knapsack.jl

function knapsack(v, w, capacity)
    n = length(v) + 1
    capacity += 1
    A = zeros(Int, n, capacity)

    for j in 1:capacity, i in 2:n
        A[i,j] = if w[i-1] < j
            max(
                A[i-1, j],
                A[i-1, j-w[i-1]] + v[i-1]
            )
        else
            A[i-1, j]
        end
    end

    return A[n, capacity], A
end

values = [ 3, 2, 4, 4 ]
weights = [ 4, 3, 2, 3 ]
capacity = 6

total, _ = knapsack(values, weights, capacity)