TheInfoList

Collation is the assembly of written information into a standard order. Many systems of collation are based on or , or extensions and combinations thereof. Collation is a fundamental element of most office , s, and s. Collation differs from ' in that the classes themselves are not necessarily ordered. However, even if the order of the classes is irrelevant, the identifiers of the classes may be members of an ordered set, allowing a to arrange the items by class. Formally speaking, a collation method typically defines a on a set of possible identifiers, called sort keys, which consequently produces a on the set of items of information (items with the same identifier are not placed in any defined order). A collation algorithm such as the defines an order through the process of comparing two given s and deciding which should come before the other. When an order has been defined in this way, a sorting algorithm can be used to put a list of any number of items into that order. The main advantage of collation is that it makes it fast and easy for a user to find an element in the list, or to confirm that it is absent from the list. In automatic systems this can be done using a or ; manual searching may be performed using a roughly similar procedure, though this will often be done unconsciously. Other advantages are that one can easily find the first or last elements on the list (most likely to be useful in the case of numerically sorted data), or elements in a given range (useful again in the case of numerical data, and also with alphabetically ordered data when one may be sure of only the first few letters of the sought item or items).

# Ordering

## Numerical and chronological

Strings representing s may be sorted based on the values of the numbers that they represent. For example, "−4", "2.5", "10", "89", "30,000". Note that pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number (as with "2" and "2.0" or, when is used, "2e3" and "2000"). A similar approach may be taken with strings representing or other items that can be ordered chronologically or in some other natural fashion.

## Alphabetical

is the basis for many systems of collation where items of information are identified by strings consisting principally of from an . The ordering of the strings relies on the existence of a standard ordering for the letters of the alphabet in question. (The system is not limited to alphabets in the strict technical sense; languages that use a or , for example , can use the same ordering principle provided there is a set ordering for the symbols used.) To decide which of two strings comes first in alphabetical order, initially their first letters are compared. The string whose first letter appears earlier in the alphabet comes first in alphabetical order. If the first letters are the same, then the second letters are compared, and so on, until the order is decided. (If one string runs out of letters to compare, then it is deemed to come first; for example, "cart" comes before "carthorse".) The result of arranging a set of strings in alphabetical order is that words with the same first letter are grouped together, and within such a group words with the same first two letters are grouped together, and so on. s are typically treated as equivalent to their corresponding lowercase letters. (For alternative treatments in computerized systems, see , below.) Certain limitations, complications, and special conventions may apply when alphabetical order is used: *When strings contain or other word dividers, the decision must be taken whether to ignore these dividers or to treat them as symbols preceding all other letters of the alphabet. For example, if the first approach is taken then "car park" will come after "carbon" and "carp" (as it would if it were written "carpark"), whereas in the second approach "car park" will come before those two words. The first rule is used in many (but not all) , the second in (so that Wilson, Jim K appears with other people named Wilson, Jim and not after Wilson, Jimbo). *Abbreviations may be treated as if they were spelt out in full. For example, names containing "St." (short for the English word ') are often ordered as if they were written out as "Saint". There is also a traditional convention in English that surnames beginning ''Mc'' and ''M are listed as if those prefixes were written ''Mac''. *Strings that represent personal names will often be listed by alphabetical order of surname, even if the comes first. For example, Juan Hernandes and Brian O'Leary should be sorted as "Hernandes, Juan" and "O'Leary, Brian" even if they are not written this way. *Very common initial words, such as ''The'' in English, are often ignored for sorting purposes. So ' would be sorted as just "Shining" or "Shining, The". *When some of the strings contain (or other non-letter characters), various approaches are possible. Sometimes such characters are treated as if they came before or after all the letters of the alphabet. Another method is for numbers to be sorted alphabetically as they would be spelled: for example ' would be sorted as if spelled out "seventeen seventy-six", and ' as if spelled "vingt-quatre..." (French for "twenty-four"). When numerals or other symbols are used as special graphical forms of letters, as in ''1337'' for or ''Se7en'' for the movie title ', they may be sorted as if they were those letters. *Languages have different conventions for treating s and certain letter combinations. For example, in the letter ''ñ'' is treated as a basic letter following ''n'', and the ''ch'' and ''ll'' were formerly (until 1994) treated as basic letters following ''c'' and ''l'', although they are now alphabetized as two-letter combinations. A list of such conventions for various languages can be found at . In several languages the rules have changed over time, and so older dictionaries may use a different order than modern ones. Furthermore, collation may depend on use. For example, German and use different approaches.

# Automation

When information is stored in digital systems, collation may become an automated process. It is then necessary to implement an appropriate collation that allows the information to be sorted in a satisfactory manner for the application in question. Often the aim will be to achieve an alphabetical or numerical ordering that follows the standard criteria as described in the preceding sections. However, not all of these criteria are easy to automate.''M Programming: A Comprehensive Guide''
Richard F. Walters, Digital Press, 1997
The simplest kind of automated collation is based on the numerical codes of the symbols in a , such as coding (or any of its s such as ), with the symbols being ordered in increasing numerical order of their codes, and this ordering being extended to strings in accordance with the basic principles of alphabetical ordering (mathematically speaking, ing). So a computer program might treat the characters ''a'', ''b'', ''C'', ''d'', and ''\$'' as being ordered ''\$'', ''C'', ''a'', ''b'', ''d'' (the corresponding ASCII codes are ''\$'' = 36, ''a'' = 97, ''b'' = 98, ''C'' = 67, and ''d'' = 100). Therefore, strings beginning with ''C'', ''M'', or ''Z'' would be sorted before strings with lower-case ''a'', ''b'', etc. This is sometimes called '. This deviates from the standard alphabetical order, particularly due to the ordering of capital letters before all lower-case ones (and possibly the treatment of spaces and other non-letter characters). It is therefore often applied with certain alterations, the most obvious being case conversion (often to uppercase, for historical reasonsHistorically, computers only handled text in uppercase (this dates back to conventions).) before comparison of ASCII values. In many collation algorithms, the comparison is based not on the numerical codes of the characters, but with reference to the collating sequence – a sequence in which the characters are assumed to come for the purpose of collation – as well as other ordering rules appropriate to the given application. This can serve to apply the correct conventions used for alphabetical ordering in the language in question, dealing properly with differently cased letters, s, , particular abbreviations, and so on, as mentioned above under , and in detail in the article. Such algorithms are potentially quite complex, possibly requiring several passes through the text. Problems are nonetheless still common when the algorithm has to encompass more than one language. For example, in dictionaries the word ''ökonomisch'' comes between ''offenbar'' and ''olfaktorisch'', while dictionaries treat ''o'' and ''ö'' as different letters, placing ''oyun'' before ''öbür''. A standard algorithm for collating any collection of strings composed of any standard symbols is the . This can be adapted to use the appropriate collation sequence for a given language by tailoring its default collation table. Several such tailorings are collected in .

## Sort keys

In some applications, the strings by which items are collated may differ from the identifiers that are displayed. For example, ''The Shining'' might be as ''Shining, The'' (see above), but it may still be desired to display it as ''The Shining''. In this case two sets of strings can be stored, one for display purposes, and another for collation purposes. Strings used for collation in this way are called ''sort keys''.

## Issues with numbers

Sometimes, it is desired to order text with embedded numbers using proper numerical order. For example, "Figure 7b" goes before "Figure 11a", even though '7' comes after '1' in . This can be extended to s. This behavior is not particularly difficult to produce as long as only integers are to be sorted, although it can slow down sorting significantly. For example, does this when sorting s. Sorting decimals properly is a bit more difficult, because different locales use different symbols for a , and sometimes the same character used as a is also used as a separator, for example "Section 3.2.5". There is no universal answer for how to sort such strings; any rules are application dependent. Ascending order of numbers differs from alphabetical order, e.g. 11 comes alphabetically before 2. This can be fixed with s: 02 comes alphabetically before 11. See e.g. . Also −13 comes alphabetically after −12 although it is less. With negative numbers, to make ascending order correspond with alphabetical sorting, more drastic measures are needed such as adding a constant to all numbers to make them all positive.

# Labeling of ordered items

In some contexts, numbers and letters are used not so much as a basis for establishing an ordering, but as a means of labeling items that are already ordered. For example, pages, sections, chapters, and the like, as well as the items of lists, are frequently "numbered" in this way. Labeling series that may be used include ordinary (1, 2, 3, ...), (I, II, III, ... or i, ii, iii, ...), or letters (A, B, C, ... or a, b, c, ...). (An alternative method for indicating list items, without numbering them, is to use a .) When letters of an alphabet are used for this purpose of , there are certain language-specific conventions as to which letters are used. For example, the letters and (which in writing are only used for modifying the preceding ), and usually also , , and , are omitted. Also in many languages that use extended , the s are often not used in enumeration.

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