2017
DOI: 10.1016/j.tcs.2016.11.005
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Linear time computation of the maximal linear and circular sums of multiple independent insertions into a sequence

Abstract: The maximal sum of a sequence A of n real numbers is the greatest sum of all elements of any linearly contiguous and possibly empty subsequence of A. It can be computed in O(n) time by means of Kadane's algorithm. Letting A (x→p) denote the sequence which results from inserting a real number x just after element A[p − 1], we show how the maximal sum of A (x→p) can be computed in O(1) worst-case time for any given x and p, provided that an O(n) time preprocessing step has already been executed on A. In particul… Show more

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