Computer science is the study of processes that interact with data and that can be represented as data in the form of programs. It enables the use of algorithms to manipulate and communicate digital information. A computer scientist studies the theory of computation and the practice of designing software systems, its fields can be divided into practical disciplines. Computational complexity theory is abstract, while computer graphics emphasizes real-world applications. Programming language theory considers approaches to the description of computational processes, while computer programming itself involves the use of programming languages and complex systems. Human–computer interaction considers the challenges in making computers useful and accessible; the earliest foundations of what would become computer science predate the invention of the modern digital computer. Machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, aiding in computations such as multiplication and division.
Algorithms for performing computations have existed since antiquity before the development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623. In 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner, he may be considered the first computer scientist and information theorist, among other reasons, documenting the binary number system. In 1820, Thomas de Colmar launched the mechanical calculator industry when he released his simplified arithmometer, the first calculating machine strong enough and reliable enough to be used daily in an office environment. Charles Babbage started the design of the first automatic mechanical calculator, his Difference Engine, in 1822, which gave him the idea of the first programmable mechanical calculator, his Analytical Engine, he started developing this machine in 1834, "in less than two years, he had sketched out many of the salient features of the modern computer".
"A crucial step was the adoption of a punched card system derived from the Jacquard loom" making it infinitely programmable. In 1843, during the translation of a French article on the Analytical Engine, Ada Lovelace wrote, in one of the many notes she included, an algorithm to compute the Bernoulli numbers, considered to be the first computer program. Around 1885, Herman Hollerith invented the tabulator, which used punched cards to process statistical information. In 1937, one hundred years after Babbage's impossible dream, Howard Aiken convinced IBM, making all kinds of punched card equipment and was in the calculator business to develop his giant programmable calculator, the ASCC/Harvard Mark I, based on Babbage's Analytical Engine, which itself used cards and a central computing unit; when the machine was finished, some hailed it as "Babbage's dream come true". During the 1940s, as new and more powerful computing machines were developed, the term computer came to refer to the machines rather than their human predecessors.
As it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation in general. In 1945, IBM founded the Watson Scientific Computing Laboratory at Columbia University in New York City; the renovated fraternity house on Manhattan's West Side was IBM's first laboratory devoted to pure science. The lab is the forerunner of IBM's Research Division, which today operates research facilities around the world; the close relationship between IBM and the university was instrumental in the emergence of a new scientific discipline, with Columbia offering one of the first academic-credit courses in computer science in 1946. Computer science began to be established as a distinct academic discipline in the 1950s and early 1960s; the world's first computer science degree program, the Cambridge Diploma in Computer Science, began at the University of Cambridge Computer Laboratory in 1953. The first computer science degree program in the United States was formed at Purdue University in 1962.
Since practical computers became available, many applications of computing have become distinct areas of study in their own rights. Although many believed it was impossible that computers themselves could be a scientific field of study, in the late fifties it became accepted among the greater academic population, it is the now well-known IBM brand that formed part of the computer science revolution during this time. IBM released the IBM 704 and the IBM 709 computers, which were used during the exploration period of such devices. "Still, working with the IBM was frustrating if you had misplaced as much as one letter in one instruction, the program would crash, you would have to start the whole process over again". During the late 1950s, the computer science discipline was much in its developmental stages, such issues were commonplace. Time has seen significant improvements in the effectiveness of computing technology. Modern society has seen a significant shift in the users of computer technology, from usage only by experts and professionals, to a near-ubiquitous user base.
Computers were quite costly, some degree of humanitarian aid was needed for efficient use—in part from professional computer operators. As computer adoption became more widespread and affordable, less human assistance was needed for common usage. Despite its short history as a formal academic discipline, computer science has made a number of fundamental contributions to science and society—in fact, along with electronics, it is
In computer science, radix sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by the individual digits which share the same significant position and value. A positional notation is required, but because integers can represent strings of characters and specially formatted floating point numbers, radix sort is not limited to integers. Radix sort dates back as far as 1887 to the work of Herman Hollerith on tabulating machines. Most digital computers internally represent all of their data as electronic representations of binary numbers, so processing the digits of integer representations by groups of binary digit representations is most convenient. Radix sorts can be implemented to start at either the most significant digit or least significant digit. For example, when sorting the number 1234 into a list, one could start with the 1 or the 4. LSD radix sorts use the following sorting order: short keys come before longer keys, keys of the same length are sorted lexicographically.
This coincides with the normal order of integer representations, such as the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. MSD radix sorts use lexicographic order, suitable for sorting strings, such as words, or fixed-length integer representations. A sequence such as "b, c, d, e, f, g, h, i, j, ba" would be lexicographically sorted as "b, ba, c, d, e, f, g, h, i, j". If lexicographic ordering is used to sort variable-length integer representations the representations of the numbers from 1 to 10 would be output as 1, 10, 2, 3, 4, 5, 6, 7, 8, 9, as if the shorter keys were left-justified and padded on the right with blank characters to make the shorter keys as long as the longest key for the purpose of determining sorted order; the topic of the efficiency of radix sort compared to other sorting algorithms is somewhat tricky and subject to quite a lot of misunderstandings. Whether radix sort is efficient, less efficient or more efficient than the best comparison-based algorithms depends on the details of the assumptions made.
Radix sort complexity is O for n keys which are integers of word size w. Sometimes w is presented as a constant, which would make radix sort better than the best comparison-based sorting algorithms, which all perform Θ comparisons to sort n keys. However, in general w cannot be considered a constant: if all n keys are distinct w has to be at least log n for a random-access machine to be able to store them in memory, which gives at best a time complexity Ω; that would seem to make radix sort at best efficient as optimal comparison-based sorts. The counter argument is that comparison-based algorithms are measured in number of comparisons, not actual time complexity. Under some assumptions the comparisons will be constant time on average, under others they will not. Comparisons of randomly generated keys takes constant time on average, as keys differ on the first bit in half the cases, differ on the second bit in half of the remaining half, so on, resulting in an average of two bits that need to be compared.
In a sorting algorithm the first comparisons made satisfies the randomness condition, but as the sort progresses the keys compared are not randomly chosen anymore. For example, consider a bottom-up merge sort; the first pass will compare pairs of random keys, but the last pass will compare keys that are close in the sorting order. This makes merge sort, on this class of inputs, take Ω time; that assumes all memory accesses cost the same, not a physically reasonable assumption as we scale n to infinity, not, in practice, how real computers work. This argument extends from the observation that computers are filled with different types of memory in different and limited quantities. Modern operating systems will position variables into these different systems automatically making memory access time differ as more and more memory is utilized. A Least significant digit Radix sort is a fast stable sorting algorithm which can be used to sort keys in integer representation order. Keys may be a string of characters, or numerical digits in a given'radix'.
The processing of the keys begins at the least significant digit, proceeds to the most significant digit. The sequence in which digits are processed by an LSD radix sort is the opposite of the sequence in which digits are processed by a most significant digit radix sort. An LSD radix sort operates in O time, where n is the number of keys, w is the average key length; this kind of performance for variable-length keys can be achieved by grouping all of the keys that have the same length together and separately performing an LSD radix sort on each group of keys for each length, from shortest to longest, in order to avoid processing the whole list of keys on every sorting pass. A radix sorting algorithm was used to sort punched cards in several passes. A computer algorithm was invented for radix sort in 1954 at MIT by Harold H. Seward. In many large applications needing speed, the computer radix sort is an improvement on comparison sorts. LSD radix sorts have resurfaced as an alternative to high performance comparison-based sorting algorithms that require Ω comparisons, where n is the number of items to be sorted.
Comparison sorts can do no better than Ω execution time but offer the flexibility of being able to sort with respect to more complicated orderings than a lexicographic one. Each k
Translation lookaside buffer
A translation lookaside buffer is a memory cache, used to reduce the time taken to access a user memory location. It is a part of the chip’s memory-management unit; the TLB stores the recent translations of virtual memory to physical memory and can be called an address-translation cache. A TLB may reside between the CPU and the CPU cache, between CPU cache and the main memory or between the different levels of the multi-level cache; the majority of desktop and server processors include one or more TLBs in the memory-management hardware, it is nearly always present in any processor that utilizes paged or segmented virtual memory. The TLB is sometimes implemented as content-addressable memory; the CAM search key is the virtual address, the search result is a physical address. If the requested address is present in the TLB, the CAM search yields a match and the retrieved physical address can be used to access memory; this is called a TLB hit. If the requested address is not in the TLB, it is a miss, the translation proceeds by looking up the page table in a process called a page walk.
The page walk is time-consuming when compared to the processor speed, as it involves reading the contents of multiple memory locations and using them to compute the physical address. After the physical address is determined by the page walk, the virtual address to physical address mapping is entered into the TLB; the PowerPC 604, for example, has a two-way set-associative TLB for data stores. Some processors have different data address TLBs. A TLB has a fixed number of slots containing segment-table entries; the virtual memory is the memory space as seen from a process. The page table stored in main memory, keeps track of where the virtual pages are stored in the physical memory; this method uses two memory accesses to access a byte. First, the page table is looked up for the frame number. Second, the frame number with the page offset gives the actual address, thus any straightforward virtual memory scheme would have the effect of doubling the memory access time. Hence, the TLB is used to reduce the time taken to access the memory locations in the page-table method.
The TLB is a cache of the page table, representing only a subset of the page-table contents. Referencing the physical memory addresses, a TLB may reside between the CPU and the CPU cache, between the CPU cache and primary storage memory, or between levels of a multi-level cache; the placement determines whether the cache uses virtual addressing. If the cache is addressed, requests are sent directly from the CPU to the cache, the TLB is accessed only on a cache miss. If the cache is physically addressed, the CPU does a TLB lookup on every memory operation, the resulting physical address is sent to the cache. In a Harvard architecture or modified Harvard architecture, a separate virtual address space or memory-access hardware may exist for instructions and data; this can lead to distinct TLBs for each access type, an instruction translation lookaside buffer and a data translation lookaside buffer. Various benefits have been demonstrated with separate data and instruction TLBs; the TLB can be used as a fast lookup hardware cache.
The figure shows the working of a TLB. Each entry in the TLB consists of two parts: a value. If the tag of the incoming virtual address matches the tag in the TLB, the corresponding value is returned. Since the TLB lookup is a part of the instruction pipeline, searches are fast and cause no performance penalty. However, to be able to search within the instruction pipeline, the TLB has to be small. A common optimization for physically addressed caches is to perform the TLB lookup in parallel with the cache access. Upon each virtual-memory reference, the hardware checks the TLB to see whether the page number is held therein. If yes, it is a TLB hit, the translation is made; the frame number is used to access the memory. If the page number is not in the TLB, the page table must be checked. Depending on the CPU, this can be done automatically using a hardware or using an interrupt to the operating system; when the frame number is obtained, it can be used to access the memory. In addition, we add the page number and frame number to the TLB, so that they will be found on the next reference.
If the TLB is full, a suitable block must be selected for replacement. There are different replacement methods like least used, first in, first out etc.. The CPU has to access main memory for data-cache miss, or TLB miss; the third case is where the desired information itself is in a cache, but the information for virtual-to-physical translation is not in a TLB. These are all slow, due to the need to access a slower level of the memory hierarchy, so a well-functioning TLB is important. Indeed, a TLB miss can be more expensive than an instruction or data cache miss, due to the need for not just a load from main memory, but a page walk, requiring several memory accesses; the flowchart provided explains the working of a TLB. If it is a TLB miss the CPU checks the page table for the page table ent
Autocomplete, or word completion, is a feature in which an application predicts the rest of a word a user is typing. In graphical user interfaces, users can press the tab key to accept a suggestion or the down arrow key to accept one of several. Autocomplete speeds up human-computer interactions when it predicts the word a user intends to enter after only a few characters have been typed into a text input field, it works best in domains with a limited number of possible words, when some words are much more common, or writing structured and predictable text. Many autocomplete algorithms learn new words after the user has written them a few times, can suggest alternatives based on the learned habits of the individual user; the original purpose of word prediction software was to help people with physical disabilities increase their typing speed, as well as to help them decrease the number of keystrokes needed in order to complete a word or a sentence. The need to increase speed is noted by the fact that people who use speech-generating devices produce speech at a rate, less than 10% as fast as people who use oral speech.
But the function is very useful for anybody who writes text people–such as medical doctors–who use long, hard-to-spell terminology that may be technical or medical in nature. Autocomplete or word completion works so that when the writer writes the first letter or letters of a word, the program predicts one or more possible words as choices. If the word he intends to write is included in the list he can select it, for example by using the number keys. If the word that the user wants is not predicted, the writer must enter the next letter of the word. At this time, the word choice is altered so that the words provided begin with the same letters as those that have been selected; when the word that the user wants appears it is selected, the word is inserted into the text. In another form of word prediction, words most to follow the just written one are predicted, based on recent word pairs used. Word prediction uses language modeling, where within a set vocabulary the words are most to occur are calculated.
Along with language modeling, basic word prediction on AAC devices is coupled with a recency model, where words that are used more by the AAC user are more to be predicted. Word prediction software also allows the user to enter their own words into the word prediction dictionaries either directly, or by "learning" words that have been written; some search returns related to genitals or other vulgar terms are omitted from autocompletion technologies, as are morbid terms There are standalone tools that add autocomplete functionality to existing applications. These programs monitor user suggests a list of words based on first typed letter. Examples are Letmetype. LetMeType, freeware, is no longer developed, the author has published the source code and allows anybody to continue development. Typingaid freeware, is developed. Intellicomplete, both a freeware and payware version, works only in certain programs which hook into the intellicomplete server program. Many Autocomplete programs can be used to create a Shorthand list.
The original autocomplete software was Smartype, which dates back to the late 1980s and is still available today. It was developed for medical transcriptionists working in WordPerfect for MS/DOS, but it now functions for any application in any Windows or Web-based program. Shorthand called Autoreplace, is a related feature that involves automatic replacement of a particular string with another one one, longer and harder to type, as "myname" with "Lee John Nikolai François Al Rahman"; this can quietly fix simple typing errors, such as turning "teh" into "the". Several Autocomplete programs, standalone or integrated in text editors, based on word lists include a shorthand function for used phrases. Context completion is a text editor feature, similar to word completion, which completes words based on the current context and context of other similar words within the same document, or within some training data set; the main advantage of context completion is the ability to predict anticipated words more and with no initial letters.
The main disadvantage is the need of a training data set, larger for context completion than for simpler word completion. Most common use of context completion is seen in advanced programming language editors and IDEs, where training data set is inherently available and context completion makes more sense to the user than broad word completion would. Line completion is a type of context completion, first introduced by Juraj Simlovic in TED Notepad, in July 2006; the context in line completion is the current line, while current document poses as training data set. When user begins a line which starts with a used phrase, the editor automatically completes it, up to the position where similar lines differ, or proposes a list of common continuations. Action completion in applications are standalone tools that add autocomplete functionality to an existing applications or all existing applications of a OS, based on the current context; the main advantage of Action completion is the ability to predict anticipated actions.
The main disadvantage is the need of a data set. Most common use of Action completion is seen in IDEs, but there are action completion tools that work globally, in parallel, across all applications of the entire PC without hindering the action completion of the respective a
Trie-sur-Baïse is a commune in the Hautes-Pyrénées department in south-western France. It is the administrative center in a canton comprising 22 villages, it is famous for its annual pig festival known as La Pourcailhade. Trie-sur-Baïse is named after Lord of Toulouse. Trie-sur-Baïse is a commune of the Pays des Coteaux, an administrative area that includes Tournay, Castelnau-Magnoac and Galan; the town lies next to the Baïse river, which runs through the Gers et de Lot-et-Garonne and Hautes-Pyrénées departments. Trie-sur-Baïse is a crossing point of five roads going to Castelnau-Magnoac, Lannemezan, Miélan and Tarbes. Trie-sur-Baïse is located in the Hautes-Pyrénées department in south-western France; the royal fortified town of Trie-sur-Baïse, the new Bastide, was founded in 1323 under a contract of a paréage signed by Jean de Trie, Seneschal of Toulouse and representative of the King, the seigneur of Bernard Duffort Manas, the seigneur of Puydarrieux Gerald of Esparros and a representative of the abbey Escaladieu, Father Roger Mauleon.
In 1355, the city was sieged and destroyed by the Prince of Wales, better known as Black Prince, as part of his devastating expeditions to the Southwest of France during the Hundred Year War. The reconstruction of the city started in 1365; the structure of the town follows the classic structure of the Bastide with the central square surrounded by stone houses and shops under the arcades. In some Bastides, the old market structures, the halles- have been replaced by more recent buildings; this is the case for Trie-sur-Baïse. 1323 - Foundation of the bastide 1325 - Inauguration of a weekly market. 1355 - Siege and destruction of the town by the Black Prince. 1360-1362 - Town invaded and pillaged by the English four times. 1363 - Reconstruction by the inhabitants. 1849 - Modernisation of the town which takes on its current form. In August 1355, the early inhabitants of Trie assembled to decide. Snow covered the ground except for one spot in the shape of a cross; this is where they built the first chapel dedicated to our "Lady of the snow", who is, to this day, the protector of the town.
The anniversary on the first Sunday of August is still a date for important local worship and rejoicing. The Carmes monastery was founded in 1365. In 1659, arson destroyed the main buildings and only the church could be saved from complete destruction; the monastery was only rebuilt 60 to 70 years later. The church was restored in 1992 and has today become a center of cultural activities. A typical example of meridional gothic architecture, the church is the centerpoint of local historical interest and its cloister has been reconstructed stone by stone at The Cloisters museum in New York City. In Trie-sur-Baïse, there are shops to satisfy everyday requirements. In addition, every Tuesday, there is a traditional market in the centre of town. From December to February, the special "marché au gras" takes place on Sundays. At the end of August is the "foire aux broutards", where over 3500 calves are sold; the local economy is based on agriculture, with corn, beets and soy, among others, grown. The region is well-known for its high-quality veal, raised "under the mother" and for duck.
Haricots Tarbais, a delicious white bean prized for its rich flavour and fine skin, is grown locally in conjunction with corn crops as the corn stalks are used to support the climbing beans. Rugby is a popular sport, with the local FCT teams playing regular matches; the handball, cycling, judo, skeet shooting and tennis clubs are active. Cycling is a popular sport in the region, with Trie being ideally located for rides on flat roads or longer rides in the mountains. There are trails for mountain biking. On 26 July 2018, stage 18 of the Tour de France departed from Trie-sur-Baïse, with the route taking the professional cyclists to the finish in Pau; the festival, called "La Grande Pourcailhade", was based around the theme of the pig and was traditionally held at the beginning of August. However, due to a lack of volunteers, notably for the pig-squealing contest, it was decided by the festival's organisers, the town's Office de Tourisme, that the festival would be cancelled for 2012 and thereafter until a more convenient date could be agreed upon.
August is a poor month due to it being the region's hottest month of the year and the time of year most French people, therefore potential volunteers, take their annual holidays. During the day and pork were the subject of various events, for example: the pig-squealing contest the sausage-eating contest the best pig disguise contest piglet racingIn the evening, dinner was served and, to end the day with a flourish, musical entertainment was provided by a celebrity. After a run of 36 years, the last festival was held in 2011; each year, on July 13 and August 13, night markets with fireworks and dancing are held from 7 pm onwards on the town square. At the end of July, an antique fair is organised where one can buy, sell or admire curios, pieces of furniture and artefacts. Around the first Sunday of August, the local fair takes place over five days with various activities for children and adults. Communes of the Hautes-Pyrénées department INSEE Homepage of Trie-sur-Baïse La bastide de Trie-sur-Baïse:documents pour la classe, at Hautes Pyrenees
String (computer science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed. A string is considered a data type and is implemented as an array data structure of bytes that stores a sequence of elements characters, using some character encoding. String may denote more general arrays or other sequence data types and structures. Depending on programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements; when a string appears in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set called an alphabet. Let Σ be a non-empty finite set of symbols, called the alphabet.
No assumption is made about the nature of the symbols. A string over Σ is any finite sequence of symbols from Σ. For example, if Σ = 01011 is a string over Σ; the length of a string s can be any non-negative integer. The empty string is the unique string over Σ of length 0, is denoted ε or λ; the set of all strings over Σ of length n is denoted Σn. For example, if Σ = Σ2 =. Note that Σ0 = for any alphabet Σ; the set of all strings over Σ of any length is the Kleene closure of Σ and is denoted Σ*. In terms of Σn, Σ ∗ = ⋃ n ∈ N ∪ Σ n For example, if Σ = Σ* =. Although the set Σ* itself is countably infinite, each element of Σ* is a string of finite length. A set of strings over Σ is called a formal language over Σ. For example, if Σ =, the set of strings with an number of zeros, is a formal language over Σ. Concatenation is an important binary operation on Σ*. For any two strings s and t in Σ*, their concatenation is defined as the sequence of symbols in s followed by the sequence of characters in t, is denoted st.
For example, if Σ =, s = bear, t = hug st = bearhug and ts = hugbear. String concatenation is an non-commutative operation; the empty string ε serves as the identity element. Therefore, the set Σ* and the concatenation operation form a monoid, the free monoid generated by Σ. In addition, the length function defines a monoid homomorphism from Σ* to the non-negative integers. A string s is said to be a substring or factor of t if there exist strings u and v such that t = usv; the relation "is a substring of" defines a partial order on Σ*, the least element of, the empty string. A string s is said to be a prefix of t if there exists a string u such that t = su. If u is nonempty, s is said to be a proper prefix of t. Symmetrically, a string s is said to be a suffix of t if there exists a string u such that t = us. If u is nonempty, s is said to be a proper suffix of t. Suffixes and prefixes are substrings of t. Both the relations "is a prefix of" and "is a suffix of" are prefix orders. A string s = uv.
For example, if Σ = the string 0011001 is a rotation of 0100110, where u = 00110 and v = 01. The reverse of a string is a string in reverse order. For example, if s = abc the reverse of s is cba. A string, the reverse of itself is called a palindrome, which includes the empty string and all strings of length 1, it is useful to define an ordering on a set of strings. If the alphabet Σ has a total order one can define a total order on Σ* called lexicographical order. For example, if Σ = and 0 < 1 the lexicographical order on Σ* includes the relationships ε < 0 < 00 < 000 <... < 0001 < 001 < 01 < 010 < 011 < 0110 < 01111 < 1 < 10 < 100 < 101 < 111 < 1111 < 11111... The lexicographical order is total if the alphabetical order is, but isn't well-founded for any nontrivial alphabet if the alphabetical order is. See Shortlex for an alternative string ordering that preserves well-foundedness. A number of additional operations on strings occur in the formal theory; these are given in the article on string operations.
Strings admit the following interpretation as nodes on a graph: Fixed-length strings can be viewed as nodes on a hypercube Variable-length strings can be viewed as nodes on the k-ary tree, where k is the number of symbols in Σ Infinite strings can be viewed as i
In computer science, an associative array, symbol table, or dictionary is an abstract data type composed of a collection of pairs, such that each possible key appears at most once in the collection. Operations associated with this data type allow: the addition of a pair to the collection the removal of a pair from the collection the modification of an existing pair the lookup of a value associated with a particular keyThe dictionary problem is a classic computer science problem: the task of designing a data structure that maintains a set of data during'search','delete', and'insert' operations; the two major solutions to the dictionary problem are a search tree. In some cases it is possible to solve the problem using directly addressed arrays, binary search trees, or other more specialized structures. Many programming languages include associative arrays as primitive data types, they are available in software libraries for many others. Content-addressable memory is a form of direct hardware-level support for associative arrays.
Associative arrays have many applications including such fundamental programming patterns as memoization and the decorator pattern. The name does not come from the associative property known in mathematics. Rather, it arises from the fact. In an associative array, the association between a key and a value is known as a "binding", the same word "binding" may be used to refer to the process of creating a new association; the operations that are defined for an associative array are: Add or insert: add a new pair to the collection, binding the new key to its new value. The arguments to this operation are the value. Reassign: replace the value in one of the pairs that are in the collection, binding an old key to a new value; as with an insertion, the arguments to this operation are the value. Remove or delete: remove a pair from the collection, unbinding a given key from its value; the argument to this operation is the key. Lookup: find the value, bound to a given key; the argument to this operation is the key, the value is returned from the operation.
If no value is found, some associative array implementations raise an exception, while others create a pair with the given key and the default value of the value type. Instead of add or reassign there is a single set operation that adds a new pair if one does not exist, otherwise reassigns it. In addition, associative arrays may include other operations such as determining the number of bindings or constructing an iterator to loop over all the bindings. For such an operation, the order in which the bindings are returned may be arbitrary. A multimap generalizes an associative array by allowing multiple values to be associated with a single key. A bidirectional map is a related abstract data type in which the bindings operate in both directions: each value must be associated with a unique key, a second lookup operation takes a value as argument and looks up the key associated with that value. Suppose that the set of loans made by a library is represented in a data structure; each book in a library may be checked out only by a single library patron at a time.
However, a single patron may be able to check out multiple books. Therefore, the information about which books are checked out to which patrons may be represented by an associative array, in which the books are the keys and the patrons are the values. Using notation from Python or JSON, the data structure would be: A lookup operation on the key "Great Expectations" would return "John". If John returns his book, that would cause a deletion operation, if Pat checks out a book, that would cause an insertion operation, leading to a different state: For dictionaries with small numbers of bindings, it may make sense to implement the dictionary using an association list, a linked list of bindings. With this implementation, the time to perform the basic dictionary operations is linear in the total number of bindings. Another simple implementation technique, usable when the keys are restricted to a narrow range of integers, is direct addressing into an array: the value for a given key k is stored at the array cell A, or if there is no binding for k the cell stores a special sentinel value that indicates the absence of a binding.
As well as being simple, this technique is fast: each dictionary operation takes constant time. However, the space requirement for this structure is the size of the entire keyspace, making it impractical unless the keyspace is small; the two major approaches to implementing dictionaries are a search tree. The most used general purpose implementation of an associative array is with a hash table: an array combined with a hash function that separates each key into a separate "bucket" of the array; the basic idea behind a hash table is that accessing an element of an array via its index is a simple, constant-time operation. Therefore, the average overhead of an operation for a hash table is only the computation of the key's hash