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List ranking, the problem of transforming a linked list into an array that represents the same sequence of items, can be viewed as computing a prefix sum on the sequence 1, 1, 1, ... and then mapping each item to the array position given by its prefix sum value; by combining list ranking, prefix sums, and Euler tours, many important problems on ...
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 ordered array using list ranking, and then performs prefix sum computations on the ordered array ...
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.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
A singly-linked list structure, implementing a list with three integer elements. The term list is also used for several concrete data structures that can be used to implement abstract lists, especially linked lists and arrays. In some contexts, such as in Lisp programming, the term list may refer specifically to a linked list rather than an array.
The simplicity of the counting sort algorithm and its use of the easily parallelizable prefix sum primitive also make it usable in more fine-grained parallel algorithms. [7] As described, counting sort is not an in-place algorithm; even disregarding the count array, it needs separate input and output arrays. It is possible to modify the ...
Given a function that accepts an array, a range query (,) on an array = [,..,] takes two indices and and returns the result of when applied to the subarray [, …,].For example, for a function that returns the sum of all values in an array, the range query (,) returns the sum of all values in the range [,].
Classifying advance and retreat edges: Do list ranking on the ETR and save the result in a two-dimensional array A. Then (u,v) is an advance edge iff A(u,v) < A(v,u), and a retreat edge otherwise. Determine the level of each node: Do a prefix sum on the ETR, where every advance edge counts as 1, and every retreat edge counts as −1.