Stack-based solution, which I got to pretty quickly.
Use a stack to simulate collisions in a single pass. Iterate through the array, and for each object, resolve collisions with the top of the stack if they move toward each other. Objects moving left (negative) collide with right-moving objects (positive) on the stack; the one with smaller mass is destroyed, and if equal, both are destroyed. Finally, return the stack contents in order.
Pro tip: Clarify the collision rules upfront (e.g., equal masses annihilate, same direction never collide) and walk through a small example to confirm understanding. This shows attention to detail and prevents misinterpretation.
Confirm collision conditions: only opposite directions collide, equal masses destroy both, and surviving objects maintain relative order. Discuss edge cases like empty array, all same direction, or no collisions.
Select a stack to efficiently manage potential collisions. Explain that each object is pushed once and popped at most once, ensuring O(n) time.
Iterate through the array. For each object, while the stack is not empty, the top is positive (moving right), and the current is negative (moving left), resolve collision by comparing absolute masses. Destroy the smaller, or both if equal. If current survives, push it onto the stack.
After processing all objects, the stack contains survivors in order. Return it. State time complexity O(n) because each element is pushed/popped once, and space complexity O(n) for the stack.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem constraints and the nature of the input (e.g., sorted, streamable, or random access). Then, systematically discuss streaming, chunking, and external memory approaches, highlighting trade-offs in time, space, and complexity. Emphasize that the choice depends on whether the input can be processed in a single pass or requires multiple passes and disk-based storage.
Pro tip: Demonstrate awareness of real-world constraints by mentioning that even with 2 GB, you must account for overhead and that external sorting or streaming algorithms often outperform naive in-memory approaches. Also, note that SoFi deals with large-scale financial data, so reliability and fault tolerance in streaming are critical.
Ask if the input is a stream or a file, if it's sorted, and if we can make multiple passes. Confirm memory limit and whether disk I/O is acceptable.
If the problem allows single-pass processing (e.g., finding max, sum, or frequency with bounded distinct keys), describe a streaming algorithm that uses O(1) or O(k) memory.
If the problem requires more complex operations (e.g., sorting, joins), split input into chunks that fit in memory, process each chunk, and write intermediate results to disk.
For sorting or grouping, use external merge sort: sort chunks in memory, write sorted runs to disk, then merge them using a heap with limited memory. For joins, use hash-based partitioning or sort-merge join.
Compare time vs. space, single-pass vs. multi-pass, and in-memory vs. disk-based. Mention compression, serialization, and parallel processing to improve performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Parallel processing of independent chunks is fine, the hard part is the merge step.
Start by clarifying the simulation's requirements and constraints, then propose a spatial decomposition strategy with ghost cells or halo regions to handle boundary interactions. Discuss synchronization mechanisms and trade-offs between communication overhead and parallelism efficiency.
Pro tip: Emphasize that correctness at boundaries often requires more frequent synchronization, so consider adaptive approaches that balance load and minimize stalls, and mention profiling to identify bottlenecks.
Ask about simulation scale, time constraints, hardware, and correctness guarantees to tailor your approach.
Propose spatial domain decomposition (e.g., uniform grid) and explain how to assign chunks to cores, considering load balancing.
Describe using ghost cells or halo regions to exchange data between adjacent chunks, ensuring collisions at boundaries are computed correctly.
Outline synchronization points (e.g., barriers) and communication patterns (e.g., message passing) to update ghost cells, discussing frequency and impact.
Compare approaches (e.g., shared vs distributed memory, lock-free vs locking) and discuss performance vs correctness trade-offs, suggesting optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Went through the obvious ones: all moving right (no collisions), all moving left (no collisions), two equal masses meeting, chain reactions.
Start by clarifying the scope of the collision simulation (e.g., 2D/3D, shapes, physics) and then outline a testing strategy that combines unit tests for individual collision detection functions with integration tests for the overall simulation. Emphasize invariants like conservation of momentum and energy, and edge cases such as boundary collisions and high-speed tunneling.
Pro tip: Mention property-based testing (e.g., QuickCheck) to automatically generate random scenarios and verify invariants, which shows you think beyond manual test cases. Also, discuss how you would test performance and scalability, as collision simulations can be computationally intensive.
Ask questions to understand the simulation's domain: what shapes, dimensions, and physics are involved? This ensures your test cases are relevant and comprehensive.
List physical and mathematical invariants that must hold true, such as conservation of momentum, energy, and no overlapping objects after resolution.
Create test cases for primitive collisions (e.g., circle-circle, AABB-AABB) including edge cases like just touching, overlapping, and separated objects.
Test multi-object scenarios, including chains of collisions, and verify that invariants hold over time steps. Include stress tests with many objects.
Cover edge cases like high-speed objects (tunneling), boundary conditions, and degenerate shapes. Also, consider performance benchmarks to ensure the simulation scales.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.