Standard 1D 0/1 knapsack DP with reverse inner loop:
let knapsack values weights cap =
let n = Array.length values in
let dp = Array.make (cap + 1) 0 in
for i = 0 to n - 1 do
let v = values.(i) and w = weights.(i) in
for c = cap downto w do
let take = dp.(c - w) + v in
if take > dp.(c) then dp.(c) <- take
done
done;
dp.(cap)
values: [|6; 10; 12; 15; 20|]
weights: [|1; 2; 3; 4; 5|]
knapsack v w 8 = 36 (* take items with weights 1, 2, 5 *)
Tests for-downto + array literal access in the same hot loop.
143 baseline programs total.