What are some natural ways of cleaning ceramic tile floors?

Our tile master told us never to use anything but one of the following:

Vinegar and water (little vinegar to a gallon of warm water)

If it gets 'cloudy' and needs a shine?: Clorox and water (again little Clorox to warm water)

Replace water often. Use just water to clean the tiles if your overdo the vinegar or Clorox.

Use a mop that doesn't leave streaks -- even if you have to make one up with just 'tea cloths' or similar. I mop the first time with the mop and then dry with an old tea cloth or clean rags that doesn't shed or streak.