The first thing I did wrong was assume I knew what the tuple format meant and just started coding.
Clarify the representation of step functions (e.g., segments defined by start time and value, with value constant until next timestamp) and handle edge cases like empty arrays or duplicate timestamps. Use a two-pointer technique to traverse both arrays in chronological order, merging timestamps and summing values, while maintaining the current value from each function. Output the merged step function as a list of (timestamp, value) pairs where the value changes only when necessary.
Pro tip: Demonstrate awareness of real-world applications at Uber, such as merging pricing or demand curves, and discuss trade-offs between time and space complexity, especially if the input arrays are large or streamed.
Ask whether each tuple represents the start of a segment with a constant value until the next timestamp, and confirm that timestamps are sorted. Discuss handling of duplicate timestamps and empty arrays.
Use two pointers to iterate through both arrays simultaneously, always advancing the one with the smaller timestamp. At each step, compute the sum of the current values from both functions and append a new segment if the sum differs from the previous.
Ensure the output only includes points where the sum changes, and handle cases where one array is exhausted by continuing with the other's remaining segments. Discuss whether to include zero-value segments.
State that time complexity is O(m+n) and space O(m+n) for the output. Mention potential optimizations like in-place merging if one array has extra capacity, or streaming if data is too large.
Walk through a simple example, such as A = [(0,1), (5,2)] and B = [(2,3), (7,4)], to verify correctness and illustrate the merging process.
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