Nächste Zahl einer gegebenen Zahlreihe erraten…

#!/usr/bin/env lua
------------------------------------------------------------------------
-- $Id: guessseq,v 1.3 2022/07/16 12:40:36 elias Exp $
-- Try to guess next number in a sequence
------------------------------------------------------------------------


function checkrow(row)
   -- Check if all numbers in a sequences are equal
   local first = row[1]
   for i = 2, #row do
      if row[i] ~= first then return false end
   end
   return true
end


function diffrow(row)
   -- Calculate difference sequence
   local next = {}
   for i = 1, #row-1 do
      next[#next+1] = row[i+1] - row[i]
   end
   return next
end


function copyrow(row)
   -- Helper function: copy sequence to a new sequence
   -- Convery everything to an interger
   local cpy = {}
   for k, v in ipairs(row) do
      cpy[k] = math.tointeger(v)
   end
   return cpy
end


function guessseq(row)
   -- Guess the next number in the sequence
   -- This works for all polynomial sequences
   local rows = {}
   row = copyrow(row)
   repeat
      rows[#rows+1] = copyrow(row)
      row = diffrow(row)
   until checkrow(rows[#rows])
   local power = #rows
   rows[power][#rows[power]+1] = rows[power][1]
   for i = power - 1, 1, -1 do
      rows[i][#rows[i]+1] = rows[i][#rows[i]] + rows[i+1][#rows[i+1]]
   end
   return rows[1], rows[1][#rows[1]]
end


function fromarg()
   -- Sequence is given as command line arguments
   local guess, num = guessseq(copyrow(arg))
   print(table.concat(guess, " "))
end


function interactive()
   -- Interactive mode
   while true do
      -- Give a prompt and read sequence
      io.output():write("guessseq> ")
      local line = io.input():read("l")
      -- Exit on EOF
      if not line then break end
      -- Parse numbers in the line
      local numbers = {}
      for n in string.gmatch(line, "(-?%d+)") do
     numbers[#numbers+1] = math.tointeger(n)
      end
      -- Give solution
      print(table.concat(guessseq(numbers), " "))
   end
end


-- Main program
if #arg > 0 then
   fromarg()
else
   interactive()
   print()
end


-- Code is prosa, not poetry.