Quoted the complexity without accounting for the sorting step, which the interviewer had to nudge me on.
First, clearly restate the problem and outline your solution's steps. Then, analyze each step's time complexity, sum them up, and simplify to the dominant term using Big-O notation, explaining why lower-order terms are dropped.
Pro tip: Always mention the worst-case scenario and justify why it's the most relevant for Google's large-scale systems. Also, briefly discuss space complexity and any trade-offs, showing you think holistically.
Confirm your understanding of the problem, including input size, constraints, and expected output. This sets the stage for accurate complexity analysis.
Describe your approach step-by-step in plain English or pseudocode. Identify loops, recursive calls, and key operations that will contribute to time complexity.
For each step, determine its time complexity in terms of the input size n. Consider nested loops, recursive relations, and library function costs.
Sum the complexities of all steps, then simplify by keeping only the dominant term and dropping constants. Express the final result in Big-O notation.
Mention space complexity, best/worst/average cases, and any trade-offs (e.g., time vs. space). This shows depth and awareness of practical implications.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Couldn't finish coding it but talked through the approach and apparently was on the right track.
First, restate the original solution and its complexity to show understanding. Then, analyze how the new constraint impacts the solution's assumptions, and systematically explore modifications, comparing trade-offs. Finally, propose an adapted solution and verify it against the new constraint.
Pro tip: Demonstrate adaptability by considering multiple approaches and explicitly discussing trade-offs, rather than jumping to a single solution. This shows maturity and the ability to navigate ambiguity.
Briefly summarize the initial problem, your approach, and its time/space complexity. This ensures alignment and sets the stage for modification.
Identify how the additional constraint affects the problem, such as changes in input size, memory limits, or required operations. Determine which parts of the original solution are impacted.
Brainstorm potential adjustments to the algorithm or data structures. Consider alternative approaches that might better satisfy the new constraint, and evaluate their feasibility.
For each viable option, analyze time and space complexity, implementation complexity, and any other relevant factors. Discuss the pros and cons to justify your choice.
Select the best approach, explain the modifications in detail, and walk through how it satisfies the new constraint. If possible, test with examples or edge cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
He asked this right after I finished coding and I actually handled it okay.
Acknowledge the interviewer's observation and explain that in-place modification is a common optimization to save space, but it introduces trade-offs. Then systematically discuss the potential issues: mutating input, side effects, and reduced clarity, while also noting when it's acceptable.
Pro tip: Show awareness that in production code, mutating input can cause subtle bugs, especially if the caller expects the original data. Mention that you'd typically clarify with the interviewer or use a separate visited set if the input must be preserved.
Confirm that you intentionally modified the grid in place to avoid extra space, which is a common optimization in DFS problems.
List the main problems: mutating the input can have side effects for the caller, it may violate assumptions about immutability, and it can make debugging harder.
Compare with using a separate visited set: in-place saves O(mn) space but risks unintended consequences; separate set is safer but uses extra memory.
Suggest ways to mitigate, such as restoring the grid afterward, documenting the mutation, or using a separate visited set if the input must be preserved.
State that the choice depends on the problem constraints and whether the caller expects the input to remain unchanged.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem and confirm that Union-Find is appropriate by identifying the dynamic connectivity or grouping requirements. Then, explain the core operations (find and union) with optimizations like path compression and union by rank, and finally implement the data structure in code, discussing time and space complexity.
Pro tip: Always mention the near-constant time complexity (O(α(n))) achieved with both path compression and union by rank, and be prepared to discuss when Union-Find is preferable over DFS/BFS for connectivity problems.
Ask questions to ensure you understand the problem's constraints, input/output, and whether dynamic connectivity is needed. Confirm that Union-Find is a suitable approach.
Describe the parent array, find operation (with path compression), and union operation (with union by rank/size). Explain how these optimizations improve efficiency.
Trace the algorithm on a small example to demonstrate how elements are connected and how find/union operations work step by step.
Write clean code for the Union-Find class and the main function that uses it to solve the problem. Include comments for clarity.
State the time complexity per operation (nearly O(1) amortized) and overall space complexity. Mention alternative approaches and when Union-Find is preferred.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.