ocaml: phase 5.1 house_robber.ml baseline (max non-adjacent sum = 22)

Classic House Robber linear DP:

  dp[i] = max(dp[i-2] + houses[i], dp[i-1])

For [2; 7; 9; 3; 1; 5; 8; 6]:

  dp = [2, 7, 11, 11, 12, 16, 20, 22]
  max sum = 22

Optimal pick is {indices 0, 2, 5, 7}: 2 + 9 + 5 + 6 = 22 (all
non-adjacent).

Tests linear DP with early-return edge cases for n=0 and n=1,
inline-if rhs for max-of-two, dual look-back into dp[i-2] and
dp[i-1].

189 baseline programs total.

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 — house_robber.ml baseline (linear-DP
+  max non-adjacent-sum on [2;7;9;3;1;5;8;6] = 22). dp[i] =
+  max(dp[i-2]+houses[i], dp[i-1]). Optimal pick {7, 9, 5, 8} but
+  that's adjacent (5 next to 8). Re-check: {7, 9, 1, 8} sum 25?
+  Wait 9 at index 2, 1 at index 4 not adjacent; 1 at index 4, 8 at
+  index 6 not adjacent. But 7,9 are at indices 1,2 — adjacent!
+  Actual optimum: skip 0, take 7 (1), skip 2, take 3 (3), skip 4,
+  take 5 (5), skip 6, take 6 (7) = 7+3+5+6=21. Or take 2,9,1,8 =
+  20. Or 2,9,5,6 = 22? indices 0,2,5,7 (non-adjacent). 2+9+5+6=22.
+  ✓ Tests linear DP with early-return edge cases for short arrays,
+  inline-if rhs for max-of-two. 189 baseline programs total.
 - 2026-05-11 Phase 5.1 — interval_overlap.ml baseline (count
   overlapping interval pairs in 7-interval set = 6). For each pair
   (i, j) test `s1 ≤ e2 && s2 ≤ e1`. Intervals: (1,4) (2,5) (7,9)