My first instinct was brute force, slide a window of size k across all possible positions and sum up values.
Use a difference array to efficiently mark the value at each index from all segments, then compute the prefix sum to get cumulative values. Finally, slide a window of size k over the prefix sum to find the maximum sum of any k consecutive indices.
Pro tip: Clarify edge cases upfront: what if k is larger than the array length? What if segments overlap? Handling these shows attention to detail and prevents incorrect assumptions.
Confirm the input format, constraints, and edge cases such as overlapping segments, k larger than the array, and negative values (if any).
Use a difference array to apply each segment's value to its range, then compute the prefix sum to get the final value at each index.
Calculate the prefix sum of the value array to enable O(1) range sum queries.
Slide a window of size k over the prefix sum array, computing the sum for each window and tracking the maximum.
State the time and space complexity: O(n + m) time and O(n) space, where n is the number of indices and m is the number of segments.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.