brute_force.lua

local function cross(vector0, vector1)
	local ux, uy = vector0[1], vector0[2]
	local vx, vy = vector1[1], vector1[2]

	return ux*vy - uy*vx
end

local function area(points)
	local area = cross(points[#points], points[1])
	for i=1, #points-1 do
		area = area + cross(points[i], points[i+1])
	end
	return 0.5*area
end

local function fakePermutate(points)
	local largest = -math.huge
	-- TODO: Permutate properly
	for i=1, 24 do
		local parea = area(points)
		if parea > largest then
			largest = parea
			-- TODO: Store
		end
	end

	return largest
end

local points = {
	{ 1, 1, },
	{ 3, 3, },
	{ 5, 5, },
	{ 8, 8, },
}

local startTime = tick()
for i=1, 220000 do
	fakePermutate(points)
end
print("done", tick() - startTime)