ocaml: phase 5.1 min_meeting_rooms.ml baseline (8 meetings, min 4 rooms)

Sweep-line algorithm via separately-sorted starts / ends arrays:

  while i < n do
    if starts[i] < ends[j] then begin busy++; rooms = max; i++ end
    else begin busy--; j++ end
  done

  intervals: (0,30) (5,10) (15,20) (10,25) (5,12)
             (20,35) (0,5)  (8,18)

At time 8, meetings (0,30), (5,10), (5,12), (8,18) are all active
simultaneously -> answer = 4.

Tests local helper bound via let (`let bubble a = ...`) for
in-place sort, dual-pointer sweep on parallel ordered event streams.

193 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -121,6 +121,7 @@
   "mortgage.ml": 1073,
   "mst_kruskal.ml": 11,
   "merge_intervals.ml": 12,
+  "min_meeting_rooms.ml": 4,
   "merge_sort.ml": 44,
   "merge_two.ml": 441,
   "min_cost_path.ml": 12,

lib/ocaml/baseline/min_meeting_rooms.ml

@@ -0,0 +1,40 @@
+let min_rooms intervals =
+  let n = List.length intervals in
+  let arr = Array.of_list intervals in
+  let starts = Array.make n 0 in
+  let ends = Array.make n 0 in
+  for i = 0 to n - 1 do
+    let (s, e) = arr.(i) in
+    starts.(i) <- s;
+    ends.(i) <- e
+  done;
+  let bubble a =
+    for i = 0 to n - 1 do
+      for j = 0 to n - 2 - i do
+        if a.(j) > a.(j + 1) then begin
+          let t = a.(j) in
+          a.(j) <- a.(j + 1);
+          a.(j + 1) <- t
+        end
+      done
+    done
+  in
+  bubble starts;
+  bubble ends;
+  let rooms = ref 0 in
+  let busy = ref 0 in
+  let i = ref 0 and j = ref 0 in
+  while !i < n do
+    if starts.(!i) < ends.(!j) then begin
+      busy := !busy + 1;
+      if !busy > !rooms then rooms := !busy;
+      i := !i + 1
+    end else begin
+      busy := !busy - 1;
+      j := !j + 1
+    end
+  done;
+  !rooms
+;;
+
+min_rooms [(0, 30); (5, 10); (15, 20); (10, 25); (5, 12); (20, 35); (0, 5); (8, 18)]