ocaml: phase 5.1 count_paths_dag.ml baseline (source-to-sink paths = 3)

Count source-to-sink paths in a DAG via Kahn's topological sort
plus accumulation:

  paths[source] = 1
  for u in topological order:
    for v in adj[u]: paths[v] += paths[u]

Same 6-node DAG as topo_sort.ml:
  0 -> {1, 2}    1 -> {3}    2 -> {3, 4}    3 -> {5}    4 -> {5}

The three witnesses 0 -> 5:
  0 -> 1 -> 3 -> 5
  0 -> 2 -> 3 -> 5
  0 -> 2 -> 4 -> 5

Tests Queue-driven Kahn order + List.rev to recover topological
order, module-level mutable arrays (in_deg, paths), accumulation
in topological traversal.

191 baseline programs total.

lib/ocaml/baseline/count_paths_dag.ml

@@ -0,0 +1,42 @@
+let n = 6
+let adj = [|
+  [1; 2];
+  [3];
+  [3; 4];
+  [5];
+  [5];
+  []
+|]
+
+let in_deg = Array.make n 0
+let paths = Array.make n 0
+
+let count_paths () =
+  for u = 0 to n - 1 do
+    List.iter (fun v -> in_deg.(v) <- in_deg.(v) + 1) adj.(u)
+  done;
+  let order = ref [] in
+  let q = Queue.create () in
+  for v = 0 to n - 1 do
+    if in_deg.(v) = 0 then Queue.push v q
+  done;
+  while not (Queue.is_empty q) do
+    let u = Queue.pop q in
+    order := u :: !order;
+    List.iter (fun v ->
+      in_deg.(v) <- in_deg.(v) - 1;
+      if in_deg.(v) = 0 then Queue.push v q
+    ) adj.(u)
+  done;
+  paths.(0) <- 1;
+  let topo = List.rev !order in
+  List.iter (fun u ->
+    List.iter (fun v ->
+      paths.(v) <- paths.(v) + paths.(u)
+    ) adj.(u)
+  ) topo;
+  paths.(n - 1)
+
+;;
+
+count_paths ()

lib/ocaml/baseline/expected.json

@@ -31,6 +31,7 @@
   "coin_change.ml": 6,
   "coin_min.ml": 6,
   "count_change.ml": 406,
+  "count_paths_dag.ml": 3,
   "count_inversions.ml": 12,
   "count_palindromes.ml": 9,
   "count_subarrays_k.ml": 7,

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.
+- 2026-05-11 Phase 5.1 — count_paths_dag.ml baseline (count
+  source-to-sink paths in the same 6-node DAG as topo_sort.ml,
+  paths 0→5 = 3). Topological sort via Kahn's (BFS), then relax
+  edges in topological order: paths[v] += paths[u] for each edge
+  u→v. paths[source] = 1. The three witnesses:
+    0 → 1 → 3 → 5
+    0 → 2 → 3 → 5
+    0 → 2 → 4 → 5
+  Tests Queue-driven Kahn order + List.rev to topological order,
+  module-level mutable arrays (in_deg / paths), accumulation in
+  topological traversal. 191 baseline programs total.
 - 2026-05-11 Phase 5.1 — stock_two.ml baseline (max stock profit
   with at most 2 transactions on [3;3;5;0;0;3;1;4] = 6). Two-pass
   DP: left[i] = max single-transaction profit in prices[0..i]