I. Resolution

One such property is the discrete. Under the discrete it is meant that the algorithm consists of describing the processing sequence of steps organized in such a way that at the initial time set by the initial situation, as a next step after each situation is converted based on the data obtained in preceding processing steps. Discrete algorithm means that it is executed step by step: every action provided algorithm is executed only after the execution has ended previous.

II. certainty

Another feature called certainty. It means that each step is uniquely determined transformation performer objects medium obtained in the preceding steps of the algorithm.

For example, in one of said cooking recipes:

Gently shake the mixture to become lumpy. Heat the brandy in a small saucepan and pour it into the mixture.

Formal Executive is unclear whether the shake mix is required, until the whole is not it will be a success, and what still values the pan. Big or small? And to what temperature it is necessary to warm the brandy. So this algorithm any artist perform quite difficult, almost impossible. We can say that the algorithm should not be present not certain words: a little, a little, a little, and so on..

III. effectiveness

The third property - the effectiveness of the algorithm. This property implies that every step (and the algorithm in general) after its completion provides an environment in which all available objects are uniquely identified. If for some - any reason impossible, the algorithm should report that the solution does not exist.

For example, in the instructions for use said cough medicine:

If the doctor has prescribed, then take 3-4 times a day 15-20 drops, best in hot sweet water.

There is not defined, for example, when the algorithm must end - when the cough will be held or when the drug is to end. performance property generally implies limb algorithm, ie. e. the completion of its operation in a finite number of steps (the number of steps can not be known in advance and is different for different initial data).

IV. perspicuity

I must say that the algorithm should be understood not only the author, but also the executor. If we propose to the Executive, such as iron wash clothes, he would never do that, because they do not understand, that is. To. Such a program it is not mortgaged. Or, for example, if we offer to some boy to bake a cake that he had, as a rule, that does not work, because they do not know how. But if we draw up a detailed work algorithm, we divide it into basic steps, such that it can easily understand and be able to perform each step, it will be able to successfully bake any cake. Each step of the algorithm necessarily represent any permissible action executor. This property is called the algorithm clear.

V. Mass

Finally, another feature of the algorithm - the mass. It means that there is a set of data that can be processed by an algorithm or the algorithm can be used to solve any problem of the same type. Mass algorithm is closely associated with intelligibility by way of example can parse example with cake, and say that more than cooking algorithm will be described, the greater the probability that the cake is baked. Also, as an example we can take the manual of electrical appliances, instructions and so on. E., Better than the algorithm of work with the devices, the easier it will be to you to understand it. From the point of view of the practical value of the important algorithms that would be the set of admissible initial data it is sufficiently large, as a rule, the algorithm practical value is not high, if it only be used once.

Content

## Algorithm properties of algorithms

The algorithm is called an accurate and understandable predpisanie performer make a sequence of actions aimed at the solution of the problem. The word "algorithm" is derived from the name al-Khwarizmi mathematician who formulated the rules of performing arithmetic operations. Initially, under the rules of the algorithm realized only perform four arithmetic operations on numbers. In the future, this concept began to be used generally to refer to a sequence of actions that lead to the solution of any task. Speaking about the algorithm of the computational process, it should be understood that the object to which the algorithm is applied are the data. An algorithm for solving a computational problem is a set of rules to transform raw data Scoring. The main - determinacy (certainty). It involves obtaining unambiguous results of computing protsecca for given input data. Due to this property of the algorithm process is mechanical in nature;
- effectiveness. It indicates the presence of the original data for which a given algorithm implemented by a computing process must after a finite number of steps to stop and give the desired result;
- mass. This property suggests that the algorithm has to be suitable for solving all the problems of this type;
- discrete. Segmentation means defined algorithm computing process into separate stages, the possibility of execution of which the provider (PC) is not in doubt.
The algorithm should be formalized by some rules through specific representational means. These include methods for recording algorithms: verbal, formula-verbal, graphic language of operator schemes, algorithmic language. The most widely used due to its clarity, a graphical (circuit block) way to write algorithms. Three main types of computational processes can be identified at all variety of problem-solving algorithms in them: - linear;
- branching;
- cyclical.
A cycle is repeated multiple computing section. The computational process, comprising one or more cycles, called |

## properties of algorithms

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**4. Properties of the algorithm**

Description of the main features helps to deepen the concept of the algorithm itself. Thus, the algorithm must have the following properties:

(*Determinacy**certainty, precision, uniqueness*). This property consists in that when setting the same initial data algorithm is repeatedly performed in exactly the same and the same result is always obtained. Determinism of the property as manifested in the fact that at each step of the algorithm always know exactly what to do next, and each action clearly understandable artist and may not be construed indefinitely. Due to this property the algorithm is mechanical in nature.reflected in the fact that using the algorithm can solve not just one specific task, and any problem of a class of similar problems with all the possible values of the original data.*Grassroots*-(*Effectiveness**directivity*)**-**meaning that the algorithm must necessarily lead to the solution of the problem, or to post that for given initial values of the problem can not be solved. Algorithmic process may not end up in vain.means that the algorithm is composed of a sequence of individual steps - elementary actions, the implementation of which is easy. It is thanks to this property, the algorithm can be implemented on a computer.*Readability*-(*The finiteness**finiteness*)**-**lies in the fact that the sequence of elementary actions of the algorithm can not be infinite, unlimited, although it may be very large (if required, for example, a large computational accuracy).- means that if the algorithm is designed to solve a specific task, then for all initial data it should always give the correct result and for any initial data will not get the wrong results. If at least one of the results contradict at least one of the previously installed and have received acknowledgment of the facts, the algorithm can not be considered valid.*Correctness*

If you developed the sequence of actions has not at least one of the properties listed above, it can not be regarded as an algorithm

## PROPERTIES algorithms of discrete definition ...

Throughout our lives we are faced with the algorithms, without even realizing it. Algorithms appear in situations that can be described as a sequence of actions. Give examples.

We will not whisper a washing machine command "to wash the stain on the collar blouses" and use only those operations that are specified in the instruction as the executable, and set them on strictly defined rules. For example, pressing the button activates the mode of washing laundry or pressing.

In this situation, we see the object 2: control (giving commands) and run (execute commands). In this example, a performer machine.

When crossing the road we follow the traffic signals ...

In this situation, we also see object 2: control (giving commands) and run (execute commands). But in this case, people performer.

"... grandfather came to the shore of the blue sea and threw the net. Grandpa caught fish, but not simple, and gold. And executes fish all his desires ... "

In everyday of their activities we understand intuitively that only in fairy tales there are wonderful versatile performers as "Goldfish", which is understood by all-all-all, and can be all-all-all, but still possess telepathic abilities to guess what would we would like.

Perhaps those of you who since childhood to their requests to their parents and grandparents to formulate within a reasonable and executable or available, achieved more satisfying than those who are asked to get the star from the sky, to buy a live pink elephant, etc. And so the solution of algorithmic tasks will be to build a language understood by a particular artist, using at each step of the algorithm, only those operations or commands that the artist is able to perform.

Thus, an algorithm - a sequence of commands by an object. Obviously, the executor of the algorithm can be like a living creature and machine.

Algorithms - clear and precise instruction executor to perform a finite sequence of instructions, resulting from the raw data to the desired result. |

*Properties algorithms (algorithms to requirements):*

** 1. Resolution. **The process of solving the problem should be divided into a series of individual steps. Thus, the formation of an ordered set of spaced apart commands (instructions). Formed algorithm structure is discontinuous (discrete) executing only one command executor can begin the following.

** 2. Clarity. **The algorithm should be clear to the Executive, and the contractor should be able to carry out his team. Therefore, the algorithm should be developed with a focus on a particular artist, that is, the algorithm can include commands only from the command system of the artist.

** 3. Determinirotnnost. **As understood, the algorithm does not include instructions the meaning of which can be perceived ambiguously. (For example, the robot will be confused command "Take two - three tablespoons of sand": which means "two or three" ?, some sand). In addition, unacceptable situation where after the next command executor is not clear which team to carry out the next step. Violation of these requirements compiler algorithm (called definite requirement, or determinism) leads to the fact that one and the same command after performing various actuators gives uneven results.

** 4. Effectiveness. **The meaning of the mandatory requirements of the algorithm is that at the exact performance of the algorithm commands the process of solving the problem should stop after a finite number of steps, and in this case, must be received by a specific answer to the problem formulation.

** 5. Mass. **Development of algorithms - the process interesting, creative, but difficult, requiring many, often collective, mental effort and time consuming. It is therefore preferable to design algorithms "provide a solution in all classes of this type of problems. For example, if the algorithm is made solutions of the quadratic equation AX

^{ 2}+ bx + c = 0, it must be variativen, i.e. solutions allow for any admissible initial coefficient values: a, b, c. About such an algorithm say, it satisfies the demand of mass.

**Form recording algorithms**

Drafting of any algorithm aims at solving some classes of problems.

There are many ways to write a formal algorithms:

1) It is part of the algorithm is written in a natural language as a numbered sequence of actions or commands. This is reminiscent of the operating instructions, for example, the grinder (descriptive form).

2) Not less frequently used in schools block diagram - a graphical way, combining simplicity and clarity.

3) Write an algorithm in a programming language

Problem 1. Create a verbal algorithm "tea infuser"

**The types of algorithms:**

- linear

- conditional (branching)

- cyclic

**Attention! **Algorithm type is determined by the nature of the problem solved in accordance with its task teams.

**Homework -** abstract, make a verbal algorithm cooking walnut drink.

RECIPE: pound nuts in a wooden mortar, dissolve in hot milk. Then cook for 10 minutes on low heat.

Serve chilled.

Product: 250 g shelled walnuts, 0.8 liters of milk, 120 g of sugar.

## WHAT ARE THE MAIN CHARACTERISTICS OF ALGORITHMS (Give an example ...

It characterizes its structure. Any algorithm consists of individual operations (steps, actions) that are performed discontinuously (in steps). This means that the algorithm has the properties of the discrete.

Determinism - the property of the algorithm, indicating that each step of the algorithm should be strictly defined and can not be subject to various interpretations. order also to be defined strictly perform the individual steps, that is, the performer must know exactly the sequence of operations. Any algorithm should be presented in such a way that it can be unambiguously (exactly) implemented performer. This property of the algorithm is also called a certainty, unambiguous and accurate.

Mass (universality) - Applicability of the algorithm to all problems of the type considered at any admissible sets of input data. It is important to emphasize that the mass is the applicability of the algorithm to all problems of this type, that is, to all the tasks for which it is intended. In addition, it must be borne in mind that the implementation of the algorithm is possible in all but admissible sets of input data.

Effectiveness (limb) - the ability to produce a specific result for valid raw data in a finite number of steps. That is, the ability to finish the process in a finite number of iterations or form message of impossibility of further data (e.g., due to the fact that the original data available to the algorithm is not applicable).

Formality - property means that any performer, performing an algorithm (eg, a computer), acting formally, that is, strictly executes instructions provided by the developer of the algorithm.