backtracking

In mathematics and computer science an algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will terminate in a corresponding recognizable end-state. Algorithms can be implemented by computer programs. Informally, the concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). The concept of algorithms was formalized in 1936 by Alan Turing's Turing machines and Alonzo Church's lambda c ...

Including:

• Algorithm - Formalization of algorithms
• Algorithm - Implementation
• Algorithm - Example
• Algorithm - History
• Algorithm - Classes
• Algorithm - Classification by implementation
• Algorithm - Classification by design paradigm
• Algorithm - Classification by field of study
• Algorithm - Classification by complexity
• Algorithm - Sources
• Algorithm - Legal issues

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The overall structure of Perl derives broadly from the programming language C. Perl is a procedural programming language, with variables, expressions, assignment statements, brace-delimited code blocks, control structures, and subroutines. Perl also takes features from shell programming. All variables are marked with leading sigils. Sigils unambiguously identify variable names, allowing Perl to have a rich syntax. Importantly, sigils allow variables to be interpolated directly into strings. Like the Unix shells, Perl has many built-in functions for common tasks, like sorting, and f ...

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Perl, Perl - History, Perl - Future, Perl - The name Perl, Perl - The camel symbol, Perl - Philosophy, Perl - Usage, Perl - Syntax, Perl - Sample code, Perl - Data structures, Perl - Control structures, Perl - Subroutines, Perl - Regular expressions, Perl - Resources, Perl - Implementations, Perl - Database interfaces, Perl - CPAN, Perl - Availability, Perl - Supported platforms, Perl - License, Perl - Opinion, Perl - Pro, Perl - Con, Perl - Fun with Perl

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The basic backtracking algorithm runs by choosing a literal, assigning a truth value to it, simplifying the formula and then recursively checking if the simplified formula is satisfiable; if this is the case, the original formula is satisfiable; otherwise, the same recursive check is done assuming the opposite truth value. This is known as the splitting rule, as it splits the problem into two simpler sub-problems. The simplification step essentially removes all clauses which become true under the assignment from the formula, and all litera ...

See also:

DPLL algorithm, DPLL algorithm - The algorithm, DPLL algorithm - Current work

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A standard pentomino puzzle is to tile a rectangular box with the pentominoes, i.e. cover it without overlap and without gaps. Each of the 12 pentominoes has an area of 5 unit squares, so the box must have an area of 60 units. Possible sizes are 6×10, 5×12, 4×15 and 3×20. The avid puzzler can probably solve these problems by hand within a few hours. A more challenging task, typically requiring a computer search, is to co ...

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Pentomino, Pentomino - Tiling rectangles, Pentomino - Filling boxes, Pentomino - Trivia, Pentomino - Board game, Pentomino - Video game

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The party was formed in 1994 by former members of the Parti libéral du Québec following the defeat of the Charlottetown Accord. This package of proposed reforms to the Canadian constitution would have provided expanded powers for Quebec and other provincial governments, and would have recognized Quebec as a distinct society within Canada. Liberals who were disappointed that the party was relu ...

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Action démocratique du Québec, Action démocratique du Québec - History, Action démocratique du Québec - Leaders of the Action démocratique du Québec, Action démocratique du Québec - Election results, Action démocratique du Québec - Other Canadian conservative parties

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Regular expression - Traditional Unix regular expressions. The "basic" Unix regular expression syntax is now defined as obsolete by POSIX, but is still widely used for the purposes of backwards compatibility. Most regular-expression–aware Unix utilities, for example grep and sed, use it by default. In this syntax, most characters are treated as literals—they match only themselves ("a" matches "a", "(bc" matches "(bc", et ...

See also:

Regular expression, Regular expression - Basic concepts, Regular expression - History, Regular expression - In formal language theory, Regular expression - Unicode vs single byte, Regular expression - Syntax, Regular expression - Traditional Unix regular expressions, Regular expression - Greedy expressions, Regular expression - POSIX modern extended regular expressions, Regular expression - Perl-compatible regular expressions PCRE, Regular expression - Patterns for irregular languages, Regular expression - Implementations and running times, Regular expression - .NET implementation

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There are many ways to classify algorithms, and the merits of each classification have been the subject of ongoing debate. Algorithm - Classification by implementation. One way to classify algorithms is by implementation means. Recursion or iteration: A recursive algorithm is one that invokes (makes reference to) itself repeatedly until a certain condition matches, which is a method common to functional programming. Iterative algorithms use repetitive constructs like loops and so ...

See also:

Algorithm, Algorithm - History, Algorithm - Formalization of algorithms, Algorithm - Implementation, Algorithm - Example, Algorithm - Classes, Algorithm - Classification by implementation, Algorithm - Classification by design paradigm, Algorithm - Classification by field of study, Algorithm - Classification by complexity, Algorithm - Legal issues

Read more here: » Algorithm: Encyclopedia II - Algorithm - Classes

Regular expression - Traditional Unix regular expressions. The "basic" Unix regular expression syntax is now defined as obsolete by POSIX, but is still widely used for the purposes of backwards compatibility. Most regular-expression–aware Unix utilities, for example grep and sed, use it by default. In this syntax, most characters are treated as literals—they match only themselves ("a" matches "a", "(bc" matches "(bc", et ...

See also:

Regular expression, Regular expression - Basic concepts, Regular expression - History, Regular expression - In formal language theory, Regular expression - Syntax, Regular expression - Traditional Unix regular expressions, Regular expression - POSIX modern extended regular expressions, Regular expression - Perl-compatible regular expressions PCRE, Regular expression - Patterns for irregular languages, Regular expression - Implementations and running times

Read more here: » Regular expression: Encyclopedia II - Regular expression - Syntax

There are many ways to classify algorithms, and the merits of each classification have been the subject of ongoing debate. Algorithm - Classification by implementation. One way to classify algorithms is by implementation means. Recursion or iteration: A recursive algorithm is one that invokes (makes reference to) itself repeatedly until a certain condition matches, which is a method common to functional programming. Iterative algorithms use repetitive constructs like loops and so ...

See also:

Algorithm, Algorithm - History, Algorithm - Formalization of algorithms, Algorithm - Implementation, Algorithm - Example, Algorithm - Algorithm analysis, Algorithm - Classes, Algorithm - Classification by implementation, Algorithm - Classification by design paradigm, Algorithm - Classification by field of study, Algorithm - Classification by complexity, Algorithm - Legal issues

Read more here: » Algorithm: Encyclopedia II - Algorithm - Classes

An uninformed search algorithm is one that does not take into account the specific nature of the problem. As such, they can be implemented in general, and then the same implementation can be used in a wide range of problems thanks to abstraction. The drawback is that most search spaces are extremely large, and an uninformed search (especially of a tree) will take a reasonable amount of time only for small examples. As such, to speed up the process, sometimes only an informed search will do.

See also:

Search algorithm, Search algorithm - Uninformed search, Search algorithm - List search, Search algorithm - Tree search, Search algorithm - Graph search, Search algorithm - Informed search, Search algorithm - Adversarial search, Search algorithm - Constraint satisfaction, Search algorithm - Other types

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However, computer memories were very small by current standards because they were expensive, being made of iron ferrite cores at that time. So Planner adopted the then common expedient of using backtracking control structures to economize on the use of computer memory. In this way, the computer only had to store one possibility at a time in exploring alternatives. One implementation decision in Micro Planner had unfortunate consequences. Lisp had adopted the programming pun of identifying NIL, the empty list with logical ...

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Planner programming language, Planner programming language - Early History of Planner, Planner programming language - Control Structure Controversy, Planner programming language - Control structure characterizations, Planner programming language - Hairy control structure, Planner programming language - Control structures are patterns of passing messages, Planner programming language - Limitation of mathematical logic, Planner programming language - Reference, Planner programming language - External link

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Prolog does not employ data types in the way common programming languages usually do. We may rather speak about Prolog lexical elements instead of data types. Prolog - Atoms. The text constants are introduced by means of atoms. An atom is a sequence consisting of letters, numbers and underscores, which begins with a lower-case letter. Usually, if a non-alphanumeric atom is needed, it is surrounded with apostrophes (e.g. 'an atom containing spaces')............ Prolog - Numbers. Most Prolog implementations do not distinguish integers from real numbers. ...

See also:

Prolog, Prolog - Data types, Prolog - Atoms, Prolog - Numbers, Prolog - Variables, Prolog - Terms, Prolog - Lists, Prolog - Strings, Prolog - Facts, Prolog - Rules, Prolog - Evaluation, Prolog - Negation, Prolog - Execution, Prolog - Parsing, Prolog - Parser example, Prolog - Examples, Prolog - QuickSort, Prolog - Towers of Hanoi, Prolog - Computer Algebra, Prolog - Implementations, Prolog - Extensions, Prolog - Resources, Prolog - Conferences, Prolog - References, Prolog - Tutorial introductions, Prolog - Tools, Prolog - External resources, Prolog - Books/ Tutorials

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A table-based top-down parser can be schematically presented as in Figure 1. +---+---+---+---+---+---+ Input: | ( | 1 | + | 1 | ) | $ | +---+---+---+---+---+---+ ^ Stack: | +-------+--------+ +---+ | | | + |<-------+ Parser +-----> Output +---+ | | | F | +------+---------+ +---+ | ^ | ) | | | +---+ +------+---------+ | $ | | Parsing | +---+ ...

See also:

LL parser, LL parser - Architecture of an LL parser, LL parser - Constructing an LL1 parsing table, LL parser - Constructing an LLk parsing table, LL parser - LLk parser generators

Read more here: » LL parser: Encyclopedia II - LL parser - Architecture of an LL parser

Perl - Example Program. In Perl, the canonical "Hello world" program is: #!/usr/bin/perl print "Hello, world!\n"; The first line is the shebang, which tells the operating system where to find the Perl interpreter. The second line prints the string Hello, world! and a newline (like a person pressing 'Return' or 'Enter'). The shebang is the usual way to invoke the interpreter on Unix systems. Windows systems may rely on the shebang, or they may associate a .plSee also:

Perl, Perl - Overview, Perl - Language features, Perl - Applications, Perl - Implementation, Perl - Availability, Perl - Language structure, Perl - Example Program, Perl - Data types, Perl - Control structures, Perl - Subroutines, Perl - Regular expressions, Perl - Database interfaces, Perl - Language design, Perl - Opinion, Perl - Pro, Perl - Con, Perl - History, Perl - Future, Perl - CPAN, Perl - Name, Perl - The Camel Symbol, Perl - Fun with Perl

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There are many ways to classify algorithms, and the merits of each classification have been the subject of ongoing debate. Algorithm - Classification by implementation. One way to classify algorithms is by implementation means. Recursion vs. Iteration: A recursive algorithm is one that invokes (makes reference to) itself repeatedly until a certain condition matches, which is a method common to functional programming. Iterative algorithms use repetitive constructs like loops and p ...

See also:

Algorithm, Algorithm - Formalization of algorithms, Algorithm - Implementation, Algorithm - Example, Algorithm - History, Algorithm - Classes, Algorithm - Classification by implementation, Algorithm - Classification by design paradigm, Algorithm - Classification by field of study, Algorithm - Classification by complexity, Algorithm - Sources, Algorithm - Legal issues

Read more here: » Algorithm: Encyclopedia II - Algorithm - Classes

Formally, a TDPL grammar G is a tuple consisting of the following components: A finite set N of nonterminal symbols. A finite set Σ of terminal symbols that is disjoint from N. A finite set P of production rules, where a rule has one of the following forms: A ← ε, where A is a nonterminal and ε is the empty string. A ← f, where f is a distinguished symbol representing unconditional failure. ...

See also:

Top-down parsing language, Top-down parsing language - Definition of a TDPL grammar, Top-down parsing language - Interpretation of a grammar, Top-down parsing language - Examples, Top-down parsing language - Generalized TDPL

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The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analysing. Sudoku - Scanning. Scanning is performed at the outset and periodically throughout the solution. Scans may have to be performed several times in between analysis periods. Scanning consists of two basic techniques: Cross-hatching: the scanning of rows (or columns) to identify which line in a particular region may contain a certain number by a process of e ...

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Sudoku, Sudoku - Introduction, Sudoku - Rules and terminology, Sudoku - Solution methods, Sudoku - Scanning, Sudoku - Marking up, Sudoku - Analysis, Sudoku - Computer solutions, Sudoku - Difficulty ratings, Sudoku - Construction, Sudoku - Variants, Sudoku - Mathematics of Sudoku, Sudoku - History, Sudoku - Popularity in the media

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The general problem of solving Sudoku puzzles on n2 x n2 boards of n x n blocks is known to be NP-complete [6]. This gives some indication of why Sudoku is difficult to solve, although on boards of finite size the problem is finite and can be solved by a deterministic finite automaton that knows the entire game tree. Solving Sudoku puzzles can be expressed as a graph colouring problem. The aim of the puzzle in its standard form is to construct a proper 9-colouring ...

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Sudoku, Sudoku - Introduction, Sudoku - Rules and terminology, Sudoku - Solution methods, Sudoku - Scanning, Sudoku - Marking up, Sudoku - Analysis, Sudoku - Computer solutions, Sudoku - Difficulty ratings, Sudoku - Construction, Sudoku - Variants, Sudoku - Mathematics of Sudoku, Sudoku - History, Sudoku - Popularity in the media

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Some countries allow algorithms to be patented when embodied in software or in hardware. Patents have long been a controversial issue (see, for example, the software patent debate). Some countries do not allow certain algorithms, such as cryptographic algorithms, to be exported from that country. ...

See also:

Algorithm, Algorithm - History, Algorithm - Formalization of algorithms, Algorithm - Implementation, Algorithm - Example, Algorithm - Algorithm analysis, Algorithm - Classes, Algorithm - Classification by implementation, Algorithm - Classification by design paradigm, Algorithm - Classification by field of study, Algorithm - Classification by complexity, Algorithm - Legal issues

Read more here: » Algorithm: Encyclopedia II - Algorithm - Legal issues

The word algorithm comes from the name of the 9th century Persian mathematician Abu Abdullah Muhammad bin Musa al-Khwarizmi. The word algorism originally referred only to the rules of performing arithmetic using Hindu-Arabic numerals but evolved via European Latin translation of al-Khwarizmi's name into algorithm by the 18th century. The word evolved to include all definite procedures for ...

See also:

Algorithm, Algorithm - History, Algorithm - Formalization of algorithms, Algorithm - Implementation, Algorithm - Example, Algorithm - Classes, Algorithm - Classification by implementation, Algorithm - Classification by design paradigm, Algorithm - Classification by field of study, Algorithm - Classification by complexity, Algorithm - Legal issues

Read more here: » Algorithm: Encyclopedia II - Algorithm - History