There are N persons in a room. Find the maximum number of Handshakes possible. Given the fact that any two persons shake hand exactly once.
Input : N = 2 Output : 1. There are only 2 persons in the room. 1 handshake take place. Input : N = 10 Output : 45.
To maximize the number of handshakes, each person should shake hand with every other person in the room. For the first person, there would be N-1 handshakes. For second person there would N-1 person available but he had already shaken hand with the first person. So there would be N-2 handshakes and so on.
So, Total number of handshake = N-1 + N-2 +….+ 1 + 0, which is equivalent to ((N-1)*N)/2
(using the formula of sum of first N natural number).
Below is the implementation of this problem.
Time Complexity : O(1)
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