Viken's stats

-- https://play.luau.org/

-- I am absolutely losing it over this polyomino nonsense.
-- I swear these rotations are conspiring behind my back.
-- I may evaporate.
-- This code will either enumerate every polyomino or take me down with it.
-- I've decided to neglect reflections and rotations because I value survival.

type Polyomino = { { number } }

local known = {} :: { [number]: { Polyomino } }

local function doPolyominoesMatch(polyomino1: Polyomino, polyomino2: Polyomino): boolean
	if #polyomino1 ~= #polyomino2 then return false end
	if #polyomino1[1] ~= #polyomino2[1] then return false end

	for y = 1, #polyomino1 do
		for x = 1, #polyomino1[y] do
			if polyomino1[y][x] ~= polyomino2[y][x] then
				return false
			end
		end
	end

	return true
end

local function isUnique(polyominoToCheck: Polyomino, n: number): boolean
	for _, polyomino in known[n] do
		if doPolyominoesMatch(polyomino, polyominoToCheck) then
			return false
		end
	end

	return true
end

local function addToPolyomino(polyomino: Polyomino, posx: number, posy: number): Polyomino
	local height = #polyomino
	local width = #polyomino[1]

	local offsetX = if posx < 1 then 1 else 0
	local offsetY = if posy < 1 then 1 else 0
	local newWidth = math.max(width + offsetX, posx)
	local newHeight = math.max(height + offsetY, posy)

	local newPolyomino = table.create(newHeight)
	for y = 1, newHeight do
		newPolyomino[y] = table.create(newWidth, 0)
	end

	for y = 1, height do
		for x = 1, width do
			newPolyomino[y + offsetY][x + offsetX] = polyomino[y][x]
		end
	end

	newPolyomino[posy + offsetY][posx + offsetX] = 1

	return newPolyomino
end

local function polyominoes(n: number): number
	known[n] = {}

	if n == 0 then
		table.insert(known[n], { { 0 } })
	elseif n == 1 then
		table.insert(known[n], { { 1 } })
	else
		for _, polyomino in known[n - 1] do
			local height = #polyomino
			local width = #polyomino[1]

			for y = 1, height do
				for x = 1, width do
					if polyomino[y][x] == 0 then continue end

					local neighbors = {
						{x + 1, y},
						{x - 1, y},
						{x, y + 1},
						{x, y - 1}
					}

					for _, neighbor in neighbors do
						local neighborx, neighbory = neighbor[1], neighbor[2]

						local isEmpty = neighborx < 1 or neighbory < 1 or neighborx > width or neighbory > height or polyomino[neighbory][neighborx] == 0

						if isEmpty then
							local newPolyomino = addToPolyomino(polyomino, neighborx, neighbory)

							if isUnique(newPolyomino, n) then
								table.insert(known[n], newPolyomino)
							end
						end
					end
				end
			end
		end
	end

	return known[n] and #known[n] or 0
end


local function printPolyomino(polyomino: Polyomino)
	for y = 1, #polyomino do
		local row = ''
		for x = 1, #polyomino[y] do
			row ..= if polyomino[y][x] == 1 then '██' else '  '
		end
		print(`  {row}`)
	end
end

for i = 0, 4 do
	local count = polyominoes(i)

	print(('='):rep(40))
	print(`n = {i}  ({count} polyominoes)`)
	print(('='):rep(40))

	for j, polyomino in known[i] do
		print(`  #{j}`)
		printPolyomino(polyomino)
		if j < #known[i] then
			print(('-'):rep(20))
		end
	end

	print()
end

print(io.read():len())