Meta interview questions & answers

Model answer

Situation

As an engineering manager at my previous company, I was responsible for leading a team of software engineers working on a critical project that involved developing a new feature for our flagship product. This project was high-stakes because it was expected to significantly enhance user engagement and drive revenue growth. My role was pivotal in ensuring that the team delivered high-quality work on time while fostering a culture of continuous improvement and professional growth.

Task

My primary goal was to motivate and guide the team to not only meet the project deadlines but also to elevate their skills and performance. A key challenge was balancing the immediate demands of the project with the long-term development of the team members.

Action

• I began by setting clear, achievable goals for the team, aligning them with both the project objectives and individual career aspirations. This alignment helped each team member see how their work contributed to the broader company goals, enhancing their motivation.
• To foster a culture of development, I implemented regular one-on-one coaching sessions. During these sessions, I provided constructive feedback and identified stretch opportunities for each team member, encouraging them to take on new challenges and responsibilities.
• I facilitated knowledge-sharing sessions where team members could present their work and learn from each other. This not only improved technical skills but also built a sense of community and collaboration within the team.
• Recognizing the importance of work-life balance, I advocated for flexible work arrangements, which helped maintain high morale and productivity.
• I also focused on creating a psychologically safe environment where team members felt comfortable sharing ideas and concerns. This openness led to innovative solutions and a more cohesive team dynamic.

Result

As a result of these efforts, the team successfully delivered the project on schedule with high quality. The feature launch exceeded user engagement targets, contributing to a notable increase in revenue. Additionally, the team's performance improved significantly, with several members receiving promotions or taking on more advanced roles. This experience reinforced my belief in the power of investing in people and the importance of balancing immediate project needs with long-term talent development. I learned that as a manager, my success is measured by the growth and achievements of my team.

Model answer

Situation

At Meta, I was a product manager responsible for enhancing user engagement on our social media platform. Our team identified a significant drop in user interaction with video content, which was crucial for our ad revenue model. The baseline metric showed a 15% decline in video views over the past quarter, impacting both user retention and advertiser satisfaction.

Task

My goal was to reverse the declining trend in video engagement by implementing a feature that would increase video views by at least 20% within six months. The challenge was to design a solution that was both technically feasible and aligned with user experience expectations.

Action

• I conducted a thorough analysis of user behavior data to identify patterns and potential causes for the decline. This involved collaborating with the data science team to validate our instrumentation and ensure data accuracy.
• Based on insights, I proposed an algorithm-driven recommendation system to surface personalized video content to users. I scoped the project by defining clear success metrics, including increased video views and user session duration.
• I worked closely with engineering and design teams to develop a prototype. We prioritized a lean MVP approach to test the core functionality quickly.
• To ensure alignment, I facilitated cross-functional meetings with stakeholders from marketing, legal, and operations to address any concerns and gather feedback.
• We faced a major trade-off between speed and quality, as engineering resources were limited. I decided to focus on a phased rollout, allowing us to gather real-time feedback and iterate rapidly.

Result

The project led to a 25% increase in video views within four months, surpassing our initial target. The phased rollout strategy allowed us to address minor issues before a full-scale launch, ensuring a smooth user experience. The feature was well-received, with positive feedback from both users and advertisers. This experience reinforced the value of data-driven decision-making and cross-functional collaboration.

Reflection

I learned the importance of balancing ambition with feasibility, especially when resources are constrained. In retrospect, I would have involved the marketing team earlier to better align our messaging strategy with the feature launch. This project taught me the critical role of iterative development and stakeholder management in driving impactful results.

Model answer

Situation

In my role as a data scientist at a leading tech company, I was tasked with leading an analytics project aimed at improving user engagement on our social media platform. The platform had seen a decline in active user sessions, which was a critical metric for our business as it directly impacted ad revenue. The stakes were high because maintaining user engagement was essential for our competitive edge and financial performance.

Task

My specific goal was to identify and implement data-driven strategies to enhance user engagement. The key constraint was to ensure that any changes would not negatively impact user experience or platform stability. I needed to balance between driving engagement and maintaining a seamless user experience.

Action

• I began by conducting a comprehensive analysis of user behavior data to identify patterns and potential areas for improvement. This involved segmenting users based on activity levels and engagement metrics.
• I selected key metrics to track, such as session duration and interaction frequency, while also considering guardrail metrics like user churn and system load to ensure we didn't compromise on user experience or platform performance.
• To test hypotheses, I designed and ran A/B tests on different features, such as personalized content recommendations and notification frequency adjustments. I ensured the credibility of results by using statistically significant sample sizes and controlling for external variables.
• I collaborated closely with the product and engineering teams to iterate on feature designs based on test outcomes, ensuring alignment with our overall product strategy and technical feasibility.
• Throughout the project, I maintained clear communication with stakeholders, presenting data-driven insights and recommendations to guide decision-making.

Result

The project led to a 15% increase in user session duration and a 10% rise in interaction frequency, significantly boosting our engagement metrics. These improvements contributed to a 5% increase in ad revenue over the following quarter. Reflecting on the project, I learned the importance of balancing innovation with user-centric design and the value of cross-functional collaboration. If I were to do it differently, I would invest more time in user interviews to complement quantitative data with qualitative insights, enhancing our understanding of user needs.

Model answer

Situation From a young age, I was fascinated by how technology could solve real-world problems. This curiosity led me to pursue a degree in computer science, where I was able to dive deep into software engineering. Currently, I am working as a software engineer at a mid-sized tech company, where I have been part of a team developing scalable web applications. The impact of our work on user experience and business growth has been significant, which has reinforced my passion for this field.

Task My primary goal has been to leverage my skills to create software solutions that not only meet user needs but also push the boundaries of what technology can achieve. I am motivated by the challenge of solving complex problems and the opportunity to innovate.

Action

• I actively seek out projects that allow me to work on cutting-edge technologies and methodologies. For example, I recently volunteered to lead a project that integrated machine learning into our existing product, which improved user engagement by 20%.
• I prioritize continuous learning and self-improvement. I regularly attend workshops and online courses to stay updated with the latest trends and best practices in software engineering.
• Collaboration is key to my motivation. I enjoy working in diverse teams where I can learn from others and contribute my unique perspective. During a recent project, I facilitated cross-functional meetings to ensure alignment and gather diverse input, which resulted in a more robust final product.
• I am driven by the potential impact of my work. Knowing that the software I develop can improve lives or streamline business processes is incredibly fulfilling. For instance, a tool I developed for internal use reduced processing time by 30%, significantly increasing team productivity.
• I also find motivation in mentoring junior engineers. Sharing knowledge and seeing others grow in their careers is rewarding and helps foster a collaborative team environment.

Result My motivation in software engineering has led to tangible results, such as increased user engagement and enhanced team productivity. These outcomes have not only benefited the company but have also provided me with a sense of accomplishment and purpose. This experience has taught me the importance of staying curious and adaptable, which I believe are crucial traits for any software engineer.

Model answer

// Question 1: Near-palindrome with one deletion
function validPalindrome(s) {
    function isPalindrome(l, r) {
        while (l < r) {
            if (s[l] !== s[r]) return false;
            l++;
            r--;
        }
        return true;
    }

    let left = 0;
    let right = s.length - 1;

    while (left < right) {
        if (s[left] !== s[right]) {
            // Try removing one character from either end
            return isPalindrome(left + 1, right) || isPalindrome(left, right - 1);
        }
        left++;
        right--;
    }
    return true;
}

// Approach for Question 1:
// - Use two pointers to check if the string is a palindrome.
// - If a mismatch is found, check if removing one of the mismatched characters results in a palindrome.
// - This is done by checking two substrings: one excluding the left character and one excluding the right character.

// Complexity for Question 1:
// Time: O(n), where n is the length of the string, as we may need to check the entire string.
// Space: O(1), as we use a constant amount of extra space.


// Question 2: Binary tree vertical order traversal
function verticalOrder(root) {
    if (!root) return [];

    const columnTable = new Map();
    const queue = [{ node: root, col: 0 }];
    let minCol = 0, maxCol = 0;

    while (queue.length > 0) {
        const { node, col } = queue.shift();

        if (!columnTable.has(col)) {
            columnTable.set(col, []);
        }
        columnTable.get(col).push(node.val);

        if (node.left) {
            queue.push({ node: node.left, col: col - 1 });
            minCol = Math.min(minCol, col - 1);
        }
        if (node.right) {
            queue.push({ node: node.right, col: col + 1 });
            maxCol = Math.max(maxCol, col + 1);
        }
    }

    const result = [];
    for (let i = minCol; i <= maxCol; i++) {
        result.push(columnTable.get(i));
    }
    return result;
}

// Approach for Question 2:
// - Use a BFS approach to traverse the tree while keeping track of the column index for each node.
// - Store nodes in a map where keys are column indices and values are lists of node values.
// - Track the minimum and maximum column indices to determine the range of columns to output.
// - Collect results from the map in order from the smallest to the largest column index.

// Complexity for Question 2:
// Time: O(n), where n is the number of nodes in the tree, as each node is processed once.
// Space: O(n), for the map and queue used to store nodes and their column indices.

Model answer

// Problem 1: Deep copy a linked list with extra pointers

function copyRandomList(head) {
    if (!head) return null;

    // Step 1: Create new nodes and interleave them with the original nodes
    let current = head;
    while (current) {
        const newNode = new Node(current.val);
        newNode.next = current.next;
        current.next = newNode;
        current = newNode.next;
    }

    // Step 2: Assign random pointers for the new nodes
    current = head;
    while (current) {
        if (current.random) {
            current.next.random = current.random.next;
        }
        current = current.next.next;
    }

    // Step 3: Separate the new list from the original list
    current = head;
    const newHead = head.next;
    while (current) {
        const newNode = current.next;
        current.next = newNode.next;
        if (newNode.next) {
            newNode.next = newNode.next.next;
        }
        current = current.next;
    }

    return newHead;
}

// Problem 2: Find the k most frequent integers in an array

function topKFrequent(nums, k) {
    const frequencyMap = new Map();

    // Count the frequency of each number
    for (const num of nums) {
        frequencyMap.set(num, (frequencyMap.get(num) || 0) + 1);
    }

    // Create an array of buckets to store numbers by frequency
    const buckets = Array(nums.length + 1).fill().map(() => []);
    for (const [num, freq] of frequencyMap.entries()) {
        buckets[freq].push(num);
    }

    // Gather the top k frequent elements
    const result = [];
    for (let i = buckets.length - 1; i >= 0 && result.length < k; i--) {
        if (buckets[i].length > 0) {
            result.push(...buckets[i]);
        }
    }

    return result.slice(0, k);
}

• Approach for Problem 1:
• Interleave Nodes: Create new nodes and interleave them with the original nodes.
• Assign Random Pointers: Set the random pointers for the new nodes using the interleaved structure.
• Separate Lists: Detach the new list from the original list to form the deep copy.
• Approach for Problem 2:
• Frequency Map: Use a hash map to count the frequency of each element.
• Bucket Sort: Use an array of buckets where the index represents frequency.
• Collect Top k: Collect elements from the highest frequency bucket downwards until k elements are gathered.

Complexity:

• Time Complexity: Both solutions run in O(n) time, where n is the number of nodes or elements.
• Space Complexity: O(n) additional space is used for both solutions, primarily for the new nodes and frequency map.

Model answer

function blockPlacementSimulator(n, m, pieces, pieceShapes) {
    // Initialize an empty grid
    const grid = Array.from({ length: n }, () => Array(m).fill(false));

    // Helper function to check if a piece can be placed at a given position
    function canPlacePiece(pieceShape, startRow, startCol) {
        for (const [dr, dc] of pieceShape) {
            const newRow = startRow + dr;
            const newCol = startCol + dc;
            if (
                newRow < 0 || newRow >= n || 
                newCol < 0 || newCol >= m || 
                grid[newRow][newCol]
            ) {
                return false;
            }
        }
        return true;
    }

    // Helper function to place a piece on the grid
    function placePiece(pieceShape, startRow, startCol) {
        for (const [dr, dc] of pieceShape) {
            grid[startRow + dr][startCol + dc] = true;
        }
    }

    // Process each piece
    for (const pieceType of pieces) {
        const pieceShape = pieceShapes[pieceType];
        let placed = false;

        // Scan the grid to find the first valid position
        for (let row = 0; row < n && !placed; row++) {
            for (let col = 0; col < m && !placed; col++) {
                if (canPlacePiece(pieceShape, row, col)) {
                    placePiece(pieceShape, row, col);
                    placed = true;
                }
            }
        }

        // If a piece cannot be placed, stop processing
        if (!placed) {
            break;
        }
    }

    return grid;
}

// Example usage
const n = 5, m = 5;
const pieces = ['A', 'B', 'C'];
const pieceShapes = {
    'A': [[0, 0], [0, 1]], // Example shape for piece A
    'B': [[0, 0], [1, 0]], // Example shape for piece B
    'C': [[0, 0], [0, 1], [1, 0]], // Example shape for piece C
    // Define other shapes as needed
};

console.log(blockPlacementSimulator(n, m, pieces, pieceShapes));

• Approach:
• Initialize an n x m grid with all cells set to false (unoccupied).
• For each piece in the sequence, attempt to place it by scanning the grid from top-left to bottom-right.
• Use helper functions to check if a piece can be placed and to place the piece if possible.
• Stop processing if a piece cannot be placed due to lack of space.
• Complexity:
• Time: O(p n m * s), where p is the number of pieces, n and m are grid dimensions, and s is the maximum size of a piece.
• Space: O(n * m) for the grid.

Model answer

// Given values
const b = 0.02; // Baseline CTR (2.0%)
const e = 0.20; // Event CTR (20.0%)
const N = 9990; // Number of baseline messages
const k = 10;   // Number of event messages

// 1. Calculate overall CTR
const C_overall = (b * N + e * k) / (N + k);

// 2. Calculate relative lift vs baseline
const relativeLift = (C_overall / b) - 1;

// 3. Derive minimum share s required for at least 10% relative increase
// C_overall >= 1.10 * b
// (b * N + e * k) / (N + k) >= 1.10 * b
// Solve for s = k / (N + k)
const requiredIncrease = 1.10 * b;
const s = (requiredIncrease - b) / (e - b);

// 4. Calculate smallest integer k for N = 1,000,000
const N_large = 1000000;
const k_min = Math.ceil((requiredIncrease - b) * N_large / (e - requiredIncrease));

console.log(`Overall CTR: ${C_overall * 100}%`);
console.log(`Relative Lift: ${(relativeLift * 100).toFixed(2)}%`);
console.log(`Minimum Share s: ${s.toFixed(4)}`);
console.log(`Smallest k for N = 1,000,000: ${k_min}`);

• Overall CTR Calculation: The overall CTR is computed using the formula \( C_{\text{overall}} = \frac{b \cdot N + e \cdot k}{N + k} \). With \( N = 9990 \) and \( k = 10 \), the overall CTR is calculated.
• Relative Lift: The relative lift is the percentage increase from the baseline CTR, calculated as \( \left(\frac{C_{\text{overall}}}{b} - 1\right) \times 100\% \).
• Minimum Share \( s \): To achieve at least a 10% increase in overall CTR, solve for \( s = \frac{k}{N + k} \) using the inequality \( C_{\text{overall}} \geq 1.10 \cdot b \).
• Smallest \( k \) for Large \( N \): With \( N = 1,000,000 \), compute the smallest integer \( k \) that achieves the target relative increase.

Complexity: Time complexity is \( O(1) \) as the calculations involve simple arithmetic operations. Space complexity is also \( O(1) \) since only a fixed number of variables are used.

Model answer

Clarify: Choose a product that you use frequently and have a deep understanding of. It could be a tech product or something from everyday life.

User segments & pain points: Identify who the product serves and what problems it solves. Explain why these aspects are important to you.

Goals & success metrics: Discuss the product's main goals and how it measures success. This could include user satisfaction, market share, or innovation.

Features & impact: Highlight key features that make the product stand out and how they impact your life or work positively.

Recommendation: Conclude with why you would recommend this product to others, emphasizing its unique value proposition and personal significance.

Model answer

The flow

1. Clarify the goal → Understand the purpose of the new feature and its expected impact.
2. Define the metric → Identify key metrics that reflect success.
3. Break it down by funnel and segment → Analyze the user journey and segment the audience.
4. Rank hypotheses → List potential reasons for success or failure.
5. Say how you'd check each → Determine methods to test each hypothesis.
6. Decision & guardrails → Make a recommendation based on findings and set boundaries.

The answer

1. Clarify the goal

• The goal of the new feature is to increase user engagement by providing a more personalized experience.
• Assumptions include that users will find the feature valuable and that it will lead to longer session times.

2. Define the metric

• Primary Metric: Increase in average session duration by 10% within the first month of launch.
• Secondary Metrics: Increase in user retention rate by 5% and a decrease in bounce rate by 3%.

3. Break it down by funnel and segment

• Funnel Stages: Feature discovery → Feature usage → Continued engagement.
• Segments: New users vs. returning users, and users from different geographic regions.

funnel
    subgraph User Funnel
    direction TB
    A[Feature Discovery] --> B[Feature Usage]
    B --> C[Continued Engagement]
    end

4. Rank hypotheses

• Hypothesis 1: Users find the feature intuitive and engaging, leading to longer sessions.
• Hypothesis 2: The feature is not easily discoverable, resulting in low usage.
• Hypothesis 3: The feature is more appealing to returning users than new users.

5. Say how you'd check each

• Use A/B testing to compare session durations between users with and without the feature.
• Conduct user surveys and feedback sessions to assess feature discoverability.
• Segment data by user type and analyze differences in engagement metrics.

6. Decision & guardrails

• Recommendation: If the feature leads to a significant increase in session duration and user retention, consider rolling it out to a broader audience.
• Guardrails: Monitor for any negative impacts on other metrics, such as a decrease in overall user satisfaction or an increase in support tickets.

Why this works

• Goal Alignment: The interviewer is testing if you can align feature success with business goals and user needs.
• Metric Selection: A strong answer identifies relevant metrics that directly measure the feature's impact.
• Analytical Rigor: Breaking down the problem by funnel and segment shows a methodical approach to understanding user behavior.
• Hypothesis Testing: Ranking and testing hypotheses demonstrate critical thinking and an evidence-based approach.
• Practical Recommendations: A weak answer fails to provide actionable insights or ignores potential negative impacts, while a strong answer includes thoughtful recommendations and guardrails.

Model answer

The flow

1. Clarify the goal → Understand the purpose of the recommendation system.
2. Define the metric → Identify key performance metrics.
3. Break it down by funnel and segment → Analyze user interactions and segments.
4. Rank hypotheses → Prioritize potential improvements or issues.
5. Say how you'd check each → Determine how to validate hypotheses.

The answer

1. Clarify the goal:

• The primary goal of a recommendation system is to increase user engagement and satisfaction by providing relevant and personalized content or product suggestions.
• Secondary goals may include increasing sales, retention, or time spent on the platform.

2. Define the metric:

• Key metrics to evaluate include:
• Precision: The proportion of recommended items that are relevant.
• Recall: The proportion of relevant items that are recommended.
• F1 Score: The harmonic mean of precision and recall, providing a balance between the two.
• Click-through Rate (CTR): The percentage of recommendations that users click on.
• Conversion Rate: The percentage of recommendations that lead to a purchase or another desired action.
• User Satisfaction: Measured through surveys or feedback.

3. Break it down by funnel and segment:

• Funnel stages could include impression, click, and conversion.
• Segments might include new users vs. returning users, different demographic groups, or different usage patterns.
• Analyze how each segment performs at each funnel stage to identify strengths and weaknesses.

funnel
    subgraph Funnel
    direction TB
    A[Impression] --> B[Click]
    B --> C[Conversion]
    end

4. Rank hypotheses:

• Hypothesis 1: Increasing the diversity of recommendations will improve user engagement.
• Hypothesis 2: Personalizing recommendations based on recent activity will increase conversion rates.
• Hypothesis 3: Improving the algorithm's understanding of user preferences will enhance precision and recall.

5. Say how you'd check each:

• Diversity Hypothesis: Conduct A/B testing to compare user engagement metrics between diverse vs. less diverse recommendation sets.
• Personalization Hypothesis: Implement a machine learning model that factors in recent activity and measure the impact on conversion rates.
• Preference Understanding Hypothesis: Enhance the algorithm with additional data sources and evaluate changes in precision and recall.

Why this works

• Testing Metrics Understanding: The interviewer assesses whether the candidate knows which metrics are critical for evaluating recommendation systems.
• Analytical Breakdown: A strong answer will segment the analysis, showing an understanding of different user behaviors and interactions.
• Hypothesis Prioritization: Demonstrating the ability to prioritize hypotheses based on potential impact shows strategic thinking.
• Validation Approach: A strong candidate will clearly articulate how they would validate each hypothesis, showing practical problem-solving skills.
• Weak Answers: Failing to specify metrics or not breaking down the analysis by segment can indicate a lack of depth in understanding recommendation systems.

Model answer

Clarify & scope: The goal is to enhance user engagement in Facebook Groups. Assume we are targeting both existing members and potential new members. The scope includes features that could increase daily active usage and interaction within groups.

User segments & pain points: Focus on active group members who may find content overwhelming or not relevant. Pain points include difficulty in finding relevant posts and lack of meaningful interaction.

Goals & success metrics: The North Star metric is the increase in daily active users (DAU) within groups. Guardrail metrics include user satisfaction and retention rates.

Solutions:

1. Content Personalization: Use AI to show more relevant posts to users based on their past interactions.
2. Enhanced Notification System: Allow users to customize notifications for specific topics or threads.
3. Interactive Features: Introduce polls or Q&A sessions to encourage participation.

Recommendation: Focus on content personalization to increase relevance and engagement.

graph TD;
  A[User] --> B[Personalized Feed];
  B --> C[Higher Engagement];

Prioritization & trade-offs: Using RICE, content personalization scores high on impact and reach but requires significant effort. Interactive features are easier to implement but may offer less immediate impact.

MVP, measurement & rollout: Start with a beta test of the personalized feed in select groups. Measure changes in engagement and satisfaction before rolling out broadly.

Model answer

1. Requirements & scale

Functional Requirements:

• Users can view a personalized news feed.
• Users can post new content.
• Users can like and comment on posts.
• The system should deliver real-time updates.

Non-Functional Requirements:

• Low latency for feed updates.
• High availability and reliability.
• Scalability to handle millions of users.
• Consistency in displaying the latest posts.

Estimates:

• Assume 100 million daily active users, with each user making 5 requests per day on average.
• Total requests per day = 500 million.
• QPS (Queries Per Second) = 500 million / 86,400 seconds ≈ 5,800 QPS.
• Average post size = 1 KB. If each user views 100 posts per day, data transfer = 100 million 100 1 KB = 10 TB/day.
• Storage: Assume 1 billion posts with an average size of 1 KB = 1 TB of storage.

2. High-level architecture

flowchart TD
    subgraph Client
        A[Mobile App]
        B[Web App]
    end

    subgraph Edge/CDN
        C[CDN]
    end

    subgraph Load Balancer
        D[Load Balancer]
    end

    subgraph API / Services
        E[Feed Service]
        F[Post Service]
        G[User Service]
    end

    subgraph Cache
        H[Redis Cache]
    end

    subgraph Datastores
        I["SQL DB (User, Post)"]
        J["NoSQL DB (Feed)"]
    end

    subgraph Message Queue
        K[Kafka]
    end

    subgraph Workers
        L[Feed Generator]
    end

    A --> C
    B --> C
    C --> D
    D --> E
    D --> F
    D --> G
    E --> H
    H --> I
    F --> I
    G --> I
    F --> K
    K --> L
    L --> J
    E --> J

3. API design

• GET /feed: Retrieve the user's news feed.
• POST /post: Create a new post.
• POST /like: Like a post.
• POST /comment: Comment on a post.
• GET /user/{id}: Retrieve user profile information.

4. Data model & storage

Datastores:

• SQL Database:
• User Table: Stores user information.
• Post Table: Stores post metadata and content.
• NoSQL Database:
• Feed Collection: Stores precomputed feeds for fast retrieval.
• Cache:
• Redis: Caches frequently accessed feeds and user data to reduce load on databases.

Partitioning Strategy:

• User Table: Partition by user ID.
• Post Table: Partition by post ID.
• Feed Collection: Partition by user ID to ensure fast access to a user's feed.

5. Deep dive

The core challenge is efficiently generating and updating the news feed. We use a fan-out-on-write approach:

sequenceDiagram
    participant User as User
    participant PostService as Post Service
    participant Kafka as Kafka
    participant FeedGen as Feed Generator
    participant NoSQL as NoSQL DB

    User->>PostService: Create Post
    PostService->>Kafka: Publish Post Event
    Kafka->>FeedGen: Consume Post Event
    FeedGen->>NoSQL: Update Feeds

1. Post Creation: When a user creates a post, the Post Service stores it in the SQL database and publishes an event to Kafka.
2. Feed Generation: The Feed Generator consumes the event and updates the relevant users' feeds in the NoSQL database.
3. Feed Retrieval: When a user requests their feed, the Feed Service retrieves it from the NoSQL database, using Redis for caching to improve performance.

6. Scale, bottlenecks & trade-offs

Scalability:

• Sharding: Both SQL and NoSQL databases are sharded by user ID to distribute load evenly.
• Caching: Redis is used to cache frequently accessed data, reducing database load.

Bottlenecks:

• Feed Generation: The fan-out-on-write approach can be resource-intensive. Scaling the Feed Generator horizontally can mitigate this.
• Real-time Updates: Ensuring low latency for real-time updates can be challenging. Using WebSockets or long polling can help.

Trade-offs:

• Consistency vs. Availability: Opt for eventual consistency in feed updates to ensure high availability.
• Push vs. Pull: Use a combination of push notifications for critical updates and pull for regular feed refreshes.
• SQL vs. NoSQL: SQL is used for structured data with relationships, while NoSQL is used for high-throughput feed storage.

Model answer

1. Requirements & scale

Functional Requirements:

• Users can create auctions with item details, start/end times, and optional reserve prices.
• Users can place bids while auctions are live.
• Users can view the current winning bid and bid history.
• Users receive near-real-time notifications for bid changes and auction endings.

Non-Functional Requirements:

• High availability and low latency for bid placements and notifications.
• Scalability to handle many concurrent auctions and bid spikes near auction end times.
• Consistency to ensure no bids are accepted after auction end times.

Estimates:

• Assume 1 million active users, with 10% participating in auctions at any time.
• Average of 100 bids per auction, with peak activity at auction end.
• If each user places 1 bid per minute during peak, estimate 100,000 bids per minute (1,667 QPS).
• Storage: Assume each auction stores 1 KB of metadata and 1 KB per bid. For 1 million auctions with 100 bids each, storage is approximately 200 GB.

2. High-level architecture

flowchart TD
    subgraph Client
        A[User Interface]
    end

    subgraph "Edge/CDN"
        B[Edge Servers]
    end

    subgraph "Load Balancer"
        C[Load Balancer]
    end

    subgraph "API / Services"
        D[Auction Service]
        E[Bid Service]
        F[Notification Service]
    end

    subgraph "Cache"
        G[Redis Cache]
    end

    subgraph "Datastores"
        H["SQL DB (Auctions)"]
        I["NoSQL DB (Bids)"]
    end

    subgraph "Message Queue"
        J[Kafka]
    end

    subgraph Workers
        K[Notification Workers]
    end

    A --> B --> C --> D
    A --> B --> C --> E
    D --> H
    E --> I
    E --> G
    E --> J
    J --> K
    K --> F
    F --> A

3. API design

• POST /auctions: Create a new auction.
• GET /auctions/{auctionId}: Retrieve auction details and current winning bid.
• POST /auctions/{auctionId}/bids: Place a bid on an auction.
• GET /auctions/{auctionId}/bids: Retrieve bid history for an auction.
• GET /notifications: Fetch notifications for bid changes and auction endings.

4. Data model & storage

Datastores:

• SQL Database (Auctions): Store auction metadata for ACID properties.
• Table: Auctions
• Columns: auctionId (PK), itemInfo, startTime, endTime, reservePrice
• NoSQL Database (Bids): Store bids for scalability and high write throughput.
• Table: Bids
• Columns: bidId (PK), auctionId (Partition Key), userId, amount, timestamp

Cache:

• Redis: Cache current winning bid and recent bid history for quick access.

5. Deep dive

The core challenge is handling bid spikes and ensuring real-time notifications. We use a combination of caching, message queues, and WebSockets for real-time updates.

sequenceDiagram
    participant U as User
    participant UI as User Interface
    participant S as Bid Service
    participant C as Redis Cache
    participant MQ as Kafka
    participant NW as Notification Worker
    participant NS as Notification Service

    U->>UI: Place Bid
    UI->>S: POST /auctions/{auctionId}/bids
    S->>C: Check Cache for Current Winning Bid
    alt Bid is Higher
        S->>C: Update Cache with New Winning Bid
        S->>MQ: Publish Bid Event
    end
    MQ->>NW: Consume Bid Event
    NW->>NS: Send Real-Time Notification
    NS->>UI: Push Notification

6. Scale, bottlenecks & trade-offs

Scaling:

• Horizontal Scaling: Use microservices architecture to scale individual components independently.
• Sharding: Partition bids by auctionId to distribute load across multiple NoSQL nodes.

Bottlenecks:

• Bid Spikes: Use Redis to cache winning bids and recent bid history to reduce database load.
• Notification Delays: Use Kafka for reliable message delivery and WebSockets for real-time notifications.

Trade-offs:

• Consistency vs. Availability: Prioritize consistency to ensure no bids are accepted post-auction end.
• Push vs. Pull Notifications: Use WebSockets for push notifications to minimize latency.
• SQL vs. NoSQL: Use SQL for auction metadata to ensure ACID properties, and NoSQL for bids to handle high write throughput.

Model answer

1. Requirements & scale

Functional Requirements:

• Detect and classify fake accounts based on friend request behaviors.
• Handle ambiguous or gray accounts with a review mechanism.
• Log and track user actions related to friend requests.

Non-Functional Requirements:

• Minimize false positives to avoid impacting legitimate users.
• Ensure scalability to handle millions of users and requests.
• Provide timely detection and reporting.

Scale Estimates:

• Assume 1 billion users with an average of 10 friend requests per user per month.
• Total friend requests per month = 10 billion.
• Average QPS (Queries Per Second) for friend requests = 3,800.
• Storage for logging: 100 bytes per request, leading to approximately 1 TB per month.

2. High-level architecture

flowchart TD
    subgraph Client
        A[User Device]
    end

    subgraph Edge/CDN
        B[CDN]
    end

    subgraph Load Balancer
        C[Load Balancer]
    end

    subgraph API / Services
        D[Friend Request Service]
        E[User Action Logger]
    end

    subgraph Cache
        F[Redis Cache]
    end

    subgraph Datastores
        G[SQL Database]
        H[NoSQL Database]
    end

    subgraph Message Queue
        I[Kafka Queue]
    end

    subgraph Workers
        J[Heuristic Analysis Worker]
    end

    A -->|Send/Receive Friend Request| B
    B --> C
    C --> D
    D -->|Log Request| E
    E -->|Store Logs| H
    D -->|Check Cache| F
    F -->|Fetch Data| G
    D -->|Publish Event| I
    I --> J
    J -->|Analyze & Flag| G

3. API design

• POST /friend-request/send: Send a friend request to another user.
• POST /friend-request/accept: Accept a received friend request.
• POST /friend-request/decline: Decline a received friend request.
• GET /friend-request/status: Retrieve the status of a sent or received friend request.

4. Data model & storage

Datastores:

• SQL Database: For structured data like user profiles and friend connections.
• NoSQL Database: For logging events and actions due to its scalability and flexibility.

Key Tables:

• FriendRequests: request_id, sender_id, receiver_id, status, timestamp.
• UserActions: action_id, user_id, action_type, timestamp.

Partition Key:

• Use user_id for partitioning to ensure even distribution and efficient querying.

5. Deep dive

The core of detecting fake accounts involves analyzing friend request patterns and user behaviors. The heuristic approach includes:

• Rate Limits: Monitor the number of friend requests sent per user per hour/day.
• Graph Patterns: Identify unusual patterns like a high number of requests with low acceptance.
• Acceptance Ratios: Calculate the ratio of accepted to sent requests.
• Burstiness: Detect sudden spikes in friend request activity.
• Post-Acceptance Messaging: If available, track messaging activity after acceptance to identify spam.

sequenceDiagram
    participant U as User
    participant S as Friend Request Service
    participant L as Logger
    participant W as Worker
    participant D as Database

    U->>S: Send Friend Request
    S->>L: Log Request
    S->>D: Store Request
    S->>W: Publish Event
    W->>D: Fetch User Data
    W->>W: Analyze Patterns
    W->>D: Flag Suspicious Accounts

6. Scale, bottlenecks & trade-offs

Scalability: Use horizontal scaling for the Friend Request Service and the Logger to handle high QPS. Employ sharding in the NoSQL database to manage large volumes of log data.

Bottlenecks: The main bottleneck is the analysis worker, which must process large volumes of data quickly. Use distributed processing frameworks to scale.

Trade-offs:

• Consistency vs. Availability: Prioritize availability for user actions, but ensure eventual consistency for analysis results.
• False Positives vs. False Negatives: Balance between catching fake accounts and minimizing impact on legitimate users by adjusting heuristic thresholds.
• Push vs. Pull: Use a push model for real-time detection and a pull model for batch analysis.

By implementing these strategies, the system can effectively identify and manage fake accounts while minimizing disruption to legitimate users.

Model answer

1. Requirements & scale

Functional Requirements:

• Measure and compare user engagement on Facebook Stories and Instagram Stories.
• Identify and mitigate potential cannibalization effects on other features like Feed, Reels, and messaging.
• Provide insights into user behavior and content performance.

Non-Functional Requirements:

• Ensure data accuracy and reliability.
• Maintain user privacy and data security.
• Provide real-time or near-real-time insights.

Scale Estimates:

• Assume 1 billion daily active users across Facebook and Instagram.
• Each user views an average of 10 stories per day.
• Estimated QPS (Queries Per Second) for story views: \(1 \text{ billion users} \times 10 \text{ views} / 86,400 \text{ seconds} \approx 115,740 \text{ QPS}\).
• Storage requirements for metadata and analytics: Assume 1 KB per story view, leading to approximately 10 TB of data per day.

2. High-level architecture

flowchart TD
  subgraph Client
    A[User Devices]
  end

  subgraph Edge/CDN
    B[CDN]
  end

  subgraph Load Balancer
    C[Load Balancer]
  end

  subgraph API / Services
    D[Stories API]
    E[Analytics Service]
  end

  subgraph Cache
    F[Redis Cache]
  end

  subgraph Datastores
    G[Relational DB]
    H[NoSQL DB]
  end

  subgraph Message Queue
    I[Kafka]
  end

  subgraph Workers
    J[Data Processing Workers]
  end

  A -->|Story Request| B
  B -->|Cache Miss| C
  C -->|Route Request| D
  D -->|Fetch Metadata| F
  F -->|Cache Miss| G
  D -->|Log Event| I
  I -->|Process Events| J
  J -->|Store Analytics| H
  E -->|Query Data| H

3. API design

• GET /stories: Retrieve stories for a user.
• POST /stories/view: Log a story view event.
• GET /analytics/stories: Fetch analytics data for stories.

4. Data model & storage

Datastores:

• Relational DB: Store user and story metadata for quick access.
• NoSQL DB: Store large volumes of analytics data, optimized for write-heavy operations.

Key Tables:

• UserStories: UserID, StoryID, Timestamp, Platform (Facebook/Instagram).
• StoryViews: StoryID, UserID, ViewTimestamp, Platform.
• Analytics: StoryID, ViewsCount, EngagementMetrics, Platform.

Partition Key:

• Use Platform and StoryID as partition keys to distribute load and optimize for platform-specific queries.

5. Deep dive

To compare Facebook and Instagram Stories while accounting for overlapping users and potential cannibalization, we can implement a difference-in-differences (diff-in-diff) approach. This method allows us to measure the causal impact of changes in one platform on user engagement, controlling for external factors.

sequenceDiagram
  participant U as User
  participant FB as Facebook Stories
  participant IG as Instagram Stories
  participant A as Analytics Service

  U ->> FB: View Story
  FB ->> A: Log View Event
  U ->> IG: View Story
  IG ->> A: Log View Event
  A ->> A: Calculate Diff-in-Diff
  A -->> U: Provide Insights

6. Scale, bottlenecks & trade-offs

Replication and Sharding:

• Use sharding for the NoSQL database based on Platform and StoryID to handle high write throughput.
• Replicate data across regions to ensure availability and low latency.

Caching:

• Implement a Redis cache for frequently accessed story metadata to reduce database load and improve response times.

Single Points of Failure:

• Ensure redundancy in the load balancer and message queue to prevent service disruptions.

Trade-offs:

• Consistency vs. Availability: Prioritize availability for user-facing services, accepting eventual consistency for analytics data.
• Push vs. Pull: Use a pull model for analytics queries to allow for flexible reporting without overloading the system with push updates.

Causal Identification Strategy:

• The diff-in-diff approach helps isolate the impact of changes in one platform while controlling for shared user bases and external factors.
• Key biases include user behavior changes over time and external events affecting both platforms simultaneously.

Decision Recommendations:

• If engagement increases on one platform but revenue decreases, consider optimizing monetization strategies.
• If creator supply increases but user retention remains flat, focus on enhancing content discovery and user engagement features.

Model answer

Solution

To solve this problem, we need to calculate two probabilities using the given priors and Bayes' theorem.

(a) Probability the room you check is occupied

1. Define events: - \( A \): The event that the room you check is occupied. - \( B \): The event that both rooms are occupied. - \( C \): The event that exactly one room is occupied. - \( D \): The event that both rooms are empty.
2. Given probabilities: - \( P(B) = \frac{1}{3} \) - \( P(C) = \frac{1}{3} \) - \( P(D) = \frac{1}{3} \)
3. Calculate \( P(A) \): - If both rooms are occupied (\( B \)), the probability of picking an occupied room is 1. - If exactly one room is occupied (\( C \)), the probability of picking an occupied room is \( \frac{1}{2} \). - If both rooms are empty (\( D \)), the probability of picking an occupied room is 0.

Therefore, using the law of total probability: \[ P(A) = P(A|B)P(B) + P(A|C)P(C) + P(A|D)P(D) = 1 \times \frac{1}{3} + \frac{1}{2} \times \frac{1}{3} + 0 \times \frac{1}{3} = \frac{1}{3} + \frac{1}{6} = \frac{1}{2} \]

(b) Probability the other room is also occupied given the room you check is occupied

1. Define event \( E \): The event that the other room is also occupied.
2. Use Bayes' theorem: - We need to find \( P(E|A) \).
3. Calculate \( P(E|A) \): - \( P(E|A) = \frac{P(A|E) \cdot P(E)}{P(A)} \)
4. Calculate components: - \( P(A|E) \): If the other room is also occupied, the probability that the room you check is occupied is 1. - \( P(E) = P(B) = \frac{1}{3} \) (since both rooms being occupied is the same as event \( B \)). - \( P(A) = \frac{1}{2} \) (from part (a)).
5. Substitute into Bayes' theorem: \[ P(E|A) = \frac{1 \times \frac{1}{3}}{\frac{1}{2}} = \frac{2}{3} \]

Conclusion

• (a) The probability that the room you check is occupied is \( \frac{1}{2} \).
• (b) Given that the room you check is occupied, the probability that the other room is also occupied is \( \frac{2}{3} \).

Model answer

Stack vs Queue

1. Data Structure Type: - Stack: A stack is a linear data structure that follows the Last In First Out (LIFO) principle. This means that the last element added to the stack will be the first one to be removed. - Queue: A queue is a linear data structure that follows the First In First Out (FIFO) principle. This means that the first element added to the queue will be the first one to be removed.
2. Basic Operations: - Stack: - Push: Add an element to the top of the stack. - Pop: Remove the element from the top of the stack. - Peek/Top: View the top element of the stack without removing it. - Queue: - Enqueue: Add an element to the end of the queue. - Dequeue: Remove the element from the front of the queue. - Front: View the front element of the queue without removing it.
3. Use Cases: - Stack: Useful in scenarios where you need to reverse items, such as undo mechanisms in text editors, parsing expressions (e.g., evaluating postfix expressions), and managing function calls (call stack). - Queue: Suitable for scenarios where order needs to be preserved, such as scheduling tasks, handling requests in a server, and breadth-first search in graphs.
4. Memory Structure: - Stack: Typically implemented using arrays or linked lists, with a pointer to the top of the stack. - Queue: Can be implemented using arrays or linked lists, with pointers to both the front and rear of the queue.
5. Complexity: - Stack: Both push and pop operations have a time complexity of O(1). - Queue: Both enqueue and dequeue operations have a time complexity of O(1) when implemented with a linked list or a circular array.

Understanding these differences helps in choosing the right data structure for specific problems based on the required operations and performance characteristics.

Model answer

Solution

To solve the problem, we need to calculate probabilities based on the given conditions. The problem involves calculating the probability of a chatbot response being "Good," which is defined as both "Helpful" and "Honest." We are given the probabilities for each of these attributes and are told they are independent.

1. Probability of a Single Good Response

• P(Helpful) = 0.8
• P(Honest) = 0.9

Since helpfulness and honesty are independent, the probability that a single response is both helpful and honest (i.e., "Good") is the product of the individual probabilities:

\[ P(\text{Good}) = P(\text{Helpful}) \times P(\text{Honest}) = 0.8 \times 0.9 = 0.72 \]

2. Probability of Two Good Responses in a Row

For two responses to both be "Good," each must independently satisfy the condition of being "Good." Therefore, the probability of two consecutive "Good" responses is:

\[ P(\text{Two Good}) = P(\text{Good}) \times P(\text{Good}) = 0.72 \times 0.72 = 0.5184 \]

3. Probability of the Fourth Response Being Good Given the First Three Are Good

The problem states that responses are independent and identically distributed (i.i.d.). Therefore, the probability of the fourth response being "Good" is unaffected by the outcomes of the previous responses. Thus, the probability remains the same as for a single response:

\[ P(\text{Fourth Good} \mid \text{First Three Good}) = P(\text{Good}) = 0.72 \]

Summary

• P(Good) for a single response: 0.72
• Probability of two good responses in a row: 0.5184
• Probability of the 4th response being good given the first three are good: 0.72

These calculations leverage the independence of the events, which allows us to multiply probabilities directly. This is a common approach when dealing with independent events in probability theory.

Model answer

1. Define Retention Clearly

• N-day (classic/cohort) retention: Measures the percentage of users who return on a specific day after their first use. For example, 7-day retention is the percentage of users who return on the 7th day after their first use. This method focuses on specific time intervals and is useful for understanding user engagement over time.
• Rolling retention (unbounded): Measures the percentage of users who return on or after a specific day. For instance, 7-day rolling retention includes users who return on the 7th day or any day after. This approach provides a broader view of user engagement by not limiting to a specific day.
• Return rate / weekly active retention: Calculates the percentage of users who return within a week. It focuses on weekly engagement patterns and is useful for products with weekly usage cycles.

2. Compute and Interpret 7-day vs 28-day Retention

• User Cohorting: Use the signup or install week to define cohorts. This allows tracking how different groups of users engage with the product over time.
• Metric Interpretation:
• 7-day retention captures short-term engagement and the initial user experience. A high rate suggests that users find immediate value.
• 28-day retention indicates long-term engagement and user stickiness. It reflects sustained interest and satisfaction with the product.

3. Short-term vs Long-term Tradeoffs

• Product Changes:
• Increasing 7-day retention: Offering a compelling onboarding experience or initial incentives might boost short-term engagement but could lead to a drop in long-term retention if the core product value isn't sustained.
• Increasing 28-day retention: Enhancing core features or community aspects might not immediately boost short-term metrics but can improve long-term user retention.
• Metric Hierarchy:
• Primary Metric: 28-day retention, as it reflects long-term user engagement.
• Diagnostic Metric: 7-day retention, to diagnose initial user experience issues.
• Guardrail Metric: Churn rate, to ensure that efforts to improve retention do not inadvertently increase user churn.

4. Pitfalls/Edge Cases in Measuring Retention

• Right-censoring: Users who have not yet reached the 7th or 28th day. Address by using survival analysis techniques.
• Seasonality: Variations due to time of year. Use year-over-year comparisons to normalize data.
• Re-installs: Users who uninstall and reinstall the app. Track unique user IDs to avoid double-counting.
• Bots: Automated interactions skewing data. Implement bot detection and filtering mechanisms.
• Changing Definitions: Inconsistent retention definitions over time. Standardize definitions and document changes for consistency.

5. A/B Test Design for Retention Improvement

• Unit of Randomization: Randomize at the user level to ensure each user has an equal chance of receiving any variant.
• Experiment Duration: Run the test for at least 28 days to capture both short-term and long-term retention effects.
• Delayed Effects: Consider potential delayed effects by extending the observation period beyond the initial 28 days if necessary.
• Variance Reduction: Use techniques like stratified sampling or covariate adjustment to reduce variance and improve test sensitivity.
• Sequential Testing: Implement sequential testing methods to allow for early stopping if significant results are observed, balancing speed and accuracy in decision-making.