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In computer science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting may also often be applied to sorting problems in which the keys are floating point numbers, rational numbers, or text strings. [1]
For every type T, except void and function types, there exist the types "array of N elements of type T". An array is a collection of values, all of the same type, stored contiguously in memory. An array of size N is indexed by integers from 0 up to and including N−1. Here is a brief example:
The set of all worst case inputs consists of all arrays where each element is the smallest or second-smallest of the elements before it. In these cases every iteration of the inner loop will scan and shift the entire sorted subsection of the array before inserting the next element. This gives insertion sort a quadratic running time (i.e., O(n 2)).
Radix sort is an algorithm that sorts numbers by processing individual digits. n numbers consisting of k digits each are sorted in O(n · k) time. Radix sort can process digits of each number either starting from the least significant digit (LSD) or starting from the most significant digit (MSD). The LSD algorithm first sorts the list by the ...
A bidirectional variant of selection sort (called double selection sort or sometimes cocktail sort due to its similarity to cocktail shaker sort) finds both the minimum and maximum values in the list in every pass. This requires three comparisons per two items (a pair of elements is compared, then the greater is compared to the maximum and the ...
Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers. IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices. IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications ...
Integer addition, for example, can be performed as a single machine instruction, and some offer specific instructions to process sequences of characters with a single instruction. [7] But the choice of primitive data type may affect performance, for example it is faster using SIMD operations and data types to operate on an array of floats.
As a baseline algorithm, selection of the th smallest value in a collection of values can be performed by the following two steps: . Sort the collection; If the output of the sorting algorithm is an array, retrieve its th element; otherwise, scan the sorted sequence to find the th element.