The prefix sum of a list in a certain index is the sum of all of the elements in the list up to and including that index. This algorithm speeds up the computation of prefix sums when the list's items can change; there are more efficient algorithms to compute prefix sums of static lists. This algorithm costs only logarithmic time and is the first known that is optimal: the product of its time and processor bounds is upper bounded by a linear function of the input size. Also given is a deterministic sublogarithmic time algorithm for prefix sum.
–Where: =sum of values in left sub-tree of Algorithm to compute values ( ): 1. Compute sum of values in each sub-tree (bottom-up) – Can be done in parallel time 𝑂log𝑛with 𝑂(𝑛)total work 2. Compute values ( )top-down from root to leaves: – To compute the value ( ), only ( )of the parent and the sum of the Horowitz And broadcasting, data sum, prefix sum, shift, data. circulation, data accumulation,... Solution Computer Algorithms Horowitz And Sahni Horowitz and sahani fundamentals of computer algorithms 2nd edition Horowitz and sahani fundamentals of computer algorithms ...
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