ocaml: phase 5.1 egg_drop.ml baseline (2 eggs, 36 floors -> 8 trials)

Classic egg-drop puzzle DP:

  dp[e][f] = 1 + min over k in [1, f] of
              max(dp[e-1][k-1], dp[e][f-k])

For 2 eggs over 36 floors, the optimal worst-case is 8 trials
(closed form: triangular number bound).

Tests 2D DP with triple-nested for-loops, max-of-two via inline
if, large sentinel constant (100000000), mixed shifted indexing
(e-1) and (f-k) where both shift independently.

163 baseline programs total.

lib/ocaml/baseline/egg_drop.ml

@@ -0,0 +1,26 @@
+let egg_drop eggs floors =
+  let dp = Array.init (eggs + 1) (fun _ -> Array.make (floors + 1) 0) in
+  for f = 1 to floors do
+    dp.(1).(f) <- f
+  done;
+  for e = 1 to eggs do
+    dp.(e).(0) <- 0;
+    dp.(e).(1) <- 1
+  done;
+  for e = 2 to eggs do
+    for f = 2 to floors do
+      let best = ref 100000000 in
+      for k = 1 to f do
+        let bre = dp.(e - 1).(k - 1) in
+        let sur = dp.(e).(f - k) in
+        let cand = 1 + (if bre > sur then bre else sur) in
+        if cand < !best then best := cand
+      done;
+      dp.(e).(f) <- !best
+    done
+  done;
+  dp.(eggs).(floors)
+
+;;
+
+egg_drop 2 36

lib/ocaml/baseline/expected.json

@@ -29,6 +29,7 @@
   "count_change.ml": 406,
   "count_inversions.ml": 12,
   "csv.ml": 10,
+  "egg_drop.ml": 8,
   "dijkstra.ml": 7,
   "exception_handle.ml": 4,
   "exception_user.ml": 26,

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.
+- 2026-05-10 Phase 5.1 — egg_drop.ml baseline (worst-case trials
+  for 2 eggs, 36 floors = 8). Classic O(e·f²) DP: dp[e][f] = 1 +
+  min over k of max(dp[e-1][k-1], dp[e][f-k]). Closed form via
+  triangular numbers gives ⌈(√(1+8·36)−1)/2⌉ = 8, matching the
+  DP answer. Tests 2D DP with triple-nested for-loops, max-of-two
+  via inline if, large sentinel constant, mixed indexing (e-1)
+  and (f-k) where both shift independently. 163 baseline programs
+  total.
 - 2026-05-10 Phase 5.1 — polygon_area.ml baseline (shoelace formula
   on pentagon, returns 2× area = 32). Vertices (0,0), (4,0), (4,3),
   (2,5), (0,3); shoelace sum |Σ(x_i·y_{i+1} − x_{i+1}·y_i)| = 32 so