Start by clarifying the problem constraints and edge cases, then propose a brute-force solution before optimizing. Discuss trade-offs between different approaches, and finally present the optimal solution with a clear explanation of its time and space complexity.
Pro tip: Always verbalize your thought process and consider multiple solutions; Google values how you think and communicate, not just the final answer. If stuck, simplify the problem or use a small example to illustrate your reasoning.
Restate the problem in your own words, ask clarifying questions about input size, constraints, and edge cases. Confirm expected output format.
Brainstorm multiple solutions, starting with a brute-force approach. Discuss their time and space complexities and identify bottlenecks.
Propose an optimal solution by improving the brute-force, e.g., using appropriate data structures or algorithmic paradigms. Explain why it's optimal.
Clearly state the time and space complexity of the optimal solution, and justify with reasoning. Compare with alternatives if relevant.
Walk through the solution with a small example, test edge cases, and discuss potential pitfalls or improvements.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clearly define what the brute-force approach entails for the problem you just solved, then derive its time complexity by analyzing the number of operations as a function of input size. Compare it to the optimal solution you implemented, highlighting the trade-offs and why the brute-force is less efficient.
Pro tip: Always relate the brute-force complexity to the optimal solution's complexity, and mention any space-time trade-offs. This shows you understand the problem deeply and can reason about algorithmic efficiency, which is crucial at Google.
Briefly describe the naive or straightforward method to solve the problem, ensuring it's clear what operations are performed.
Determine the variable(s) representing input size (e.g., n, m) and the key operations that dominate the runtime.
Count how many times the basic operations are executed in terms of the input size, then express it using Big O notation.
Contrast the brute-force complexity with the optimal solution's complexity, explaining the improvement and any trade-offs.
Mention when the brute-force might be acceptable (e.g., small inputs) and why the optimal solution is preferred for large-scale systems.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, restate the original problem and identify its core constraints and assumptions. Then systematically propose generalizations by relaxing constraints or adding dimensions, and for each variant, walk through edge cases and discuss how the solution approach would need to change. Focus on demonstrating structured thinking and adaptability rather than jumping to code.
Pro tip: Show that you can prioritize which generalizations are most valuable by tying them to real-world scenarios or business impact, and explicitly state any assumptions you make about the new problem's constraints.
Briefly summarize the original problem, its input/output, constraints, and the current solution's time and space complexity. This establishes a baseline for extension.
List ways to make the problem harder: larger input sizes, additional dimensions, relaxed constraints (e.g., duplicates, negative numbers), or new operations (e.g., updates, queries). Choose one or two most relevant to the role or company.
For each chosen generalization, explain how the original algorithm would fail or need modification. Discuss potential approaches (e.g., different data structures, algorithmic paradigms) and their trade-offs.
Enumerate edge cases introduced by the generalization, such as empty inputs, extreme values, or boundary conditions. Explain how you would handle them without coding, focusing on logic and invariants.
Conclude by summarizing the most promising extension and why, and mention any open questions or further considerations. This shows you can evaluate and prioritize effectively.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, acknowledge the flaw in the initial approach and explain why it fails to meet linear time. Then, propose a corrected algorithm that achieves O(n) time, clearly stating the data structures and techniques used. Finally, walk through the algorithm with an example and analyze its time and space complexity.
Pro tip: Demonstrate adaptability by explicitly connecting the flaw to a specific algorithmic concept (e.g., overlapping subproblems or unnecessary nested loops) and showing how your fix addresses it. This shows deep understanding rather than just memorization.
Analyze the initial approach to pinpoint why it is not linear time, such as nested loops or redundant computations. Clearly state the bottleneck.
Outline a high-level approach that avoids the flaw, using techniques like hashing, two pointers, or dynamic programming to achieve O(n) time.
Explain the steps of your algorithm, including data structures and how they ensure linear time. Walk through a small example to illustrate.
State the time and space complexity of your solution, emphasizing the linear time bound and any trade-offs.
Discuss edge cases and how you would test the solution to ensure correctness and performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This was the follow-up in round two, came up around the 35-minute mark so time was tight.
Start by restating the original problem and identifying the specific constraints you plan to relax. Then, describe the generalized problem, outline a modified algorithm that handles the broader case, and analyze its time and space complexity, comparing it to the original solution.
Pro tip: Demonstrate that you consider edge cases and trade-offs by discussing how the generalized solution performs under different input distributions and whether it remains optimal. Mention any potential optimizations or alternative approaches if the generalization leads to inefficiency.
Briefly summarize the original problem and its constraints to establish a baseline. This ensures you and the interviewer are aligned on what 'broader' means.
Specify which constraints are relaxed or which new parameters are introduced. For example, if the original problem assumed a sorted array, the generalized version might handle unsorted data or allow duplicates.
Explain the step-by-step approach for the broader problem. Highlight any changes from the original algorithm, such as using a different data structure or handling additional cases.
Provide the time and space complexity of the generalized algorithm. Compare it to the original solution and discuss any trade-offs, such as increased time for greater generality.
Mention how the algorithm handles edge cases and whether further optimizations are possible. This shows thoroughness and practical insight.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.