solver + auto flag | open source

local function solve(clues)
    local known = {}
    local changed = true
    while changed do
        changed = false
        local residuals, byTile = {}, {}
        for _, clue in ipairs(clues) do
            local need, remaining = clue.count, {}
            for _, id in ipairs(clue.ids) do
                if known[id] == nil then
                    remaining[id] = true
                else
                    need -= known[id]
                end
            end
            local count = 0
            for _ in pairs(remaining) do count += 1 end
            if need < 0 or need > count then return {}, false end
            if count > 0 and (need == 0 or need == count) then
                local value = if need == 0 then 0 else 1
                for id in pairs(remaining) do known[id] = value end
                changed = true
            elseif count > 0 then
                local residual = {ids = remaining, count = count, need = need}
                table.insert(residuals, residual)
                for id in pairs(remaining) do
                    byTile[id] = byTile[id] or {}
                    table.insert(byTile[id], residual)
                end
            end
        end

        if not changed then
            for _, small in ipairs(residuals) do
                local first = next(small.ids)
                for _, large in ipairs(byTile[first]) do
                    if small == large or small.count > large.count then continue end
                    local subset = true
                    for id in pairs(small.ids) do
                        if not large.ids[id] then