649. Dota2 Senate

Problem Statement

link: LeetCode.cn LeetCode In the world of Dota2, there are two parties: the Radiant and the Dire.

The Dota2 senate consists of senators coming from two parties. Now the Senate wants to decide on a change in the Dota2 game. The voting for this change is a round-based procedure. In each round, each senator can exercise one of the two rights:

Ban one senator’s right: A senator can make another senator lose all his rights in this and all the following rounds. Announce the victory: If this senator found the senators who still have rights to vote are all from the same party, he can announce the victory and decide on the change in the game. Given a string senate representing each senator’s party belonging. The character ‘R’ and ‘D’ represent the Radiant party and the Dire party. Then if there are n senators, the size of the given string will be n.

The round-based procedure starts from the first senator to the last senator in the given order. This procedure will last until the end of voting. All the senators who have lost their rights will be skipped during the procedure.

Suppose every senator is smart enough and will play the best strategy for his own party. Predict which party will finally announce the victory and change the Dota2 game. The output should be “Radiant” or “Dire”.

Example:

Input: senate = "RD" Output: "Radiant"

Input: senate = "RDD" Output: "Dire"

Solution Approach

The solution uses a queue-based approach to simulate the round-based procedure, where senators from each party are placed in separate queues, and in each round, the senator with the earlier index bans the opponent’s senator and re-queues themselves to the end with an updated index to maintain the cycle until one party has no remaining senators.

Algorithm

1. Queue Initialization: Initialize two queues to keep track of the indices of the Radiant and Dire senators.
2. Round Simulation: In each round, compare the front senators of both queues and allow the one with the lower index to ban the other’s right to vote, then re-queue the winning senator with an updated index.
3. Determine Victory: Continue the simulation until one of the queues is empty, and declare the party with remaining senators as the victor.

Implement

    class Solution:
        def predictPartyVictory(self, senate: str) -> str:
            n = len(senate)
            radiant = collections.deque()
            dire = collections.deque()

            for i, ch in enumerate(senate):
                if ch == "R":
                    radiant.append(i)
                else:
                    dire.append(i)

            while radiant and dire:
                if radiant[0] < dire[0]:
                    radiant.append(radiant[0] + n)
                else:
                    dire.append(dire[0] + n)
                radiant.popleft()
                dire.popleft()
            return "Radiant" if radiant else "Dire"

    
    

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