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"Elegant" (compact) programs, "good" (fast) programs : The notion of "simplicity and elegance" appears informally in Knuth and precisely in Chaitin:

Chaitin prefaces his definition with: "I'll show you can't prove that a program is 'elegant'"—such a proof would solve the Halting problem (ibid).

Algorithm versus function computable by an algorithm : For a given function multiple algorithms may exist. This is true, even without expanding the available instruction set available to the programmer. Rogers observes that "It is . . . important to distinguish between the notion of algorithm , i.e. procedure and the notion of function computable by algorithm , i.e. mapping yielded by procedure. The same function may have several different algorithms". [32]

Unfortunately there may be a tradeoff between goodness (speed) and elegance (compactness)—an elegant program may take more steps to complete a computation than one less elegant. An example that uses Euclid's algorithm appears below.

Computers (and computors), models of computation : A computer (or human "computor" [33] ) is a restricted type of machine, a "discrete deterministic mechanical device" [34] that blindly follows its instructions. [35] Melzak's and Lambek's primitive models [36] reduced this notion to four elements: (i) discrete, distinguishable locations , (ii) discrete, indistinguishable counters visit sale online Marsèll asymmetric sandals cheap sale discounts many kinds of online discount latest collections vBP8F1
(iii) an agent, and (iv) a list of instructions that are effective relative to the capability of the agent. [38]

Minsky describes a more congenial variation of Lambek's "abacus" model in his "Very Simple Bases for Computability ". cheap low shipping discount release dates Santoni loafer sneakers outlet cheap quality cost for sale outlet marketable i8QYGzaQ
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proceeds sequentially through its five (or six, depending on how one counts) instructions, unless either a conditional IF–THEN GOTO or an unconditional GOTO changes program flow out of sequence. Besides HALT, Minsky's machine includes three assignment (replacement, substitution) [40] operations: ZERO (e.g. the contents of location replaced by 0: L ← 0), SUCCESSOR (e.g. L ← L+1), and DECREMENT (e.g. L ← L − 1). [41] Rarely must a programmer write "code" with such a limited instruction set. But Minsky shows (as do Melzak and Lambek) that his machine is Turing complete with only four general types of instructions: conditional GOTO, unconditional GOTO, assignment/replacement/substitution, and HALT. [42]

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How council homes are allocated

Councils usually allocate council and housing association homes through:

Your council might use either system or a combination of both.

In some areas, you can apply directly to local housing associations and ask to go on their waiting lists.Ask your council for details of any housing associations operating separate waiting lists in your area.

What is a council housing allocation scheme?

Each council has its own allocations policy or scheme.

A council's housing allocation scheme should tell you:

Where to find a council's allocation policy

Your council should have its allocations policies on its website.

Find your council's website.

Leaflets explaining the allocations policyare usually available at libraries and council offices.

The council's housing department or information servicecan help you find information.

Who gets priority for housing

All councils must give reasonable preference for housing to people who:

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It does not always mean that you will be treated as a high or urgent priority.

Waiting time for council housing

Council and housing association homes are usually in short supply.

It can take years to get housed. Some people never get a council or housing association home.

Your chances of getting a home depend on:

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or applying as homeless .

Number of housingoffers

The number of properties you are considered for depends on your council's policy.

If your councilruns achoice based lettingsscheme, ask how many properties you can bid for in one go. Some councils expect you to accept any property you successfully bid for ifthe propertyis suitable for your needs.

If your council makes direct offers, you must wait until the council says a home is available for you. Some councils will only make one suitable offer but others will make more offers.

You may be suspended from the council housing register for a period if you turn down a suitable offer so check the policy before refusing an offer.

Suitable and unsuitable housing

The housing you're offered should be suitable for you andpeople living with you.

The council looks at practical issues such as:

The councilshould also consider whether the accommodation isclose enough to support services you need or special schools.

The council should not offer you accommodation in an areathat is likely toput you at risk of racial harassment or domestic abuse .

How to challenge unsuitable offers

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if you think the housing you've been offered is unsuitable.

In many areas council housing is in short supply. There is no guarantee you'll be offered something better.

Get help from a housing adviser

Get advice if you want to challenge an offer or if you think your priority or needs haven't been properly assessed.

Last updated 06 Oct 2016 | © Shelter

For a detailed presentation of the various points of view on the definition of "algorithm", see Algorithm characterizations .

An informal definition could be "a set of rules that precisely defines a sequence of operations." [18] which would include all computer programs, including programs that do not perform numeric calculations. Generally, a program is only an algorithm if it stops eventually. [19]

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

Boolos, Jeffrey 1974, 1999 offer an informal meaning of the word in the following quotation:

No human being can write fast enough, or long enough, or small enough† ( †"smaller and smaller without limit ...you'd be trying to write on molecules, on atoms, on electrons") to list all members of an enumerably infinite set by writing out their names, one after another, in some notation. But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the n th member of the set , for arbitrary finite n . Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine , or by a human who is capable of carrying out only very elementary operations on symbols. [20]

An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus, Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large. Thus an algorithm can be an algebraic equation such as y = m + n – two arbitrary "input variables" m and n that produce an output y . But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example):

The concept of algorithm is also used to define the notion of decidability . That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic , the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.

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