Dota2 Senate - Leetcode Solution

The Dota2 Senate problem is a problem that involves choosing between two teams on the Dota2 game and drafting them in a Senate system. The problem poses a challenge on choosing the optimal winners without causing an unnecessary stalemate or tie in the game.

Given a string senate representing the initial senate composition, the task is to determine the winners assuming that every senator is allowed to vote on their favorite team only. The winner is the team that has more than half of the votes from the senators.

The solution to this problem can be implemented using a queue and a hashmap.

The first step is to iterate over the senate and enqueue each senator into the queue, where the key represents the team "R" or "D" and the value represents the senator's position in the senate.

After initializing the queue and hashmap, we execute the following loop:

1. Dequeue the first senator from the queue and obtain their respective team.
2. Check if the team has the majority of the votes. a. If it does, remove the senator from the queue and continue to the next senator in the queue. b. If it does not, add the senator's position to the end of their team's waitlist.
3. If the queue is empty after all senators have voted, return the team with the most votes.

The hashmap is used to keep track of the waitlist for each team. If a team does not have the majority of the votes, their senators are added to the waitlist. The waitlist keeps track of the position of the senators, which are re-added to the queue after the other team has voted.

The loop above continues until one of the teams acquires the majority of the votes or the queue is empty, which implies a stalemate in the game.

The time complexity of the solution is O(n), where n is the number of senators in the queue, and the space complexity is O(n) for the waitlist hashmap.

Here is the code implementation of the solution in Python:

class Solution:
    def predictPartyVictory(self, senate: str) -> str:
        queue = collections.deque()
        waitlist = {"R": [], "D": []}
        
        # Add each senator to the queue
        for i, senator in enumerate(senate):
            queue.append((senator, i))
            
        while queue:
            senator, pos = queue.popleft()
            
            # Check if the senator's team has the majority of votes
            if len(queue) < 2 * len(waitlist[senator]):
                return senator
            
            # Add the senator to their team's waitlist if they do not have the majority
            waitlist[senator].append(pos)
            
            # Re-add the senator to the queue if the other team has already voted
            other_senator = "R" if senator == "D" else "D"
            if len(waitlist[other_senator]) > 0:
                queue.append((other_senator, waitlist[other_senator].pop(0)))
                
        # If the queue is empty, return the winner with the most votes
        return "Radiant" if senate.count("R") > senate.count("D") else "Dire"

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