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Problem: Dota2 Senate

Explore the Dota2 Senate problem where two parties vie for victory through a round-based voting system. Learn to simulate the optimal banning strategy using two queues to represent Radiant and Dire senators. Understand how queue operations model the procedure and achieve efficient senator elimination until one party wins.

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Statement

In the world of Dota22, there are two parties: the Radiant and the Dire.

The Dota22 senate is composed of senators belonging to these two parties. The senate must vote on a change to the game through a round based procedure. In each round, every senator (in order) who still has voting rights may exercise exactly one of the following actions:

  • Ban a senator: Choose one other senator and permanently revoke all of their rights for the current round and all subsequent rounds.

  • Announce victory: If all senators who still retain voting rights belong to the same party, this senator may declare victory for that party.

You are given a string senate of length n, where each character is either 'R' (representing a Radiant senator) or 'D' (representing a Dire senator). The procedure begins with the first senator and proceeds sequentially to the last, then repeats in rounds. Senators who have lost their rights are skipped. This continues until one party announces victory.

Assume every senator plays optimally for their own party. Return "Radiant" if the Radiant party will win, or "Dire" if the Dire party will win.

Note: The ...