English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The maximal sum of a sequence "A" of "n" real numbers is the greatest sum ofall elements of any strictly contiguous and possibly empty subsequence of "A",and 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"between elements "A[p-1]" and "A[p]", 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 particular, this implies that, given "m" pairs "(x_0, p_0), ...,(x_{m-1}, p_{m-1})", we can compute the maximal sums of sequences "A^(x_0 ->p_0), ..., A^(x_{m-1} -> p_{m-1})" in "O(n+m)" time, which matches the lowerbound imposed by the problem input size, and also improves on thestraightforward strategy of applying Kadane's algorithm to each sequence"A^(x_i -> p_i)", which takes a total of "Theta(n.m)" time. Our maincontribution, however, is to obtain the same time bound for the morecomplicated problem of computing the greatest sum of all elements of anystrictly or circularly contiguous and possibly empty subsequence of "A^(x ->p)". Our algorithms are easy to implement in practice, and they were motivatedby and find application in a buffer minimization problem on wireless meshnetworks.

Linear Time Computation of the Maximal Linear and Circular Sums of Multiple Independent Insertions into a Sequence