From b3ee88e9bbec8fa127d5133c7e9406b18248654d Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Mon, 11 May 2026 02:44:40 +0000
Subject: [PATCH] ocaml: phase 5.1 kth_two.ml baseline (8th smallest of two
 sorted = 8)

Two-pointer merge advancing the smaller-head pointer k times,
without materializing the merged array:

  while !count < k do
    let pick_a =
      if !i = m then false        (* a exhausted, take from b *)
      else if !j = n then true    (* b exhausted, take from a *)
      else a.(!i) <= b.(!j)
    in
    if pick_a then ... else ...;
    count := !count + 1
  done

For a = [1;3;5;7;9;11;13], b = [2;4;6;8;10;12]:
  merged order: 1,2,3,4,5,6,7,8,9,10,11,12,13
  8th element = 8.

Tests nested if/else if/else flowing into a bool, dual-ref
two-pointer loop, separate count counter for k-th constraint.

184 baseline programs total.
---
 lib/ocaml/baseline/expected.json |  1 +
 lib/ocaml/baseline/kth_two.ml    | 27 +++++++++++++++++++++++++++
 plans/ocaml-on-sx.md             | 10 ++++++++++
 3 files changed, 38 insertions(+)
 create mode 100644 lib/ocaml/baseline/kth_two.ml

diff --git a/lib/ocaml/baseline/expected.json b/lib/ocaml/baseline/expected.json
index 17bbf814..c2530159 100644
--- a/lib/ocaml/baseline/expected.json
+++ b/lib/ocaml/baseline/expected.json
@@ -102,6 +102,7 @@
   "json_pretty.ml": 24,
   "kadane.ml": 6,
   "kmp.ml": 5,
+  "kth_two.ml": 8,
   "knapsack.ml": 36,
   "lambda_calc.ml": 7,
   "lcs.ml": 4,
diff --git a/lib/ocaml/baseline/kth_two.ml b/lib/ocaml/baseline/kth_two.ml
new file mode 100644
index 00000000..1395f5e5
--- /dev/null
+++ b/lib/ocaml/baseline/kth_two.ml
@@ -0,0 +1,27 @@
+let kth_two a b k =
+  let m = Array.length a in
+  let n = Array.length b in
+  let i = ref 0 and j = ref 0 and count = ref 0 in
+  let result = ref 0 in
+  while !count < k do
+    let pick_a =
+      if !i = m then false
+      else if !j = n then true
+      else a.(!i) <= b.(!j)
+    in
+    if pick_a then begin
+      result := a.(!i);
+      i := !i + 1
+    end else begin
+      result := b.(!j);
+      j := !j + 1
+    end;
+    count := !count + 1
+  done;
+  !result
+
+;;
+
+let a = [| 1; 3; 5; 7; 9; 11; 13 |] in
+let b = [| 2; 4; 6; 8; 10; 12 |] in
+kth_two a b 8
diff --git a/plans/ocaml-on-sx.md b/plans/ocaml-on-sx.md
index 5eaec083..fe1ccc6b 100644
--- a/plans/ocaml-on-sx.md
+++ b/plans/ocaml-on-sx.md
@@ -407,6 +407,16 @@ _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.
+- 2026-05-11 Phase 5.1 — kth_two.ml baseline (8th smallest in
+  merged [1;3;5;7;9;11;13] ∪ [2;4;6;8;10;12] = 8). Two-pointer
+  merge that advances the smaller-head pointer k times. Pick rule:
+    pick_a = (j past end) ? true
+           : (i past end) ? false
+           : a[i] <= b[j]
+  Combined order is 1,2,3,4,5,6,7,8,…; 8th element = 8. Tests
+  nested `if/else if/else` flowing into a bool, dual-ref two-
+  pointer loop, separate count counter for the k-th constraint.
+  184 baseline programs total.
 - 2026-05-11 Phase 5.1 — permutations_gen.ml baseline (enumerate all
   24 permutations of [1;2;3;4], count those with first<last = 12).
   Recursive build via fold-pick-recurse: