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Introsort
Introsort or introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance. It begins with quicksort, it switches to heapsort when the recursion depth exceeds a level based on (the logarithm of) the number of elements being sorted and it switches to insertion sort when the number of elements is below some threshold. This combines the good parts of the three algorithms, with practical performance comparable to quicksort on typical data sets and worst-case O(''n'' log ''n'') runtime due to the heap sort. Since the three algorithms it uses are comparison sorts, it is also a comparison sort. Introsort was invented by David Musser in , in which he also introduced introselect, a hybrid selection algorithm based on quickselect (a variant of quicksort), which falls back to median of medians and thus provides worst-case linear complexity, which is optimal. Both algorithms were introduced with the purpose of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quicksort
Quicksort is an efficient, general-purpose sorting algorithm. Quicksort was developed by British computer scientist Tony Hoare in 1959 and published in 1961, it is still a commonly used algorithm for sorting. Overall, it is slightly faster than merge sort and heapsort for randomized data, particularly on larger distributions. Quicksort is a divide-and-conquer algorithm. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. For this reason, it is sometimes called partition-exchange sort. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. Most implementations of quicksort are not stable, meaning that the relative order of equal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Introselect
In computer science, introselect (short for "introspective selection") is a selection algorithm that is a hybrid of quickselect and median of medians which has fast average performance and optimal worst-case performance. Introselect is related to the introsort sorting algorithm: these are analogous refinements of the basic quickselect and quicksort algorithms, in that they both start with the quick algorithm, which has good average performance and low overhead, but fall back to an optimal worst-case algorithm (with higher overhead) if the quick algorithm does not progress rapidly enough. Both algorithms were introduced by David Musser in , with the purpose of providing generic algorithms for the C++ Standard Library that have both fast average performance and optimal worst-case performance, thus allowing the performance requirements to be tightened. However, in most C++ Standard Library implementations, a different "introselect" algorithm is used, which combines quickselect and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a List (computing), list into an Total order, order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the Algorithmic efficiency, efficiency of other algorithms (such as search algorithm, search and merge algorithm, merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for Canonicalization, canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. For optimum efficiency, the input data should be stored in a data structure which allows random access ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unstable Sort
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. For optimum efficiency, the input data should be stored in a data structure which allows random access rather than one that allows only sequential access. History and concepts From the beginning of computi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Sort
A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator forms a total preorder over the data, with: # if ''a'' ≤ ''b'' and ''b'' ≤ ''c'' then ''a'' ≤ ''c'' (transitivity) # for all ''a'' and ''b'', ''a'' ≤ ''b'' or ''b'' ≤ ''a'' ( connexity). It is possible that both ''a'' ≤ ''b'' and ''b'' ≤ ''a''; in this case either may come first in the sorted list. In a stable sort, the input order determines the sorted order in this case. A metaphor for thinking about comparison sorts is that someone has a set of unlabelled weights and a balance scale. Their goal is to line up the weights in order by their weight without any information except that obtained by placing two weights on the scale and seeing which one i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heapsort
In computer science, heapsort is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. Unlike selection sort, heapsort does not waste time with a linear-time scan of the unsorted region; rather, heap sort maintains the unsorted region in a heap data structure to more quickly find the largest element in each step. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantage of a more favorable worst-case runtime (and as such is used by Introsort as a fallback should it detect that quicksort is becoming degenerate). Heapsort is an in-place algorithm, but it is not a stable sort. Heapsort was invented by J. W. J. Williams in 1964. This was also the birth of the heap, presented a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a List (computing), list into an Total order, order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the Algorithmic efficiency, efficiency of other algorithms (such as search algorithm, search and merge algorithm, merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for Canonicalization, canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. For optimum efficiency, the input data should be stored in a data structure which allows random access ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Algorithm
{{Unreferenced, date=May 2014 A hybrid algorithm is an algorithm that combines two or more other algorithms that solve the same problem, and is mostly used in programming languages like C++, either choosing one (depending on the data), or switching between them over the course of the algorithm. This is generally done to combine desired features of each, so that the overall algorithm is better than the individual components. "Hybrid algorithm" does not refer to simply combining multiple algorithms to solve a different problem – many algorithms can be considered as combinations of simpler pieces – but only to combining algorithms that solve the same problem, but differ in other characteristics, notably performance. Examples In computer science, hybrid algorithms are very common in optimized real-world implementations of recursive algorithms, particularly implementations of divide-and-conquer or decrease-and-conquer algorithms, where the size of the data decreases as one moves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting Algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a List (computing), list into an Total order, order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the Algorithmic efficiency, efficiency of other algorithms (such as search algorithm, search and merge algorithm, merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for Canonicalization, canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. For optimum efficiency, the input data should be stored in a data structure which allows random access ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LLVM
LLVM is a set of compiler and toolchain technologies that can be used to develop a front end for any programming language and a back end for any instruction set architecture. LLVM is designed around a language-independent intermediate representation (IR) that serves as a portable, high-level assembly language that can be optimized with a variety of transformations over multiple passes. LLVM is written in C++ and is designed for compile-time, link-time, run-time, and "idle-time" optimization. Originally implemented for C and C++, the language-agnostic design of LLVM has since spawned a wide variety of front ends: languages with compilers that use LLVM (or which do not directly use LLVM but can generate compiled programs as LLVM IR) include ActionScript, Ada, C#, Common Lisp, PicoLisp, Crystal, CUDA, D, Delphi, Dylan, Forth, Fortran, Free Basic, Free Pascal, Graphical G, Halide, Haskell, Java bytecode, Julia, Kotlin, Lua, Objective-C, OpenCL, PostgreSQL's SQL and PLpg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU Standard C++ Library
The GNU Compiler Collection (GCC) is an optimizing compiler produced by the GNU Project supporting various programming languages, hardware architectures and operating systems. The Free Software Foundation (FSF) distributes GCC as free software under the GNU General Public License (GNU GPL). GCC is a key component of the GNU toolchain and the standard compiler for most projects related to GNU and the Linux kernel. With roughly 15 million lines of code in 2019, GCC is one of the biggest free programs in existence. It has played an important role in the growth of free software, as both a tool and an example. When it was first released in 1987 by Richard Stallman, GCC 1.0 was named the GNU C Compiler since it only handled the C programming language. It was extended to compile C++ in December of that year. Front ends were later developed for Objective-C, Objective-C++, Fortran, Ada, D and Go, among others. The OpenMP and OpenACC specifications are also supported in the C and C++ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Niklaus Wirth
Niklaus Emil Wirth (born 15 February 1934) is a Swiss computer scientist. He has designed several programming languages, including Pascal (programming language), Pascal, and pioneered several classic topics in software engineering. In 1984, he won the Turing Award, generally recognized as the highest distinction in computer science, for developing a sequence of innovative computer languages. Biography Wirth was born in Winterthur, Switzerland, in 1934. In 1959, he earned a Bachelor of Science (B.S.) degree in electronic engineering from the Swiss Federal Institute of Technology Zürich (ETH Zürich). In 1960, he earned a Master of Science (MSc) from Université Laval, Canada. Then in 1963, he was awarded a PhD in Electrical Engineering and Computer Science (EECS) from the University of California, Berkeley, supervised by the computer design pioneer Harry Huskey. From 1963 to 1967, he served as assistant professor of computer science at Stanford University and again at the Univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
