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:
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 1:
Input: senate = "RD" Output: "Radiant" Explanation: The first senator comes from Radiant and he can just ban the next senator's right in round 1. And the second senator can't exercise any rights anymore since his right has been banned. And in round 2, the first senator can just announce the victory since he is the only guy in the senate who can vote.
Example 2:
Input: senate = "RDD" Output: "Dire" Explanation: The first senator comes from Radiant and he can just ban the next senator's right in round 1. And the second senator can't exercise any rights anymore since his right has been banned. And the third senator comes from Dire and he can ban the first senator's right in round 1. And in round 2, the third senator can just announce the victory since he is the only guy in the senate who can vote.
Constraints:
n == senate.length1 <= n <= 104senate[i] is either 'R' or 'D'.We utilize two separate queues to maintain indices of Radiant and Dire senators. In each round, senators from both parties execute their rights and effect bans on their opponent. The process continues until one queue becomes empty, indicating that all senators from one party have been eliminated.
In the solution, we employ a queue to separately track Radiant and Dire senators' indices. For each senate round, we compare indices of both parties. The senator with a smaller index, indicating an earlier position, bans the other and gets scheduled for the next round with an increased index (index + senate length). The queue that first becomes empty indicates the losing party.
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Time Complexity: O(n), where n is the length of the senate, since each senator is processed a finite number of times.
Space Complexity: O(n), for storing indices in queues.
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