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