Clarify the problem definition first, then propose a recursive DFS solution that computes the longest same-value path in the left and right subtrees and combines them if the current node's value matches its children. Analyze time and space complexity, and discuss edge cases and potential optimizations.
Pro tip: Explicitly state your assumptions about what constitutes a 'path' (e.g., must it be a simple path? can it go through the root?) and confirm with the interviewer before coding. This shows attention to detail and avoids wasted effort.
Ask questions to define 'path' (e.g., can it go up and down? must it be contiguous? can it include nodes with different values?) and confirm the expected return type (length in nodes or edges).
Explain that you'll use DFS to compute, for each node, the longest same-value path in its left and right subtrees, and then combine them if the node's value matches its children's values.
Define a helper function that returns the longest same-value path starting from the current node and going down. At each node, compare its value with its children's values to decide whether to extend the path.
Use a global variable to keep track of the maximum path length found so far, updating it at each node by considering the sum of left and right extensions (if both children match).
State that the time complexity is O(n) and space complexity is O(h) for recursion stack. Discuss edge cases like empty tree, single node, all nodes same value, and skewed trees.
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Use the STAR method to structure your answers, focusing on specific examples that highlight your adaptability, collaboration, and problem-solving skills. Emphasize how you navigate ambiguity, handle disagreements constructively, and contribute to team success, aligning with Google's values of innovation and user focus.
Pro tip: Show self-awareness by acknowledging what you learned from challenging situations and how you adapted your approach; Google values humility and a growth mindset.
Briefly describe the situation and task, ensuring it's relevant to the question and highlights a challenging or ambiguous scenario.
Explain the specific steps you took, emphasizing your thought process, collaboration with others, and how you navigated ambiguity or disagreement.
Share the results of your actions, quantifying impact where possible and showing how you contributed to team or project success.
Conclude with what you learned from the experience and how it has influenced your subsequent work or approach to similar situations.
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Onsite, first day back after the five-month gap.
Clarify the problem constraints (task durations, dependencies, preemption, CPU homogeneity) and define the objective (minimize makespan). Then propose a greedy algorithm like Longest Processing Time first (LPT) for identical CPUs, and for the follow-up, use binary search on the number of CPUs combined with a feasibility check (e.g., can K CPUs finish within a given time?).
Pro tip: Mention that the problem is NP-hard for arbitrary constraints, so you'd use heuristics or approximation algorithms; for the follow-up, binary search on CPUs is efficient because feasibility is monotonic. Also, discuss trade-offs between optimality and practical runtime.
Ask about task dependencies, preemption, CPU homogeneity, and whether the goal is to minimize makespan or maximize throughput. Confirm if tasks can be split.
For identical CPUs and independent tasks, use LPT: sort tasks descending and assign each to the least loaded CPU. For dependent tasks, consider list scheduling or critical path methods.
State that LPT gives a 4/3-approximation for makespan. If optimality is required, mention dynamic programming or branch-and-bound for small inputs, but acknowledge NP-hardness.
Binary search on the number of CPUs K. For each K, check if a schedule exists with makespan ≤ T* (the optimal makespan with unlimited CPUs). Feasibility can be checked via greedy simulation or bin packing.
Mention real-world factors like CPU heterogeneity, task priorities, and dynamic arrivals. Suggest using priority queues for efficient simulation.
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This is the one I'm least confident about.
Start by clarifying the problem constraints (e.g., input size, whether points are distinct, and if rectangles can be axis-aligned or rotated). Then propose an efficient algorithm: group points by x-coordinate, for each pair of x-coordinates find all pairs of y-coordinates that exist at both x's, and compute the maximum area. Discuss time/space complexity and potential optimizations.
Pro tip: Mention that the naive O(n^4) approach is too slow for large inputs, and that using a hash set for point lookup can reduce the complexity to O(n^2) on average. Also, consider edge cases like collinear points or duplicate points.
Ask about input size, whether points are distinct, if rectangles must be axis-aligned, and if the rectangle can be degenerate (zero area).
Explain that checking all quadruples of points is O(n^4) and impractical for large n, but it's a good starting point to understand the problem.
Group points by x-coordinate. For each pair of x-coordinates, find the intersection of y-values. For each pair of common y-values, check if the four corners exist (using a hash set). Compute area and track maximum.
The approach runs in O(n^2) on average with a hash set, but worst-case O(n^3) if many points share x-coordinates. Space is O(n) for the hash set.
Discuss handling duplicate points, collinear points, and whether to consider rotated rectangles. Mention that if rectangles can be rotated, the problem becomes more complex (e.g., using dot product and distance checks).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.