###### algorithms

- This flexibility, together with the efficiency of the above comparison sorting algorithms on modern computers, has led to widespread preference for comparison sorts in most practical work. (wikipedia.org)
- Other integer sorting algorithms, such as radix sort, are not asymptotically faster than comparison sorting, but can be faster in practice. (wikipedia.org)
- Further, the data is often taken to be in an array, which allows random access, rather than a list, which only allows sequential access, though often algorithms can be applied with suitable modification to either type of data. (wikipedia.org)
- Among the authors of early sorting algorithms around 1951 was Betty Holberton (née Snyder), who worked on ENIAC and UNIVAC. (wikipedia.org)
- algorithms not based on comparisons, such as counting sort, can have better performance. (wikipedia.org)
- consider sorting a solved problem-asymptotically optimal algorithms have been known since the mid-20th century-useful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006. (wikipedia.org)
- Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and upper and lower bounds. (wikipedia.org)
- Sorting algorithms are often classified by: Computational complexity (worst, average and best behavior) in terms of the size of the list (n). (wikipedia.org)
- For typical serial sorting algorithms good behavior is O(n log n), with parallel sort in O(log2 n), and bad behavior is O(n2). (wikipedia.org)
- Comparison-based sorting algorithms need at least Ω(n log n) comparisons for most inputs. (wikipedia.org)
- Some algorithms are either recursive or non-recursive, while others may be both (e.g., merge sort). (wikipedia.org)
- Stability: stable sorting algorithms maintain the relative order of records with equal keys (i.e., values). (wikipedia.org)
- Stable sort algorithms sort identical elements in the same order that they appear in the input. (wikipedia.org)
- Stable sorting algorithms choose one of these, according to the following rule: if two items compare as equal, like the two 5 cards, then their relative order will be preserved, so that if one came before the other in the input, it will also come before the other in the output. (wikipedia.org)
- In computer science, big O notation is used to classify algorithms according to how their running time or space requirements grow as the input size grows. (wikipedia.org)
- A large number of algorithms to perform activities such as searching and sorting are provided in the STL, each implemented to require a certain level of iterator (and therefore will work on any container that provides an interface by iterators). (wikipedia.org)
- Apart from these, algorithms are provided for making heap from a range of elements, generating lexicographically ordered permutations of a range of elements, merge sorted ranges and perform union, intersection, difference of sorted ranges. (wikipedia.org)
- Algorithms like sort, partial_sort, nth_element and all sorted containers use a binary predicate that must provide a strict weak ordering, that is, it must behave like a membership test on a transitive, non reflexive and asymmetric binary relation. (wikipedia.org)

###### algorithm

- 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. (wikipedia.org)
- When the keys form a small (compared to n) range, counting sort is an example algorithm that runs in linear time. (wikipedia.org)
- The number of comparisons that a comparison sort algorithm requires increases in proportion to n log ( n ) {\displaystyle n\log(n)} , where n {\displaystyle n} is the number of elements to sort. (wikipedia.org)
- In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order. (wikipedia.org)
- A sorting algorithm is stable if whenever there are two records R and S with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list. (wikipedia.org)
- But most agree that algorithm has something to do with defining generalized processes for the creation of "output" integers from other "input" integers - "input parameters" arbitrary and infinite in extent, or limited in extent but still variable-by the manipulation of distinguishable symbols (counting numbers) with finite collections of rules that a person can perform with paper and pencil. (wikipedia.org)
- 4. Input: a good algorithm must be able to accept a set of defined input. (wikipedia.org)
- The sort-merge join (also known as merge join) is a join algorithm and is used in the implementation of a relational database management system. (wikipedia.org)
- The key idea of the sort-merge algorithm is to first sort the relations by the join attribute, so that interleaved linear scans will encounter these sets at the same time. (wikipedia.org)
- In practice, the most expensive part of performing a sort-merge join is arranging for both inputs to the algorithm to be presented in sorted order. (wikipedia.org)
- For example, an algorithm to reverse a sequence can be implemented using bidirectional iterators, and then the same implementation can be used on lists, vectors and deques. (wikipedia.org)
- The Yoshimine sort is an algorithm that is used in quantum chemistry to order lists of two electron repulsion integrals. (wikipedia.org)

###### Merge

- Some of the most well-known comparison sorts include: Quicksort Heapsort Shellsort Merge sort Introsort Insertion sort Selection sort Bubble sort Odd-even sort Cocktail shaker sort Cycle sort Merge insertion (Ford-Johnson) sort Smoothsort Timsort There are fundamental limits on the performance of comparison sorts. (wikipedia.org)
- The latter condition, called interesting order, can occur because an input to the join might be produced by an index scan of a tree-based index, another merge join, or some other plan operator that happens to produce output sorted on an appropriate key. (wikipedia.org)
- So, in the worst case sort-merge join will run in O ( P r + P s ) {\displaystyle O(P_{r}+P_{s})} I/Os. (wikipedia.org)

###### integers

- an example is integer sorting, where all keys are integers. (wikipedia.org)

###### stable

- In a stable sort, the input order determines the sorted order in this case. (wikipedia.org)

###### heapsort

- Selection sorts include shaker sort and heapsort. (wikipedia.org)

###### deque

- The standard sequence containers include vector, deque, and list. (wikipedia.org)

###### sequence

- These are input iterators (that can only be used to read a sequence of values), output iterators (that can only be used to write a sequence of values), forward iterators (that can be read, written to, and move forward), bidirectional iterators (that are like forward iterators, but can also move backwards) and random access iterators (that can move freely any number of steps in one operation). (wikipedia.org)

###### permutations

- Given a list of distinct numbers (we can assume this because this is a worst-case analysis), there are n factorial permutations exactly one of which is the list in sorted order. (wikipedia.org)

###### Iterator

- For example, a vector would have a random access iterator, but a list only a bidirectional iterator. (wikipedia.org)

###### requirement

- The only requirement is that the operator obey two of the properties of a total order: if a ≤ b and b ≤ c then a ≤ c (transitivity) for all a and b, either a ≤ b or b ≤ a (totalness or trichotomy). (wikipedia.org)

###### Bubble

- Bubble sort was analyzed as early as 1956. (wikipedia.org)
- Exchange sorts include bubble sort and quicksort. (wikipedia.org)

###### notation

- For most basic operations including mathematical computations, HyperTalk favored natural-language ordering of predicates over the ordering used in mathematical notation. (wikipedia.org)

###### insertion

- many adaptive sorts such as insertion sort run in O(n) time on an already-sorted or nearly-sorted list. (wikipedia.org)

###### typically

- non-comparison sorts typically require specialized versions for each datatype. (wikipedia.org)
- Frequently, the totally symmetric irreducible representation is assigned the lowest index in the list, typically 1 in Fortran or 0 in the C programming language. (wikipedia.org)

###### 2002

- In early 2002, the English-language ruby-talk mailing list was receiving more messages than the Japanese-language ruby-list, demonstrating Ruby's increasing popularity in the English-speaking world. (wikipedia.org)

###### data

- A comparison sort examines the data only by comparing two elements with a comparison operator. (wikipedia.org)
- When sorting some kinds of data, only part of the data is examined when determining the sort order. (wikipedia.org)
- More formally, the data being sorted can be represented as a record or tuple of values, and the part of the data that is used for sorting is called the key. (wikipedia.org)
- 1. It receives data & instructions from the input device. (scribd.com)
- 2.CPU (a) Memory unit (b) Arithmetic Logic unit (c) Control Unit : : : Stores program and data Performs arithmetic and logical functions Interprets program instructions and controls the input and output devices 3. (scribd.com)
- Once data are fed into the main memory from input devices, they are held and transferred as needed to ALU where processing takes place. (scribd.com)

###### output

- The output is a permutation (reordering but with all of the original elements) of the input. (wikipedia.org)
- If the input iterable is empty, the output iterable will also be empty. (python.org)
- For example, a "sort" command is unable to produce any output until all input records have been read, as the very last record received just might turn out to be first in sorted order. (wikipedia.org)
- Dr. Alexia Massalin's experimental operating system, Synthesis, would adjust the priority of each task as they ran according to the fullness of their input and output buffers. (wikipedia.org)

###### different

- Despite these limitations, comparison sorts offer the notable practical advantage that control over the comparison function allows sorting of many different datatypes and fine control over how the list is sorted. (wikipedia.org)
- This allows the possibility of multiple different correctly sorted versions of the original list. (wikipedia.org)
- Ex : Names of students and their marks in different subjects listed in random order. (scribd.com)

###### alphabetical

- Ex : When the names of students are arranged in alphabetical order, total and average marks are calculated & presented in a tabular form, it is information. (scribd.com)

###### comparisons

- This is a consequence of the limited information available through comparisons alone - or, to put it differently, of the vague algebraic structure of totally ordered sets. (wikipedia.org)
- Non-comparison sorts (such as the examples discussed below) can achieve O(n) performance by using operations other than comparisons, allowing them to sidestep this lower bound (assuming elements are constant-sized). (wikipedia.org)

###### time

- A comparison sort must have an average-case lower bound of Ω(n log n) comparison operations, which is known as linearithmic time. (wikipedia.org)
- Adaptability: Whether or not the presortedness of the input affects the running time. (wikipedia.org)

###### example

- For example, in the card sorting example to the right, the cards are being sorted by their rank, and their suit is being ignored. (wikipedia.org)

###### often

- This can be achieved via an explicit sort operation (often an external sort), or by taking advantage of a pre-existing ordering in one or both of the join relations. (wikipedia.org)
- This can often be replaced by input indirection or a here string, and use of cat and piping rather than input redirection is known as useless use of cat. (wikipedia.org)

###### include

- A query includes a list of columns to include in the final result, normally immediately following the SELECT keyword. (wikipedia.org)

###### average-case

- Ideal behavior for a serial sort is O(n), but this is not possible in the average case. (wikipedia.org)

###### problem

- From the beginning of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. (wikipedia.org)

###### possible

- The Ω(n log n) lower bound applies only to the case in which the input list can be in any possible order. (wikipedia.org)
- On the other hand, if the molecule has some symmetry operations, then further ordering is possible. (wikipedia.org)

###### Function

- The letter O is used because the growth rate of a function is also referred to as order of the function. (wikipedia.org)
- such comparison operator or comparator function must guarantee strict weak ordering. (wikipedia.org)
- Any given basis set may be ordered so that each function can assigned a unique index. (wikipedia.org)
- This means that a computer program for two electron integral processing can precompute the list of basis function symmetry combinations (symmetry blocks) for which integrals may be non zero and ignore all other symmetry combinations. (wikipedia.org)

###### practical

- Matsumoto describes the design of Ruby as being like a simple Lisp language at its core, with an object system like that of Smalltalk, blocks inspired by higher-order functions, and practical utility like that of Perl. (wikipedia.org)

###### elements

- Elements of the input iterable may be any type that can be accepted as arguments to func . (python.org)

###### versions

- in their place were special string literals, or "lists" of "items" delimited by commas (in later versions the "itemDelimiter" property allowed choosing an arbitrary character). (wikipedia.org)

###### records

- Other operators have at times been suggested or implemented, such as the skyline operator (for finding only those records that are not 'worse' than any others). (wikipedia.org)

###### comparison sort

- Whether or not they are a comparison sort. (wikipedia.org)

###### early

- In a 1999 post to the ruby-talk mailing list, he describes some of his early ideas about the language: I was talking with my colleague about the possibility of an object-oriented scripting language. (wikipedia.org)

###### includes

- The Schrödinger equation, for a system with two or more electrons, includes the Coulomb repulsion operator. (wikipedia.org)

###### return

- ftp localhost This runs the ftp client with input user, press return, then pass. (wikipedia.org)

###### functions

- Thus two types of ordering can be used: the non-zero symmetry blocks of two electron ingtegrals are ordered (the programmer is at liberty to define this order) the dimension of each block can be computed since the number of basis functions of each symmetry is known. (wikipedia.org)

###### easily

- Comparison sorts generally adapt more easily to complex orders such as the order of floating-point numbers. (wikipedia.org)
- This operator used a natural language syntax making for easily readable, self-documenting code. (wikipedia.org)