I knew what Monte Carlo meant in theory but had never actually coded one under pressure.
Start by clarifying the data model and simulation parameters, then outline a Monte Carlo algorithm that samples remaining obstacles from historical data and compares simulated totals to the personal best. Emphasize code structure, efficiency, and statistical correctness while discussing potential trade-offs.
Pro tip: Mention that you would seed the random number generator for reproducibility and use vectorized operations or parallelization to handle 10,000 trials efficiently, showing awareness of performance in production systems.
Confirm the structure of Run and RunCollection, how historical data is stored, and what 'in-progress' means (e.g., obstacles completed so far). Ask about performance constraints and whether the personal best is fixed or dynamic.
Outline a Monte Carlo loop: for each trial, copy the current run's completed obstacles, then for each remaining obstacle, randomly sample a completion time from historical data (e.g., from all runs or similar runs). Sum the times to get a simulated total.
Describe how to sample from historical data efficiently: precompute distributions per obstacle, use random.choice or numpy.random.choice, and consider caching or pre-aggregation to avoid repeated scans.
After each trial, compare the simulated total to the personal best. Count successes and divide by the number of trials (10,000) to estimate the probability. Optionally compute confidence intervals.
Talk about time/space complexity, potential biases in sampling (e.g., using all historical data vs. recent runs), and optimizations like parallelization or early stopping if the probability converges.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.