This one took me longer to parse than I expected.
Start by clarifying the problem constraints and edge cases, then outline a single-pass algorithm that scans the checkpoints in order, handling charging segments by ignoring them, and using linear interpolation or extrapolation to compute the remaining time. Emphasize the O(n) time and O(1) space complexity, and explain how the monotonicity of the discharge curve ensures numerical stability.
Pro tip: Mention that you would validate the input (e.g., checkpoints sorted by time, SOC values within [0,100]) and discuss how to handle floating-point precision issues by using a small epsilon when comparing SOC values.
Ask questions to confirm the input format, whether the curve is piecewise linear, and how to handle charging segments, duplicate SOC values, and missing zero-SOC endpoints. Discuss assumptions about monotonicity and numerical precision.
Propose a single-pass algorithm: iterate through checkpoints, skip charging segments (where SOC increases), and for the segment containing the current SOC, compute the remaining time via linear interpolation. If no zero-SOC endpoint exists, extrapolate using the last discharge segment.
Explain how to handle duplicate SOC values (e.g., by taking the first occurrence in a discharge segment), ensure monotonicity by only considering decreasing SOC, and use epsilon comparisons to avoid floating-point errors.
Confirm O(n) time and O(1) space, and discuss why this is optimal. Mention that preprocessing (e.g., sorting) would increase complexity, so the single-pass approach is preferred.
Argue that the discharge curve is monotone decreasing (ignoring charging), so interpolation is well-defined and stable. Use linear interpolation which is numerically stable for well-conditioned data, and avoid division by near-zero by checking segment length.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.