Minimum number of calls to be made?

Question

There are 'n' number of detectives..each one knows an information, how many minimum calls should they make so all the detectives know all the n number of information ?

My answer: I came up with 2n-3 (that is, n-1 + n-2) solution where a detective calls n-1 other detectives and shares information mutually (in this way the last detective and the first has all the information). Then the remaining n-2 detectives who doesn't have the whole data calls either the first detective or the last to gain the remaining information.

(This is a question asked by my friend).

Answer 1

2n-3 is not correct.

Consider the case of n=4, 2n-3 would predict that 2*4-3=5 calls are needed.

However, we can do it in 4 calls via:

A calls B
C calls D
A calls C
B calls D