Design CPU-Cycle Window Alignment for Misaligned Time Series

Interview Prompt

Design and implement an algorithm that buckets two CPU-cycle time series whose timestamps do not align and produces time windows on a common basis. Treat every segment between adjacent samples as a linear function for interpolation. Before choosing data structures, make the missing contract explicit: window boundaries, endpoint inclusion, whether each window needs a point value or aggregate, behavior outside a series' sampled range, and the required output shape.

Constraints & Assumptions

• Each input series is ordered by CPU-cycle timestamp and adjacent samples define a piecewise-linear segment.
• The two series may have no matching timestamps.
• Window-aligned output must use one explicitly stated timestamp or interval convention for both series.
• Do not silently assume union-of-sample timestamps, overlap-only output, or a particular row schema.

Clarifying Questions to Ask

• Are window boundaries supplied by the caller, fixed-width from an origin, or derived by another rule?
• Does a bucket report a value at one representative timestamp or an average over the interval?
• Should a window without bracketing samples be omitted, marked missing, or extrapolated?
• Which side owns a sample that lands exactly on a boundary?