ocaml: phase 5.1 quickselect.ml baseline (median of 9 elements = 5)

Hoare quickselect with Lomuto partition: recursively narrows the
range to whichever side contains the kth index. Mutates the array
in place via .(i)<-v. The median (k=4) of [7;2;9;1;5;6;3;8;4] is 5.

  let rec quickselect arr lo hi k =
    if lo = hi then arr.(lo)
    else begin
      let pivot = arr.(hi) in
      let i = ref lo in
      for j = lo to hi - 1 do
        if arr.(j) < pivot then begin
          let t = arr.(!i) in
          arr.(!i) <- arr.(j); arr.(j) <- t;
          i := !i + 1
        end
      done;
      ...
    end

Exercises array literal syntax + in-place mutation in the same
program, ensuring [|...|] yields a mutable backing.

138 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -110,6 +110,7 @@
   "prime_factors.ml": 17,
   "pythagorean.ml": 16,
   "queens.ml": 2,
+  "quickselect.ml": 5,
   "quicksort.ml": 44,
   "roman.ml": 44,
   "reverse_int.ml": 54329,

lib/ocaml/baseline/quickselect.ml

@@ -0,0 +1,25 @@
+let rec quickselect arr lo hi k =
+  if lo = hi then arr.(lo)
+  else begin
+    let pivot = arr.(hi) in
+    let i = ref lo in
+    for j = lo to hi - 1 do
+      if arr.(j) < pivot then begin
+        let t = arr.(!i) in
+        arr.(!i) <- arr.(j);
+        arr.(j) <- t;
+        i := !i + 1
+      end
+    done;
+    let t = arr.(!i) in
+    arr.(!i) <- arr.(hi);
+    arr.(hi) <- t;
+    if !i = k then arr.(!i)
+    else if !i < k then quickselect arr (!i + 1) hi k
+    else quickselect arr lo (!i - 1) k
+  end
+
+;;
+
+let a = [|7; 2; 9; 1; 5; 6; 3; 8; 4|] in
+quickselect a 0 8 4

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 — quickselect.ml baseline (Hoare quickselect
+  median of [7;2;9;1;5;6;3;8;4] = 5). Lomuto partition scheme:
+  recursively partitions on the last element as pivot, narrows the
+  range to the side containing the kth index. Mutates the array
+  in place via `.(i) <- v`. Verifies that array literal syntax
+  works for in-place mutation paths, not just reads. 138 baseline
+  programs total.
 - 2026-05-10 Phase 5.1 — array literals + lis.ml baseline (longest
   increasing subsequence on a 9-element array = 6). Added parser
   support for `[| e1; e2; ...; en |]` syntax: desugars to