ocaml: phase 5.1 grid_paths.ml baseline (count paths in 4x6 grid = 210)

DP filling a flattened 2D array:

  dp.(0, 0)         = 1
  dp.(i, j)         = dp.(i-1, j) + dp.(i, j-1)
  index             = i * (n+1) + j

For a 4x6 grid (5x7 dp matrix), the count is C(10, 4) = 210.

Tests Array as 2D via row-major flatten + nested for + multi-step
conditional access (above/left guarded by 'if i > 0' / 'if j > 0').

87 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -31,6 +31,7 @@
   "frequency.ml": 5,
   "gcd_lcm.ml": 60,
   "grep_count.ml": 3,
+  "grid_paths.ml": 210,
   "group_consec.ml": 53,
   "hailstone.ml": 111,
   "hanoi.ml": 1023,

lib/ocaml/baseline/grid_paths.ml

@@ -0,0 +1,17 @@
+let count_paths m n =
+  let dp = Array.make ((m + 1) * (n + 1)) 0 in
+  dp.(0) <- 1;
+  for i = 0 to m do
+    for j = 0 to n do
+      if i > 0 || j > 0 then begin
+        let above = if i > 0 then dp.((i - 1) * (n + 1) + j) else 0 in
+        let left = if j > 0 then dp.(i * (n + 1) + j - 1) else 0 in
+        dp.(i * (n + 1) + j) <- above + left
+      end
+    done
+  done;
+  dp.(m * (n + 1) + n)
+
+;;
+
+count_paths 4 6

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _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 — grid_paths.ml baseline (count distinct
+  paths in (4+1)x(6+1) grid = C(10,4) = 210). DP fills a flattened
+  2D array: `dp.(0,0) = 1`, others `dp.(i,j) = dp.(i-1,j) + dp.(i,
+  j-1)`. Index = `i * (n+1) + j`. Tests Array as 2D via row-major
+  flatten + nested for + multi-step conditional access. 87 baseline
+  programs total.
 - 2026-05-09 Phase 5.1 — fib_doubling.ml baseline (Fibonacci by
   doubling, fib(40) = 102334155). Uses the identity F(2k) = F(k) *
   (2*F(k+1) - F(k)) and F(2k+1) = F(k)^2 + F(k+1)^2 to compute fib