Greedy running sum, pretty mechanical once you see it.
Use a greedy algorithm that scans the array once, accumulating segment sums and starting a new segment whenever adding the next element would exceed the bandwidth limit. This yields the minimum number of segments because any valid partition must cut at least at the same points. Clearly state the time and space complexity and discuss edge cases.
Pro tip: Mention that this is the classic 'minimum number of bins' problem where greedy is optimal due to the contiguous constraint, and proactively discuss how you would handle invalid inputs (e.g., a single frame larger than the limit).
Confirm that segments must be contiguous, that the sum of each segment must be ≤ bandwidth limit, and ask about edge cases like empty array or elements exceeding the limit.
Explain that you will iterate through the array, maintaining a running sum for the current segment, and start a new segment when adding the next element would exceed the limit.
Use a small example (e.g., [1,2,3,4,5] with limit 6) to demonstrate how the greedy algorithm partitions the array and returns the minimum count.
State that the algorithm runs in O(n) time and O(1) extra space, and argue that greedy is optimal because any valid partition must make a cut whenever the cumulative sum exceeds the limit.
Cover cases like an element larger than the limit (return -1 or error), empty array (return 0), and mention that if segments didn't need to be contiguous, the problem would be NP-hard (bin packing).
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This one took me an embarrassingly long time to reframe.
Recognize this as the classic interval point cover problem: each circle corresponds to an interval [center - radius, center + radius] on the line. Sort intervals by their right endpoints, then greedily place an arrow at the right endpoint of the first interval, skip all intervals containing that point, and repeat. This yields the minimum number of arrows in O(n log n) time.
Pro tip: Explicitly connect the problem to the interval scheduling/point cover pattern, and mention that the greedy choice is optimal because placing an arrow at the earliest finishing interval's right endpoint maximizes coverage. Also, clarify edge cases like overlapping circles and identical intervals.
Convert each circle (center, radius) into an interval [center - radius, center + radius]. This reduces the problem to covering all intervals with the minimum number of points.
Sort the intervals in ascending order of their right endpoints. This ordering is key for the greedy strategy.
Initialize count = 0 and last_arrow = -infinity. Iterate through sorted intervals; if the current interval's left endpoint > last_arrow, place a new arrow at its right endpoint, increment count, and update last_arrow.
After processing all intervals, the count is the minimum number of arrows needed to burst all circles.
State time complexity O(n log n) due to sorting, space O(1) or O(n) depending on sorting. Discuss edge cases: no circles, all circles overlapping, circles with zero radius.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.