From 5b38f4d4998bd7d0d2730278cfc21eaefd221856 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Sat, 9 May 2026 15:32:11 +0000
Subject: [PATCH] ocaml: phase 5.1 triangle.ml baseline (Pascal-shape min path
 sum, 2+3+5+1 = 11)

Bottom-up DP minimum-path through a triangle:

       2
      3 4
     6 5 7
    4 1 8 3

  let min_path_triangle rows =
    initialise dp from last row;
    for r = n - 2 downto 0 do
      for c = 0 to row_len - 1 do
        dp.(c) <- row.(c) + min(dp.(c), dp.(c+1))
      done
    done;
    dp.(0)

The optimal path 2 -> 3 -> 5 -> 1 sums to 11.

Tests downto loop, Array.of_list inside loop body, nested arr.(i)
reads + writes, and inline if-then-else for min.

74 baseline programs total.
---
 lib/ocaml/baseline/expected.json |  1 +
 lib/ocaml/baseline/triangle.ml   | 17 +++++++++++++++++
 plans/ocaml-on-sx.md             | 11 +++++++++++
 3 files changed, 29 insertions(+)
 create mode 100644 lib/ocaml/baseline/triangle.ml

diff --git a/lib/ocaml/baseline/expected.json b/lib/ocaml/baseline/expected.json
index 818e582e..953cb99a 100644
--- a/lib/ocaml/baseline/expected.json
+++ b/lib/ocaml/baseline/expected.json
@@ -70,6 +70,7 @@
   "zip_unzip.ml": 1000,
   "sieve.ml": 15,
   "sum_squares.ml": 385,
+  "triangle.ml": 11,
   "twosum.ml": 5,
   "unique_set.ml": 9,
   "validate.ml": 417,
diff --git a/lib/ocaml/baseline/triangle.ml b/lib/ocaml/baseline/triangle.ml
new file mode 100644
index 00000000..bac3483e
--- /dev/null
+++ b/lib/ocaml/baseline/triangle.ml
@@ -0,0 +1,17 @@
+let min_path_triangle rows =
+  let n = List.length rows in
+  let dp = Array.make n 0 in
+  let last = List.nth rows (n - 1) in
+  let i = ref 0 in
+  List.iter (fun x -> dp.(!i) <- x; i := !i + 1) last;
+  for r = n - 2 downto 0 do
+    let row = Array.of_list (List.nth rows r) in
+    for c = 0 to Array.length row - 1 do
+      dp.(c) <- row.(c) + (if dp.(c) < dp.(c + 1) then dp.(c) else dp.(c + 1))
+    done
+  done;
+  dp.(0)
+
+;;
+
+min_path_triangle [[2]; [3; 4]; [6; 5; 7]; [4; 1; 8; 3]]
diff --git a/plans/ocaml-on-sx.md b/plans/ocaml-on-sx.md
index 9fee206a..0e36da8e 100644
--- a/plans/ocaml-on-sx.md
+++ b/plans/ocaml-on-sx.md
@@ -407,6 +407,17 @@ _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 — triangle.ml baseline (Pascal-shape min path
+  sum, 2+3+5+1 = 11). Bottom-up DP over the triangle:
+    2
+    3 4
+    6 5 7
+    4 1 8 3
+  Initialise dp from last row, then for each row above, replace
+  dp.(c) with row.(c) + min(dp.(c), dp.(c+1)). Final answer in
+  dp.(0). Tests downto loop, Array.of_list inside loop, nested
+  arr.(i) reads + writes, and List.nth iteration. 74 baseline
+  programs total.
 - 2026-05-09 Phase 5.1 — max_path_tree.ml baseline (max root-to-leaf
   sum in a binary tree, 1+3+7 = 11). Recursive ADT `tree = Leaf |
   Node of int * tree * tree`. max_path returns 0 at Leaf, else