I will answer the question the way you asked it. A few definitions
1 day is a 24 hr period, thus 1 day includes an overnight.So it could be 8am to 8am, or 6pm to 6pm, and so forth.2 days would be 48 hrs
0.5 day is 6 to 12 hrs, but no overnight.

Then
Amsterdam-2.5 days
Berlin-3 days
Rome-4 days
Barcellona-1.5 days
Lucerne-0.5 days
Zermatt-1 day
Interlaken/Bernese Oberland 3.5 days

Add 1 day for each day trip out of the city.