Go Handshakes Math | Dataford Interview Questions

A Capgemini Government Solutions conference has a fixed number of members. During each phase, every member shakes hands with every other member exactly once. For example, the pre-meeting and post-meeting phases represent two separate rounds, so the same pair may shake hands twice.

Given the number of members and the number of phases, return the total number of handshakes. Do not simulate individual pairs.

Formal Specification

Implement count_handshakes(member_count, phases).

Input: two integers, member_count, the number of conference members, and phases, the number of independent handshake phases.
Output: an integer representing the total number of handshakes across all phases.
Each unordered pair of members contributes exactly one handshake per phase.

Constraints

2 <= member_count <= 10^9
1 <= phases <= 10^9
The result fits within a signed 64-bit integer
Each pair shakes hands exactly once in each phase

Function Signature

def count_handshakes(member_count, phases):

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