ocaml: phase 5.1 merge_intervals.ml baseline (LeetCode #56, total length 9+3 = 12)

Sort intervals by start, then sweep maintaining a current (cs, ce)
window — extend ce if next start <= ce, else push current and start
fresh:

  let merge_intervals xs =
    let sorted = List.sort (fun (a, _) (b, _) -> a - b) xs in
    let rec aux acc cur xs =
      match xs with
      | [] -> List.rev (cur :: acc)
      | (s, e) :: rest ->
        let (cs, ce) = cur in
        if s <= ce then aux acc (cs, max e ce) rest
        else aux (cur :: acc) (s, e) rest
    in
    match sorted with
    | [] -> []
    | h :: rest -> aux [] h rest

  [(1,3);(2,6);(8,10);(15,18);(5,9)]
  -> [(1,10); (15,18)]
  total length = 9 + 3 = 12

Tests List.sort with custom comparator using tuple patterns, plus
tuple destructuring in lambda + let-tuple from accumulator + match
arms.

92 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -51,6 +51,7 @@
   "levenshtein.ml": 11,
   "memo_fib.ml": 75025,
   "mortgage.ml": 1073,
+  "merge_intervals.ml": 12,
   "merge_sort.ml": 44,
   "merge_two.ml": 441,
   "module_use.ml": 3,

lib/ocaml/baseline/merge_intervals.ml

@@ -0,0 +1,21 @@
+let merge_intervals xs =
+  let sorted = List.sort (fun (a, _) (b, _) -> a - b) xs in
+  let rec aux acc cur xs =
+    match xs with
+    | [] -> List.rev (cur :: acc)
+    | (s, e) :: rest ->
+      let (cs, ce) = cur in
+      if s <= ce then
+        let new_e = if e > ce then e else ce in
+        aux acc (cs, new_e) rest
+      else
+        aux (cur :: acc) (s, e) rest
+  in
+  match sorted with
+  | [] -> []
+  | h :: rest -> aux [] h rest
+
+;;
+
+let m = merge_intervals [(1, 3); (2, 6); (8, 10); (15, 18); (5, 9)] in
+List.fold_left (fun acc (s, e) -> acc + e - s) 0 m

plans/ocaml-on-sx.md

@@ -407,6 +407,14 @@ _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.
+- 2026-05-09 Phase 5.1 — merge_intervals.ml baseline (LeetCode #56,
+  total length 9 + 3 = 12). Sort by start, then sweep maintaining a
+  current `(cs, ce)` window — extend `ce` if next start ≤ ce, else
+  push current and start new. `[(1,3);(2,6);(8,10);(15,18);(5,9)]`
+  merges to `[(1,10);(15,18)]`, total length 9+3 = 12. Tests
+  List.sort with custom cmp + tuple destructuring everywhere
+  (closure lambda with tuple-pattern, let-tuple from accumulator,
+  match arms). 92 baseline programs total.
 - 2026-05-09 Phase 5.1 — hamming.ml baseline (Hamming distance,
   3 + 2 + (-1) = 4). Counts position-wise differences in equal-length
   strings; returns -1 sentinel for length mismatch.