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Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and update the values. It also supports an efficient rank-search operation for finding the longest prefix whose sum is no more than a specified value.
Prefix sum, in computing; Pushout (category theory) (also called an amalgamated sum or a cocartesian square, fibered coproduct, or fibered sum), the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domainor pushout, leading to a fibered sum in category theory; QCD sum rules, in quantum field theory
dimensional hypercube is a network topology for parallel computers with processing elements. The topology allows for an efficient implementation of some basic communication primitives such as Broadcast, All-Reduce, and Prefix sum. [1]
Prefix-sum on a binary tree can be implemented with an upward and downward phase. In the upward phase reduction is performed, while the downward phase is similar to broadcast, where the prefix sums are computed by sending different data to the left and right children.
The former first lady was notably absent from President Jimmy Carter's state funeral service, leading Barack Obama and Donald Trump to be seated next to one another
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List ranking can equivalently be viewed as performing a prefix sum operation on the given list, in which the values to be summed are all equal to one. The list ranking problem can be used to solve many problems on trees via an Euler tour technique, in which one forms a linked list that includes two copies of each edge of the tree, one in each direction, places the nodes of this list into an ...