Backtracking is possible in an iterative approach.

Backtracking is a general algorithm for finding all ( or some ) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c (" backtracks ") as soon as it determines that c cannot possibly be completed to a valid solution.

Backtracking is an important tool for solving constraint satisfaction problems, such as crosswords, verbal arithmetic, Sudoku, and many other puzzles.

Backtracking is also utilized in the ( diff ) difference engine for the MediaWiki software.

* Backtracking is also utilized in the " diff " ( version comparing ) engine for the MediaWiki software.

Backtracking to previous screens is rarely required.

Backtracking starts at the highest scoring matrix cell and proceeds until a cell with score zero is encountered, yielding the highest scoring local alignment.

* Backtracking and Baumert 1965 was adopted to economize on the use of time and storage by working on and storing only one possibility at a time in exploring alternatives.

Backtracking can be applied only for problems which admit the concept of a " partial candidate solution " and a relatively quick test of whether it can possibly be completed to a valid solution.

Backtracking depends on user-given " black box procedures " that define the problem to be solved, the nature of the partial candidates, and how they are extended into complete candidates.

Richard Frost also used memoization to reduce the exponential time complexity of parser combinators, which can be viewed as “ Purely Functional Top-Down Backtracking ” parsing technique.

Backtracking on his previous assertion that Bush could continue without Pulsford, Rossdale stated that he started a new band because he didn ’ t want to dilute everything Bush had accomplished by changing members.

The set of equations ( 5 ), ( 6 ), and the starting equation ( 7 ) is of a recursive type well suited to programming on the digital computer.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.

However, the recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

This extreme growth can be exploited to show that f, which is obviously computable on a machine with infinite memory such as a Turing machine and so is a computable function, grows faster than any primitive recursive function and is therefore not primitive recursive.

Seed AI is a hypothesized type of strong artificial intelligence capable of recursive self-improvement.

A common adaptive method is recursive subdivision, in which a curve's control points are checked to see if the curve approximates a line segment to within a small tolerance.

The recursive equation is best introduced in a slightly more general form

Although the above recursive formula can be used for computation it is

It is not feasible to carry out such a computation using the above recursive formulae, since at least ( a constant multiple of ) p < sup > 2 </ sup > arithmetic operations would be required.

Note that this is different from the recursive languages which can be decided by an always-halting Turing machine.

Note that the set of grammars corresponding to recursive languages is not a member of this hierarchy.

Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.

The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields " yes " ( or true ) ( more accurately the number b in location B is greater than or equal to the number a in location A ) THEN the algorithm specifies B ← B − A ( meaning the number b − a replaces the old b ).

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.

While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.

" For some people, a program is only an algorithm if it stops eventually ; for others, a program is only an algorithm if it stops before a given number of calculation steps.

A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers ; an example ( there are others ) is described by the flow chart above and as an example in a later section.

The concept of algorithm is also used to define the notion of decidability.

In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension.

Gurevich: "... Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage, an algorithm is a computational process defined by a Turing machine ".

Typically, when an algorithm is associated with processing information, data is read from an input source, written to an output device, and / or stored for further processing.

Stored data is regarded as part of the internal state of the entity performing the algorithm.

Because an algorithm is a precise list of precise steps, the order of computation will always be critical to the functioning of the algorithm.

In computer systems, an algorithm is basically an instance of logic written in software by software developers to be effective for the intended " target " computer ( s ), in order for the target machines to produce output from given input ( perhaps null ).

is the length of time taken to perform the algorithm.

Simulation of an algorithm: computer ( computor ) language: Knuth advises the reader that " the best way to learn an algorithm is to try it.