#649

Medium

auto_awesomeQueue-driven state processing

LeetCode Problem Workspace

Dota2 Senate

The Dota2 Senate problem involves simulating voting rounds between Radiant and Dire senators until one party wins, using a queue-driven approach.

string greedy queue

Problem Statement

In the Dota2 world, the Senate consists of senators from two rival parties: Radiant ('R') and Dire ('D'). The Senate is tasked with deciding on a game change using a round-based voting procedure. Each senator, in each round, can either ban the voting right of the next senator or vote for the change, depending on whether they are able to act.

Given a string representing the Senate, where each character indicates the party affiliation of a senator, the goal is to determine which party will dominate the voting. In each round, senators use their voting rights strategically to either block the opposing party's rights or advance their own. The simulation ends when one party has no senators left with voting rights.

Examples

Example 1

Input: senate = "RD"

Output: "Radiant"

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"

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.length
1 <= n <= 104
senate[i] is either 'R' or 'D'.

Solution Approach

Queue-driven Simulation

Simulate the rounds using two queues, one for each party. Each senator from both parties gets a turn to vote. In each round, the senator with the voting right bans the opposing senator's right. After each ban, the affected senator is placed at the back of their party's queue to try again in the next round.

Greedy Banning Strategy

In each round, the senator from the leading party bans the right of the opposing senator. This ensures that the party with the most voting senators gets a higher chance of winning, as the process continues until one party has no remaining voters.

Termination Condition

The simulation ends when either the Radiant or Dire party runs out of senators with voting rights. The party with remaining voters is declared the winner.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the number of senators (n) and the queue operations involved. Each senator is processed multiple times (at most twice), resulting in a time complexity of O(n). The space complexity is O(n) due to the queues used for storing the senators.

What Interviewers Usually Probe

The candidate demonstrates an understanding of queue-driven simulations.
The candidate identifies how the greedy strategy ensures fairness in rounds.
The candidate effectively discusses the termination condition and ensures the simulation is properly concluded.

Common Pitfalls or Variants

Common pitfalls

Confusing the ban operation with direct elimination, leading to incorrect simulation steps.
Overcomplicating the simulation by introducing unnecessary data structures or steps.
Not accounting for senators who are banned and should not be processed again.

Follow-up variants

Increasing the number of senators and testing for efficiency.
Allowing a different strategy for banning votes, such as alternating between parties.
Simulating a case with more than two parties involved in the voting process.

FAQ

How does the Dota2 Senate problem utilize queues?

The problem uses two queues to simulate voting rounds, where senators are processed in order, and those who are banned are moved to the back of the queue for the next round.

What is the greedy strategy in Dota2 Senate?

The greedy strategy involves a senator banning the next senator's voting right to prevent the opposing party from gaining any advantage, ensuring the party with more active senators has the upper hand.

What happens when a party runs out of senators with voting rights?

When a party has no remaining senators with voting rights, the opposing party is declared the winner as they have no one left to block or vote.

What is the time complexity of the Dota2 Senate problem?

The time complexity is O(n), where n is the number of senators. Each senator is processed at most twice in the simulation.

Can there be more than two parties in the Dota2 Senate problem?

While the problem is typically set with two parties, it can be extended to simulate multiple parties, though this would require changes to the implementation.

terminal

Solution

Solution 1: Queue + Simulation

We create two queues $qr$ and $qd$ to record the indices of the Radiant and Dire senators, respectively. Then we start the simulation, where in each round we dequeue one senator from each queue and perform different operations based on their factions:

class Solution:
    def predictPartyVictory(self, senate: str) -> str:
        qr = deque()
        qd = deque()
        for i, c in enumerate(senate):
            if c == "R":
                qr.append(i)
            else:
                qd.append(i)
        n = len(senate)
        while qr and qd:
            if qr[0] < qd[0]:
                qr.append(qr[0] + n)
            else:
                qd.append(qd[0] + n)
            qr.popleft()
            qd.popleft()
        return "Radiant" if qr else "Dire"

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