n-1) so overlapping matches still
+  count (so "abab" hits at positions 0, 2, 7, 9, 14). Tests nested
+  while-inside-for, char comparison via `pat.[i]`, Array.make 0,
+  combined string + array indexing. 140 baseline programs total.
 - 2026-05-10 Phase 5.1 — union_find.ml baseline (disjoint-set union
   on n=10 with 6 unions → 4 components). Path-compressing find:
   recursively walks parent links, splices subtree onto root in place.