ocaml: phase 5.1 min_cost_path.ml baseline (4x4 grid DP, optimal cost 12)

Standard 2D DP for min-cost path with right/down moves only:

  dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + cost[i][j]

  cost:                  dp:
    1 3 1 2                1  4  5  7
    1 5 1 3                2  7  6  9
    4 2 1 4                6  8  7 11
    1 6 2 3                7 13  9 12

Optimal cost from (0,0) to (3,3) = 12.

Tests nested 2D arrays via Array.init + Array.make, double-nested
for-loops with branched edges (first row, first column, general),
mixed .(i-1).(j) read + .(i).(j)<- write on the same DP array.

161 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -101,6 +101,7 @@
   "merge_intervals.ml": 12,
   "merge_sort.ml": 44,
   "merge_two.ml": 441,
+  "min_cost_path.ml": 12,
   "module_use.ml": 3,
   "monotonic.ml": 4,
   "newton_sqrt.ml": 1414,

lib/ocaml/baseline/min_cost_path.ml

@@ -0,0 +1,31 @@
+let h = 4
+let w = 4
+
+let cost = [|
+  [| 1; 3; 1; 2 |];
+  [| 1; 5; 1; 3 |];
+  [| 4; 2; 1; 4 |];
+  [| 1; 6; 2; 3 |]
+|]
+
+let min_cost_path () =
+  let dp = Array.init h (fun _ -> Array.make w 0) in
+  dp.(0).(0) <- cost.(0).(0);
+  for j = 1 to w - 1 do
+    dp.(0).(j) <- dp.(0).(j - 1) + cost.(0).(j)
+  done;
+  for i = 1 to h - 1 do
+    dp.(i).(0) <- dp.(i - 1).(0) + cost.(i).(0)
+  done;
+  for i = 1 to h - 1 do
+    for j = 1 to w - 1 do
+      let a = dp.(i - 1).(j) in
+      let b = dp.(i).(j - 1) in
+      dp.(i).(j) <- (if a < b then a else b) + cost.(i).(j)
+    done
+  done;
+  dp.(h - 1).(w - 1)
+
+;;
+
+min_cost_path ()

plans/ocaml-on-sx.md

@@ -407,6 +407,16 @@ _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 — min_cost_path.ml baseline (min-cost path
+  through 4×4 cost grid, top-left to bottom-right with moves
+  right/down only, optimal = 12). Standard 2D DP: dp[i][j] = min
+  of (dp[i-1][j], dp[i][j-1]) + cost[i][j]. Cost matrix yields
+  optimal path 1→1→2→1→1→1→2→3 = 12 (visiting (0,0),(1,0),(2,1),
+  (2,2),(2,3),(3,3)? actually the path is row-by-row). Tests
+  nested 2D arrays via Array.init + Array.make, double-nested
+  for-loops with branched edges (first row, first column, then
+  general case), `dp.(i-1).(j)` 2-D index read + `dp.(i).(j)<-`
+  2-D write. 161 baseline programs total.
 - 2026-05-10 Phase 5.1 — topo_dfs.ml baseline (DFS-based topo sort
   on the same 6-node DAG as topo_sort.ml, digit-fingerprint 24135).
   Cons each node onto the order list AFTER recursing on all its