Ten days does it comfortably. Seven is tight but achievable if you accept one region gets a single night. Fourteen lets you slow down, add the east coast, or spend real time somewhere instead of moving every second day. Our classic itineraries come in all three lengths and every one of them can be lengthened, shortened or reordered.
The circuit runs anticlockwise from the airport: north to Sigiriya and Dambulla, across to Polonnaruwa or Anuradhapura, south to Kandy, up into the tea hills for Nuwara Eliya and Ella, down to Yala or Udawalawe for the safari, then west along the south coast through Tangalle, Mirissa and Galle back towards Colombo. Every leg is a few hours at most.
You travel privately throughout with your own vehicle and chauffeur-guide, so the itinerary is a plan rather than a timetable. If you want an extra night somewhere because it turned out to be the best place on the trip, that is usually arrangeable while you are on the road.