Ace Your Google Algorithm Interview in the New Year: Chess Player Ranking Problem Explained
The New Year is here, and it’s the perfect time to push forward with your career goals. For those aiming to land a role at top-tier companies like Google, technical interviews often involve solving challenging algorithm problems. Today, we’ll walk through one such problem—the Chess Player Ranking problem. This article will simulate the complete interview process, highlight csoahelp’s real-time assistance, and help you better prepare for your own interview journey in 2025.
Problem Description
Here’s the original problem, as presented by the interviewer:
There is a chess contest between N players. Each chess player has a distinct rank (positive integer number from 1 to N).
Assume that in a chess game between two players, the higher ranked player always wins. The rank remains constant during the contest. Best player would have rank 1 and worst player would have rank N.
Unfortunately, we don't know the player ranks. But we know the outcome of M games in the following format:
Player #X won Player #Y.Given the results of M games above, are there any players whose rank can be precisely determined? If so, return the player numbers and ranks of such players.
Example:
N = 5, M = 5
Player #4 won #3
Player #4 won #2
Player #3 won #2
Player #1 won #2
Player #2 won #5
Answer:
The rank of 2 players can be determined precisely:
- Player #2 (rank is 4): They lost to players #1, #3, #4 and won player #5.
- Player #5 (rank is 5): They lost to player #2 and we know that player #2 has already lost to #1, #3, and #4.
Breaking the Ice and Clarifying the Problem
The interview begins with the interviewer introducing the problem and asking the candidate to confirm their understanding.
Interviewer:
Today’s problem is about determining the precise rankings of chess players based on game results. We’ll assume rankings follow strict rules, with the higher-ranked player always winning. Does the problem make sense?
csoahelp (Real-time advice):
Before diving into solutions, clarify the rules and ask about edge cases. For example:
- Are there players who didn’t participate in any matches?
- How should those players be handled?
- Are we only expected to return players whose rankings can be precisely determined?
Candidate:
Thanks for the clear explanation! I’d like to confirm a few points:
- Can we assume that the higher-ranked player always wins, with no exceptions?
- If some players haven’t participated in any games, is it safe to say their ranks can’t be determined?
- Should we only return players with definitive rankings, or should we also list players whose ranks are indeterminate?
Interviewer:
Great questions. Yes, the higher-ranked player always wins. Players with no matches cannot have their ranks determined, and you only need to return players with precise rankings.
Discussing the Approach
Once the problem is clear, the candidate begins explaining their approach. csoahelp helps the candidate stay focused and structured, anticipating follow-up questions.
csoahelp (Real-time advice):
Frame the problem as a directed graph:
- Each player is a node.
- A match result “Player X won Player Y” becomes a directed edge from X to Y.
- Use graph traversal to determine if a player’s rank is uniquely identifiable by their win/loss paths.
Propose multiple approaches, such as topological sorting or transitive closure (Floyd-Warshall), to show flexibility in solving the problem.
Candidate:
Here’s my approach:
- I’ll model the problem as a directed graph where each node represents a player, and each directed edge represents a win/loss result.
- To determine if a player’s rank can be uniquely identified, I’ll check if their win/loss relationships span all other players.
- One way to achieve this is by computing the graph’s transitive closure using the Floyd-Warshall algorithm. This will allow us to find all possible paths in the graph and determine if a player is directly or indirectly connected to all others.
Does this approach sound reasonable?
Interviewer:
That sounds like a solid starting point. What’s your fallback plan if there are many players but very few matches?
csoahelp (Real-time advice):
If M (number of matches) is small, suggest using topological sorting. It’s more efficient for sparse graphs, with a time complexity of O(N + M).
Candidate:
If the number of matches is small, I’d use topological sorting instead of Floyd-Warshall. By calculating in-degrees and out-degrees for each player, I can determine their relative ranking in linear time, O(N + M).
Time and Space Complexity
The interviewer now asks the candidate to analyze the computational complexity of their solution.
Interviewer:
Great. Can you explain the time and space complexity of your approach? Are there any bottlenecks?
csoahelp (Real-time advice):
Break the analysis into two parts:
- Floyd-Warshall: Time complexity is O(N³) for computing all-pairs reachability; space complexity is O(N²) for the adjacency matrix.
- Topological Sorting: Time complexity is O(N + M); space complexity is O(N + M) for storing edges in an adjacency list.
Candidate:
Sure. For the Floyd-Warshall approach:
- The time complexity is O(N³), as it requires three nested loops to compute reachability for all player pairs.
- The space complexity is O(N²), as we use an adjacency matrix to store the graph.
For the topological sorting approach:
- The time complexity is O(N + M), where N is the number of players and M is the number of matches.
- The space complexity is also O(N + M), as we store the graph using an adjacency list.
Floyd-Warshall is better suited for dense graphs, while topological sorting is more efficient for sparse graphs.
Interviewer:
Good analysis. I like how you’ve tailored your approach to different scenarios.
Behavioral Question
The interviewer wraps up with a behavioral question to assess the candidate’s teamwork and problem-solving skills.
Interviewer:
Tell me about a time when you worked with a team to solve a complex problem.
csoahelp (Real-time advice):
Choose an example with a clear structure:
- Describe the problem briefly.
- Explain your specific role and the steps you took to resolve it.
- Highlight the results and what you learned from the experience.
Candidate:
Sure. During a previous project, our team was tasked with improving the response time of a heavily used API. We discovered that database queries were the main bottleneck. I proposed introducing a caching mechanism, which reduced query load by 70%. I worked closely with the team to implement this solution and test its effectiveness. As a result, we improved the API’s response time by 50%. This experience taught me the importance of collaboration and systematic problem-solving.
Interviewer:
That’s a great example. Thanks for sharing!
How csoahelp Made the Difference
Throughout this interview simulation, csoahelp played a critical role in the candidate’s success by:
- Clarifying the Problem: Providing real-time suggestions to ask thoughtful clarifying questions and identify edge cases.
- Structuring the Approach: Offering frameworks like graph modeling, transitive closure, and topological sorting to build a clear solution.
- Handling Complexity Questions: Guiding the candidate through detailed time and space complexity analysis.
- Behavioral Question Support: Helping the candidate present past experiences effectively, with an emphasis on teamwork and problem-solving.
By leveraging csoahelp, candidates can approach technical interviews with confidence, fluency, and precision.
New Year, New Goals: Let csoahelp Help You Succeed
As we step into 2025, it’s the perfect time to aim high and achieve your career dreams. Whether it’s Google, LinkedIn, or another dream company, csoahelp will guide you through every step of the interview process, ensuring you’re always prepared to shine. Let’s make this New Year your most successful one yet!
经过csoahelp的面试辅助，候选人获取了良好的面试表现。如果您需要面试辅助或面试代面服务，帮助您进入梦想中的大厂，请随时联系我。
If you need more interview support or interview proxy practice, feel free to contact us. We offer comprehensive interview support services to help you successfully land a job at your dream company.
