ocaml: phase 5.1 histogram_area.ml baseline (largest rectangle = 10)

Linear-time stack algorithm for largest rectangle in histogram:

  for i = 0 to n do
    let h = if i = n then 0 else heights.(i) in
    while top-of-stack's height > h do
      pop the top, compute its max-width rectangle:
        width = (no-stack ? i : i - prev_top - 1)
        area  = height * width
      update best
    done;
    if i < n then push i
  done

Sentinel pass at i=n with h=0 flushes the remaining stack.

For [2; 1; 5; 6; 2; 3], bars at indices 2 (h=5) and 3 (h=6) form
a width-2 rectangle of height 5 = 10.

Tests guarded patterns with `when` inside while-cont-flag, nested
`match !stack with | [] -> i | t :: _ -> i - t - 1` for width
computation.

178 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -75,6 +75,7 @@
   "hamming.ml": 4,
   "hanoi.ml": 1023,
   "hist.ml": 75,
+  "histogram_area.ml": 10,
   "huffman.ml": 224,
   "int_sqrt.ml": 1027,
   "is_prime.ml": 25,

lib/ocaml/baseline/histogram_area.ml

@@ -0,0 +1,27 @@
+let max_rect heights =
+  let n = Array.length heights in
+  let stack = ref [] in
+  let best = ref 0 in
+  for i = 0 to n do
+    let h = if i = n then 0 else heights.(i) in
+    let cont = ref true in
+    while !cont do
+      match !stack with
+      | top :: rest when heights.(top) > h ->
+        let height = heights.(top) in
+        stack := rest;
+        let width = match !stack with
+          | [] -> i
+          | t :: _ -> i - t - 1
+        in
+        let area = height * width in
+        if area > !best then best := area
+      | _ -> cont := false
+    done;
+    if i < n then stack := i :: !stack
+  done;
+  !best
+
+;;
+
+max_rect [| 2; 1; 5; 6; 2; 3 |]

plans/ocaml-on-sx.md

@@ -407,6 +407,15 @@ _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.
+- 2026-05-11 Phase 5.1 — histogram_area.ml baseline (largest
+  rectangle in histogram [2;1;5;6;2;3] = 10). Linear-time stack
+  algorithm: push indices while heights are non-decreasing; on
+  drop, pop and compute the bar's max-width rectangle. Sentinel
+  iteration at i=n with h=0 flushes remaining stack. The bars at
+  indices 2 and 3 (heights 5 and 6) form a width-2 rectangle of
+  height 5 = 10. Tests `match … with | top :: rest when h > … -> …
+  | _ -> …` guarded patterns inside a while-cont-flag loop, nested
+  match on the same stack ref. 178 baseline programs total.
 - 2026-05-11 Phase 5.1 — lps_dp.ml baseline (longest palindromic
   subsequence in "BBABCBCAB" = 7). Classic 2D O(n²) DP over
   substring lengths: dp[i][j] = dp[i+1][j-1] + 2 when s[i]=s[j],