Start by clarifying the problem and assumptions, then outline a Monte Carlo simulation approach: for each trial, sample completion times for remaining obstacles from historical data, compute total time, and compare to personal best. Finally, discuss implementation details, edge cases, and trade-offs.
Pro tip: Mention that you would use the empirical distribution of historical times and handle missing data carefully, and that you would optimize by precomputing distributions or using vectorized operations for performance.
Ask questions to understand the data structure, historical data availability, and definition of 'match or beat'. Confirm that incomplete runs provide valid samples for obstacles they reached.
Outline the Monte Carlo loop: for each trial, for each remaining obstacle, randomly sample a time from the historical times for that obstacle, sum with the in-progress run's time so far, and compare to personal best.
Discuss how to handle obstacles with no historical data (e.g., skip, use default, or fail gracefully), and ensure sampling is done correctly (e.g., with replacement).
Suggest optimizations: pre-group historical times by obstacle, use arrays for fast sampling, and consider parallelization or vectorization for 10,000 trials.
Mention testing with known distributions, and discuss trade-offs between accuracy and performance, and between different sampling strategies.
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