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Nice catch. I think you've got it. In the example, P1 wins P2, and P2 wins P3, can be thought as there are directed edges P1 -> P2, P2 -> P3 in the graph, and P1 and P3 won't be in a match so there is no possibility for us to have a P3 -> P1, so there is no cycle. And we just need to topological sort all players which will gives us the rank. The winner of the tournament is the player who loses to nobody (no incoming edge in the graph).
- dchen215 February 02, 2015