What are the main types of algorithms called?

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• Golovna Within the framework of structural programming, problems that require algorithmic solutions can be described in terms of the following algorithmic structures:
• Following.
• It transmits a successive series of commands from the bottom up. Just as the algorithm consists not only of linear structures, but also of linear ones.
• Rozgaluzhennya.

Vikonannaya program goes one of two, no matter how small or blind.

Select the fork and place it in front of the washbasin at the entrance of the table and the data that came here.
Cycle

.
It conveys the possibility of repeating song actions many times.

Keep repeating a lot during the cycle.
Function (subprogram)

.
While the mind is concluding (the result of a logical expression is true), the body is concluding in the cycle.

After the final analysis, the investments are checked again.
In order to ensure that the algorithm does not get stuck in a cycle, there is a change in the whole cycle (in addition to other actions), as a result of which the output will change as it changes in the mind.

The cycle may not end even once, since the brain gave false from the very beginning.
do loop

In this cycle, first of all, the mind is checked only after the end of the body cycle.

As soon as the mind turns true, the expressions are repeated again.

No matter what the mind is like, the body of this cycle will come to an end.

for loop

This cycle is also called the “For” cycle.

This header contains three parameters: the initial value of the change (v), the main value (before) and the change for another arithmetic operation on the skin cycle (croc).

Algorithms may be simple and complex, but they all have common ideas.

Behind these figures, it is customary to see three types of algorithms, which are known to us.

In algorithms, commands are written one by one in order.

It is not obligatory to trace the stench in recording the sequence.

Internal messages can be sent to different commands.

The following teams have been assigned to the algorithm, so it looks like board games, in which participants roll dice and move fields.

Moreover, in the margins there may be comments on the style: “Turn 2 steps back” or “Go 5 steps forward” (Fig. 1).

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At the moment of start, the heaters are as hot as the cooking.

As they roll dice and transfer their chips around the looped playing field, plots of indestructible different colors emerge.

Having stumbled upon the business brought by the enemy, the gravest of goiters and pay the established rent.

Having purchased all plots of one group of colors, the participant can have booths and hotels on them, which will increase the size of the orenda.

The meta of everything that happens is banal - disgrace all superniks.

Today, with official makers - the Parker Brothers company, which has been releasing Monopoly since 1935 - the legendary board game was born in this way.

The right did not reach mass promotion, then The Landlord's Game gradually expanded across Northern America in artisanal copies.

The surge of interest to the table coincided with the fate of the Great Depression: thousands of unemployed people were eager to find themselves with penny bags, even at the gaming table.

The appearance of a captivating person on Charles Darrow's estate became the center of attention for several months - and after appearing, it gave fame to the monopoly winemaker for more than a decade.

There were, of course, also those who were interested in the need to snatch items from the legal authorities.

Unlicensed "Monopolies" flooded China. A number of clones have been and are being produced in our region - Broker, Cooperative, Manager (Fig. 6)..

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6. Gra "Manager" ()

With the recent rethinking of Durrow's role in Monopoly and the end of copyright law, such companies will not be able to sue.

Let’s just assume that dear Elizabeth Mega was not in the world, the rules of “Monopoly” have long since passed into the dorm room.

However, part of the Hasbro patent still covers the design of chips, graphic design, and the sequence of clicks on the playing field.

An algorithm in which commands are listed in the order in which they are written, one after another, is called

linear

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3. Light bulb ()

For example, the linear algorithm for replacing a light bulb that has burned out (Fig. 3):

1. turn on the light;<условие>2. Unscrew the light bulb that has burned out;<действия 1>,

3. screw in a new light bulb;<действия 2>

4. Turn down the device to check whether the light is on.

Using a block diagram, the algorithm can be represented as follows:

(block diagram (Fig. 7.) amazingly similar to the outline)

Situations, if the sequence of necessary actions is visible in the future, are rarely resolved.<действия 2>In life, you often have to make decisions based on the situation that has developed.

1. turn on the light;<условие>2. Unscrew the light bulb that has burned out;<действия 1>

As we walk along the road, we take a parasol and put on a raincoat;

If it’s hot, it’s cool to have a light chill.

The form of organization of actions, in which either one or another sequence of actions is carried out, is called let's unwind.

It is clear from the flowchart that the 6th grade student has forgotten the keys to his apartment and says: “Since my mother is at home, I will come and sit down to do my homework.

Since my mother is not at home, I will go play football with my friends until my mother comes.

If there are no friends on the street, I’ll go riding until my mother comes.”

(block diagram (Fig. 8.) amazingly similar to the outline)

Necessary and sufficient intelligence

We have already discussed with you that it is necessary and sufficient intelligence.

The butt of the necessary thinking can be as follows:

To become a doctor, it is necessary to obtain medical education.

Of course, medical knowledge is necessary for working as a doctor, but it is not sufficient.

True, not all graduates of medical schools become doctors.

The butt of a sufficient mind can be as follows: To make it cooler, just turn on the air conditioner. This reason is sufficient: as soon as you turn on the air conditioner, it will actually become colder.

However, this is not necessary, and to achieve this, you can turn on the fan and open the window.

Of course, there are necessary and sufficient minds at once (these minds are called

equally strong

).

For example:

In order for summer to come, it is necessary and sufficient for spring to end.

In truth, if spring is over, summer comes, and if spring is not over, then summer is impossible to come.

So, the end of spring and the beginning of summer are equally strong.

The concepts of necessary, sufficient and equal minds are very important in such a branch of mathematics as mathematical logic.

Moreover, the smells are often heard when proving various theorems. In fact, there are often problems in which some actions need to be repeated several times until the task is completed..

For example, if you need to sort through a box of apples in order to fertilize the rotten ones, then we need to repeat the following actions: 1. Take an apple..

We need to develop algorithms that prevent such situations.

Let's take a look at the algorithm of the alarm clock on the phone, which can ring at 8:00 a.m., and then ring through every 10 minutes, without making a sound.

In this case, the block diagram looks like this: (block diagram (Fig. 9) section at the end of the summary)

In this lesson we discussed three types of algorithms - linear algorithms, uneven algorithms and repeated algorithms.

In the next lesson, the formation of algorithms will be practically discussed.

Sieve of Eratosthenes

Guess the meaning of a prime natural number.

We'll forgive you for calling a natural number, just like that There are only two parts: one and the number itself. Other numbers are called warehouse

.

Whose number 1 ceases to be neither forgiven nor stored.

Use prime numbers: 2, 3, 5, 7 Add the numbers: 4, 6, 8.

In the 3rd century BC, the Greek mathematician Eratos-phene proposed an algorithm for finding all prime numbers less than a given number P:;

1. write down all natural numbers from 1 to

n

2. vicreslity 1;

3. add the smallest of non-valuable numbers;

4. recite all the numbers that are multiples of the number added in the previous step;

5. If there are unsigned numbers in the list, then go to line 3, otherwise all number additions are simple.

This is a cyclic algorithm.

When you quit, repetitions of 3-5 lines are added, and the documents in the output list are deprived of an unknown number.

Let's look at the results of this algorithm.

We write simple numbers from 1 to 25.

Write numbers from 1 to 25.

We’ll raise 1. Now we’ll raise the two.

Let's see all the guys' numbers.

If not all numbers are included, then we add 3. Now we add all the numbers that are divisible by 3.

Since not all numbers are included, then we add 5. Now we add the number 25.

Since not all numbers are included, we can say 7.It is not possible to recalculate anything, unless all the numbers are included, which means 11.

It is not possible to recalculate anything, if not all numbers are included, then we add 13. Again, we cannot recalculate anything – we add 17, then 19 and 23.

Now all the numbers are defined.

Simple numbers can be eliminated: 2, 3, 5, 7, 11, 13, 17, 19, 23.

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7.

3. Bosova L.L., Bosova A.Yu.

Computer science lessons for grades 5-6: Methodical handbook.

- M: BINOM.

Laboratory of knowledge, 2010

1. Internet portal “Our Merezha” ()

2. Internet portal “Hypermarket Know” ()

3. Internet portal “kaz.docdat.com” ()

Home improvement

1. §3.4 (Bosova L.L. Informatics and ICT: Handbook for 6th grade).

81 zavdannya 2, 6 (Bosova L.L. Informatics and ICT: Handbook for 6th grade).

3. Side

82 departments 9, 11, 13, 14 (Bosova L.L. Informatics and ICT: Handbook for 6th grade).

4. * Stor.

83 zavdannya 15 (Bosova L.L. Informatics and ICT: Handbook for 6th grade).

The computer science teacher got scared

DU "Secondary school No. 19

Akimat of Kostan"

Eleusizova Ainash Dosimkhanovna

Subject:

Goals:

promotion of interest to learning the subject;

vihovannya navichki shvidkogo mislennya;

development of creative activity of students;

development of cognitive interests.

Zavdannya:

1. Osvitny

consolidate the understanding of the algorithm, the Vikonavian system, the Vikonavian command system, and the methods of presenting algorithms;

Familiarize students with the types of algorithms: linear, uneven, cyclical;

Learn to identify algorithms by looking at flowcharts;

2. Developing

Activate the cognitive activity of students through multimedia learning tools;

Develop more figurative, critical, divergent thinking;

3. Vikhovny Increased motivation of students during the lesson;

Achievement of knowledgeable level of mastering of material by students; The formation of a sense of collectivism and healthy supernaturalism;

Formation of algorithmic thinking.

Before you know it:

Know the types of algorithms;

know the concept: linear, cyclic algorithms, what is wrong;

Note the stagnation of knowledge and the elimination of practical tasks.

Lesson type:combinations.

Technology:

formation of communicative competence;

Method:

part-time, practical.

informational (verbal);

scientific-illustrative;

Let’s begin before introducing new material.

We can guess what we learned last lesson.

1. Checking your homework.

Check the crossword puzzles made by your students at home.

Types:

graphic

ending

Information

Vikonavets

algorithm

software

computer

tool

2. Working with Activote (addendum 4) with music and sound support (sent to a sound file).

“Repetition is mother’s honor,” that’s what the greats said.

The teacher explains the algorithm for unleashing test orders.

Children in the area work with Activote.

III.

Development of new material.

1. The theoretical part. Children, in order to become familiar with the types of algorithms, we will immediately look at the next page of the flipchart and write down the necessary information in the form.

To begin with, we need to remember how geometric figures are formed when folding block diagrams.

Umovni assignments for block diagrams

(Flipchart side 5-6)

The beginning or the end of the program

- data entry

- dii

-Umova decided on the program

-view of tributes or text

--cycle with parameter

-Subprogram

There are three types of algorithms: (back to flipchart 7)

Linear

I'm getting upset Cyclical Linear algorithms

Butt 1(Flipchart side 9).

Kazka "Chicken Ryaba"

Rozgaluzhuvaniy algorithm- an algorithm that requires

The beginning of the singing mind is either one or another sequence of actions (flipchart side 10)

Full form (Flipchart side 11)

Uneven shape

butt 2. (Flipchart side 11)

(Flipchart side 12-13)

If you are ready, then open the parasol (the shape of the algorithm is not correct, which will be resolved). butt 3.

"Buy frosty".Cyclic algorithm- (Flipchart side 14)

butt 4. (Flipchart side 15.)

Algorithm "Napovnennya".

Nochalo Kinets

2. Primary fastening.

Version of training department

(collectively)(Flipchart side 16-17).

Learn to follow and fill in the flowcharts on the flipchart.

Training-task No. 1 (side of flipchart 18).

"Clean the kilim"

On the interactive board, following the help of the indicator, transfer the correct order of actions)

Training exercise No. 2 (back to flipchart 19).

Fill in the flowchart with the words “If you are sick, rejoice, but if you are healthy, take care.”

Name the type of the algorithm. Training assignment No. 3 (side of flipchart 20).

Check it out by dragging the drawing onto the right place.

Fizkultkhvilinka

(Flipchart side 21).

Let us lead with our hands -

Otherwise, we are drowning in the sea.

One two three chotiri -

The axis washed to the shore,

To pick up the brushes,

Pochnemo nahili vikonuvati -

We finalized the algorithm and reached the song mark: we rested, relaxed.

4. Vikonannya of practical robots.Working from different cards.

(Flipchart side 22).

And let us return to the words of the French scientist Gustave Guillaume: “The path is made by the one who walks, but computer science is weak.”

Indicate the arrows to which type of algorithm the image data should be assigned.

Give the algorithms a name (flipchart page 23).

Fill out the table with two butts for skin type to the algorithm (flipchart side 24).

Paint

Option 1.( flipchart side 25).

"Planting of the Sajanian."

Option 2.( flipchart side 26).

IV . Home improvement

(Flipchart side 27).

1. Vivchiti synopsis.

2. Draw on A4 format an example of a cyclic algorithm and a block - a diagram of the kazka “Kolobok”. V.

Lesson bag.

(Flipchart side 28). This is where the lesson ends. Our meta is reached.

We repeated the basic concepts of the algorithm, learned about the types of algorithms, successfully applied the knowledge practically, guessed fairy tales and proverbs.
VI
.

Reflection.

.

(Flipchart side 29).

What did you get to do in class today?

– What did you forget? - What was wrong?

VII. Evaluation. : Today you will have instead of an icon - emoticons, with which I will evaluate your success in class.

Addendum 2 .

We can guess what we learned last lesson.

Technological map No. 1

Lesson topic:

Types of algorithms: linear, cyclical, and uneven.

To begin with, we need to remember how geometric figures are formed when folding block diagrams.

Umovni assignments for block diagrams

(Flipchart side 5-6)

The beginning or the end of the program

- data entry

- dii

-Umova decided on the program

Objectives of the lesson

Let's learn how to classify the types of algorithms;

-Subprogram

There are three types of algorithms: (back to flipchart 7)

Linear Let's learn to represent algorithms in the form of flowcharts

Vikonanny tester zavdan z tester Linear algorithms

Butt 1 2. The theoretical part

Umovni assignments for block diagrams:

Rozgaluzhuvaniy algorithm- arrows – direct to the process

The beginning of the singing mind is either one or another sequence of actions (flipchart side 10) There are three types of algorithms: -linear

Full form

- An algorithm in which commands are listed in the order they are written, then sequentially one by one.

(Flipchart side 8)

butt 2.

(Flipchart side 12-13)

If you are ready, then open the parasol (the shape of the algorithm is not correct, which will be resolved). butt 1.

- An algorithm in which either one or another sequence of actions occurs.
In the verbal description of the algorithm, which is being solved, the words “like”, “that”, “otherwise” are used. (Flipchart side 14)

: “if the mind comes together, then... otherwise...”.

Dії transfer and under the hour of the vykonannaya of the mind, і for yo nekonannaі.

: “if the mind is changed, then …” The actions are transferred only for the mind.

Algorithm "Napovnennya".

3. ochalo Once upon a time, you have a new mind.

Training workshop No. 1.

Fold the “Clean the kilim” algorithm.

Training workshop No. 2.

1. Name the type of algorithm.

2. Save the algorithm.

Write down the following flowchart for help: “If you are sick, rejoice, but if you are healthy, take care.”

Training workshop No. 3.

Boy, let’s remember some readings, assignments from literature.

You read what you read once and try to complete it from memory.

Check it out by dragging the drawing onto the right place.

Fizkultkhvilinka

(Flipchart side 21).

Let us lead with our hands -

Otherwise, we are drowning in the sea.

One two three chotiri -

The axis washed to the shore,

To pick up the brushes,

Pochnemo nahili vikonuvati -

So in our work, we won’t tell you what to do without a lot of mercy.

The boy's ideas are like block diagrams.

4. Fizkultkhvilinka.

The boy's ideas are like block diagrams.

On the rack it’s five – sit down for the party.

The boy's ideas are like block diagrams.

Apply it

linear algorithm Paint rozgaluzhuvanogo algorithm

Option 1.( flipchart side 25).

"Planting of the Sajanian."

Option 2.( flipchart side 26).

cyclic algorithm

Add the algorithm to the program

, vikoryst commands for moving and copying.

Episode from the fairy tale “Geese and Swans”.

Programming means recording something from the wikis of someone else's little-known language.

With the development of this galusa knowledge, the students went even further and began to write down “shos”, but without understanding how it sounded Russian.

Beginners start writing code in C++ or PHP, vikoryst and impersonal libraries, and they still don’t understand how those who create them sound like their own people.

The computer cannot display the data, but it cannot be completed in the order indicated.

"What is a calculator?"

1. - Power up the vi.
2. It is also the fruit of many programmers who created the program, which creates algorithms for eliminating unnecessary results.
3. Let's look at the abstract situation.

What should you do if you ask someone to know the root of the square trinomial if they are not familiar with the methods of unraveling relationships?

Obviously, you need to learn how to unravel square equations.

• It follows this scheme:
• Select the method of release.
• Read all the details of the chosen method.
• Explain the first two points to the soon-to-be vicon with my knowledgeable mind.
• Then it will be possible to give the final solution to the square alignment.

And since the first two lines are simple and understandable - all methods of solving the description are described in the standard literature, then the third line is complex.

How can you guarantee that the ideas that are being advocated in the hour of great destruction will be accepted by the Vikonavians in the same way as you understand?

This is where we come to the point of understanding the algorithm.

Practice shows that in order to correctly explain what someone needs to follow the following steps:

calculate the output data (change the square ratio);

Massiveness.

Any algorithm that is decomposed for the most important task must be stagnant until it is specified for all valid output data.

Computer capabilities

p align="justify"> For the correct creation of algorithms on a computer, it is important to understand their capabilities.

Let's take a look at the magnitude of what EOM does.

They can be divided into numerical and textual, permanent and variable.

1. Under constant numbers we mean all numbers: 3.15, 100, 10 5 Their peculiarity is the invariability throughout all robot programs.
2. Variable values ​​change their meaning as the code is written and are usually indicated by letters: x, y, max, min etc.
3. Textual variables, like numeric ones, can be either permanent or variable.
4. The first option has just the text: “good”, “a i b” and in. The other has the same symbolic meanings, like numeric ones: name, city, etc.
5. to save such change.

Operations that involve building a computer:

Read data from storage devices (keyboard, mouse, files).

Calculation of values ​​using various mathematical functions: add, add, sin, cos, ln, etc. - each program has its own set of assigned functions.

Displaying data (on screen, on paper, web interface).

Transition between stages of software development.

Algorithmic language can be called a superior form of recording as opposed to verbal.

The design of the structure, as well as the design of the entrances, is discussed.

The downside of the verbal form and algorithmic language is the simplicity of the algorithm, which gets worse when its size increases.

• Therefore, these methods can be used instead of transmitting small algorithms to the senses.
• Types of algorithms
• There are a lot of algorithms created to accomplish various tasks.

For example, any teacher of high mathematics has hundreds of algorithms: unraveling a system of linear equations, finding extrema of a function, calculating an integral, etc. However, upon a detailed examination of their structure, it appears that All algorithms can be divided into several types.

Let's take a look at the types of algorithms and their applications.

linear (calculation of the result of addition and multiplication, exchange of values ​​of several units);

1. what is going on (the value of the largest number);
2. - Power up the vi.
3. cyclical (sorting by array, calculation by factorial).
4. These are the basic types.
5. Varto also notes that in the lower literature there is another fourth type - recursive.
6. However, there is no special meaning to the schematic notation and is implemented through the basic ones.

The report on the algorithm for calculating butts will be presented below.

Principles of algorithmization

Calculate the output data.

Linear

Linear is an algorithm in which the steps go sequentially one after another.

Any algorithm that does not compromise both cycles and linear ones.

Let's take a look at the example of the algorithm, which is such a problem: a hare and a hare sit in two cages, you need to switch their places.

The key to solving this problem is the additional temperature, which must be followed in order to replace the creatures.

Rozgaluzhuvani algorithms

As the name suggests, the algorithm is a bunch of needles.

The essence of the work lies in the choice of one of the possible options for the computational process depending on any mind.

1. Schematically, the layout is represented by a diamond-shaped block, in the middle of which there is a mind, and on the sides of it there are piles of choice, depending on whether it is true or not.
2. The algorithm that breaks down and the application of its stagnation can be found everywhere.
3. The program has a typical if-else structure, which is also possible.
4. Let's use the algorithm to solve the problem of finding the greatest middle of three numbers.

Cyclic algorithm

A cyclical algorithm is one in which there are numerous repetitions of the same steps, in which changes can be made without the significance of the specific change for which the expansion is carried out.

Types of the cyclic algorithm and its application will be discussed below, but for now we will reconsider the main deadlines for the wake-up cycle.

Prevalence of the cob value of the seeds.

• Without Vikonannya, the mental cycle, which covers everything, will not be able to work, otherwise you will be rewarded.
• Block for calculating results.
• This is the whole body of the cycle.
• Genetic algorithms.

Bring biological ideas to your work.

In fact, the most widely used forms of representation of algorithms are:

· verbal (natural writing);

· graphic (images with graphic symbols);

· pseudocodes (formalized descriptions of algorithms in mental algorithmic language, which include both elements of our programming, phrases of natural language, conventional mathematical notations, etc.);

· Program (text movami programming). Verbal method

recording algorithms is a description of the subsequent stages of data processing.

The algorithm is specified in a sufficiently natural way.

For example.

Write down an algorithm for finding the largest dilator (NDD) of two natural numbers.

The algorithm can buti will advance:

· Set two numbers;

· If the numbers are equal, then take one from them as evidence and compare,

Otherwise, continue with the algorithm;

· Program (text movami programming).· Calculate more than the numbers;

· Replace the larger number with the difference of the larger and smaller numbers;

· Repeat the algorithm from step 2.

Descriptions of the algorithm are limited to any natural numbers and can lead to the maximum of the given task.

There is no wide expansion for the following reasons:· Such inventories are not strictly formalized;

· suffer from a wealth of records; · Allow for ambiguity in the misunderstanding of certain attributions. Graphic method The expression of algorithms is more compact and similar to verbal ones.

This graphical manifestation is called

algorithm diagram

or else

block diagram.

When presented graphically, the algorithm is displayed as a sequence of interconnected functional blocks, each of which represents one or more actions.

The block diagram for each type of action (entering output data, calculating the value of expressions, changing minds, managing repetitions of actions, completing processing, etc.) is represented by a geometric figure, presented in the form of a block symbol.

Block symbols are connected by transition lines, which indicate the viciousness of the final action.

Represents a solution for either a switching function with one input or two or more alternative outputs, of which only one can be used after calculating the outputs from the middle element.<, =); в программировании − условные операторы if (два выхода: true, false) и case (множество выходов).

The entry element is indicated by a line, which indicates the entry at the top vertex of the element.

If there are two or three exits, then the skin exit is indicated by a line that comes out of the tops that have been lost (side and bottom).

If there are more than three exits, their traces are shown with one line that comes out from the top (usually the bottom) of the element, which is then unraveled.

The following calculation results can be recorded using the lines that represent the steps.

Apply the decision: in the zagalny variant - povnyannya (three outputs: >,