UVa 10583 - Ubiquitous Religions

Summary
You must keep track of how many different possible religions people can have. You are only given information about which people have the same religion, not the religion that they actually practice.

Explanation
This can be solved as an Union Find problem. The reasoning is that the transitive property holds: if person X shares a religion with person Y, and person Y shares a religion with person Z, then person X shares a religion with person Z. We can use Union Find to keep track of this.

Input
10 9 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 10 4 2 3 4 5 4 8 5 8 100 1 1 2 3 5 1 2 2 1 1 2 2 1 1 2 0 0

Output
Case 1: 1 Case 2: 7 Case 3: 99 Case 4: 2