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Типы
алгоритмов
Аl=
3;горитм
- это точная
инструкция
исполнителn=
2;,
в понятной
для него фор=
ме,
определяющk=
2;я
процесс дос=
тижения
поставленнl=
6;й
цели на
основе имею
=
97;ихся
исходных
данных за ко=
нечное
число шагов.
Аl=
3;горитм
считается
правильным,
если его вып=
086;лнение
дает
правильный
результат.
Соответствk=
7;нно
алгоритм
содержит
ошибки, если
можно
указать
такие
допустимые
исходные
данные или
условия, при
которых
выполнение
алгоритма
либо не
завершится
вообще, либо
не будет пол=
091;чено
никаких
результатоk=
4;,
либо получе
=
85;ные
результаты
окажутся
неправильнm=
9;ми.
=
52;ожно
выделить тр
=
80;
крупных
класса
алгоритмов: =
вычислителn=
0;ные,
информациоl=
5;ные
и управляющ
=
80;е.
Вm=
9;числительн=
099;е
алгоритмы,
как правило, =
1088;аботают
со
сравнительl=
5;о
простыми
видами
данных
(числа,
матрицы), но
сам процесс
вычисления
может быть
долгим и
сложным.
&=
#1048;нформацион=
;ные
алk=
5;оритмы
представляn=
2;т
собой набор
сравнительl=
5;о
простых
процедур, но
работающих
=
89;
большими
объемами
информации
(таковы алго=
088;итмы
в базах
данных).
У=
1087;равляющие
алk=
5;оритмы
характерны
тем, что
данные к ним =
1087;оступают
от внешних
процессов,
которыми он
=
80;
управляют.
Результат
работы этих
алгоритмов
различные
управляющиk=
7;
воздействиn=
3;.
Дl=
3;я
записи
алгоритмов
используют
самые разно
=
86;бразные
средства.
Выбор
средства
определяетl=
9;я
типом
исполняемоk=
5;о
алгоритма.
Для исполни
=
90;еля-человек&=
#1072;
обычно
используют
привычные
средства
родного
языка и
математики,
графическиk=
7;
средства,
специальныk=
7;
учебные язы
=
82;и.
Для
компьютера
применяют
языки прогр
=
72;ммирования
и языки
заданий
(программа,
командные
файлы).
В
информатикk=
7;
для записи
алгоритмов
обычно
используют &=
#1073;лок
- схемы, в
которых
каждое
действие
алгоритма
обозначаетl=
9;я
определённl=
6;й
геометричеl=
9;кой
фигурой, а
порядок
выполнения
действий ук
=
72;зывается
стрелками. Н=
072;пример:

Основны=
;е
алгоритмичk=
7;ские
конструкциl=
0;.
При
составлениl=
0; алгоритмов
довольно ча
=
89;то
встречаютсn=
3; случаи,
когда
некоторую
последоватk=
7;льность
команд нужн
=
86;
выполнить
несколько
раз подряд. В
таких
ситуациях
используют
управляющуn=
2;
структуру ЦИКЛ,
которая
организует
многократнl=
6;е
выполнение
=
91;казанного
действия.=
Циклом
называют
такую форму
организациl=
0; дейст=
;вий в
алгоритме, =
087;ри
которой одн
=
72;
и та же
последоватk=
7;льность
действии (Р)
выполняетсn=
3;
несколько
раз (или ни
разу), в
зависимостl=
0;
от
выполнения некот=
;орого
условия (Q=
span>). Такой
способ
организациl=
0;
действий
также назыв
=
72;ют
повторениk=
7;м.
Используетl=
9;я
несколько
различных
форм записи
циклов.
1)
ЦИКЛ
ПОКА или цикл с п=
088;едусловие&=
#1084;.
Словесная
запись этог
=
86;
цикла
выглядит та
=
82;:
Пока имеет место=
;
условие Q
выполнять Р ил=
и
в
сокращенноl=
4; (стандартно&=
#1084;)
виде:
ПОКА h=
2;ЫПОЛНЯЕТСЯ
(Q) , ДЕЛАТЬ=
; (Р).
Блок-схема
этого цикла
следующая:=
=
=
Выпол=
;нение
цикла ПОКА
начинается
=
89;
проверки
условия. Пер=
077;ход
к выполнени=
02; действия
P имеет
место тольк
=
86;
в том случае, &=
#1077;сли
выполняетсn=
3;
условие. В
частности
может оказа
=
90;ься,
что действи
=
77; P не будет
выполнено н
=
80;
разу, если с с&=
#1072;мого
начала
условие не
выполняетсn=
3;. Для
того, чт
=
86;бы
цикл не повторялс=
03;
бесконечно, =
085;еобходимо
в теле цикла
осуществлn=
3;ть
действия, пр=
080;водящие к увели=
;чению
ложности.
2)
ЦИКЛ
ДО-ци&=
#1082;л
с
постусловиk=
7;м
Повто=
;рять
Р дl=
6;
момента
наступлениn=
3;
условия Q
<=
span
style=3D'font-size:12.0pt'>Блок-схk=
7;ма
этого цикла
такова:
Цикл ДО
начинает
работать с
осуществлеl=
5;ия
действия P.
Таким обl=
8;азом
тело цикла
будет:
выполнено
хотя бы один
раз. В этом ег&=
#1086;
отличие от
цикла ПОКА. П=
1086;сле
выполнения
=
90;ела
цикла Р
проверяетсn=
3; условие
Q и, если
оно не
выполняетсn=
3;,
происходит
переход к по=
074;торному
выполнению.
цикла. Когда
условие
выполняетсn=
3;, происходит
выход из
цикла. Здесь
также
необходимо
позаботитьl=
9;я
о том,
=
95;тобы
в теле цикла
происходилl=
0;
преобразовk=
2;ния
в сторону истин=
085;ости
условия Q.<=
/p>
В
обоих
вышеприведk=
7;нных
циклах коли
=
95;ество
повторений
=
94;икла
заранее
неизвестно, =
085;о
часто бывае
=
90;
известно
сколько раз
необходимо &=
nbsp; выполнит=
ь
цикл. В этих с&=
#1083;учаях
используют
=
94;икл
с параметро
=
84;.
3) ЦИКЛ С
ПАРАМЕТРОМ =
(цикл n-раз,ц=
1080;кл
для каждого, =
1072;рифметичес=
кий
цикл).
Можно
записать ег
=
86;
так:
Для кk=
2;ждого
значения
параметра
,изменяющег
=
86;ся
от А до В =
1089; шагом
С выполнять =
056;.
Или в
стандартноl=
1;
форме:
Для I=3DА до В ша=
;г
С выполнять =
056;.
Блок-схему
этого цикла
можно предс
=
90;авить
так:
&nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; Перем=
077;нная
I
называетсn=
3; парам=
1077;тром
цикла или
=
I:=3DA &nbs=
p; &=
nbsp; &=
nbsp; счетчик&=
#1086;м
цикла. Тело ц=
1080;кла
выполняетсn=
3; при
=
&nb=
sp; =
&nb=
sp; =
каk=
8;дом
значении
параметра I в
границах от А до
=
&nb=
sp; =
&nb=
sp; =
В с
заданным
шагом С.
=
&nb=
sp; =
&nb=
sp;
да
=
&nb=
sp;
I>B
=
&nb=
sp;
нет
=
=
P
=
&nb=
sp;
I:=3DI+C
<=
/p>
=
1042; пpоце
=
89;се
pешения
большинствk=
2;
задач
возникает
необходимоl=
9;ть
в зависимос
=
90;и
от
выполнения некотоpог=
086;
условия
=
87;pоизводить
те или иные д=
1077;йствия.
Hапpи
=
84;еp
- вести
вычисления
либо по
одним,
либо по =
076;pугим
фоpмулам.
Вычислитеl=
3;ьный пpоцесс в
этом случае pеализует=
089;я
по одному из
нескольких, за=
;pание
пpедусмо
=
90;pенных
напpавле
=
85;ий
или Вh=
5;ТВЕЙ,
а алгоpит=
084;, pеk=
2;лизующий такой=
; пpl=
6;цесс
называется РАЗВЕ=
1058;ВЛЯЮЩИМСЯ.
Для этих
целей в а=
083;гоpитмах
используютl=
9;я
специальнm=
9;е уп=
;pавляющие
стpуктуpы -ВЕТВЛЕ=
053;ИЕ
или РА=
;ЗВИЛКА.
ВЕТВ=
ЛЕНИЕ
- это такая
форма
организациl=
0;
действий в ал=
;горитме,при
которой в
зависимостl=
0;
от
выполнения
или невыпол
=
85;ения
некоторого
условия
совершаетсn=
3;
либо одна,
либо другая
последоватk=
7;льность
действий.
Слова=
ми
это можно
записать та
=
82;:
=
45;сли
имеет место
условие Q, то
исполнять S1, иначе
исполнять S2.
Или в
стандартноl=
1;
форме:
=
45;сли
Q, то S1-l=
0;наче
S2. <=
o:p>
В тех сл=
;учаях,когда
альтернатиk=
4;ное
действие S2
отсутствуеm=
0;,
используеm=
0;ся
короткая
запись:
=
45;сли
Q, то S.
=
1058;акая
форма запис
=
80;
ветвления
называется
СОКРАЩЕННi=
4;Й, в отлич=
;ие от=
ПОЛНОЙ,
приведенноl=
1;
выше.
В
графическоl=
4;
виде
(блок-схема)
обе формы мо=
078;но
представитn=
0; следу=
;ющим
образом:
<=
/p>

=
Да =
&nb=
sp; Нет =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
Да
<=
/p>
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
=
&nb=
sp; Нет
=
<=
/p>
=
Полная m=
2;орма =
&nb=
sp;
=
&nb=
sp; Сок=
1088;ащенная
форма
В
тех случаях, когда=
; S1 и S2
реализуютсn=
3;
целым
набором
действий,
имеющим
длинную
запись,
возникает
необходимоl=
9;ть
точно
обозначить
начало и кон=
077;ц
такой
записи.
Иногда для
этого испол=
00;зуют
слова-огран
=
80;чители:
НАЧАЛО и
КОНЕЦ. Иногд=
072;
для указани=
03;
любого мест
=
72;,
где
заканчиваеm=
0;ся S2
используюm=
0; слово
ВСЕ.
Окончание S1
осуществляk=
7;т
слово ИНАЧЕ.
Например:=
Если
Q то S1 иначе S2
все
Разветв=
;ляющиеся
алгоритмы.
Команда вет
=
74;ления.
1. Алгорит=
;м-
это понятно
=
77;
и точное
предписаниk=
7;
исполнителn=
2;
выполнить
конечную
последоватk=
7;льность
команд,
приводящую
от исходных
данных к
искомому
результату.
Всякий
алгоритм
составляетl=
9;я
из простых к=
086;манд,
команд обра
=
97;ения
к
вспомогатеl=
3;ьным
алгоритмам
=
80;
структурныm=
3;
команд. К =
089;труктурным<=
/span>
относятся
команда
ветвления и
команда цик
=
83;а.
=
Ветвлен=
;ие-(развилl=
2;а)-это
алгоритмичk=
7;ская
альтернатиk=
4;а.
По этой
команде
исполнителn=
0;
выбирает
один из двух
путей исl=
7;олнительна=
103;
алгоритма с
непременныl=
4;
выходом на
общее
продолжениk=
7;.
Выбор
происходит
по
какому-либо
условию. В
блок-схемах
алгоритмов
(графическо
=
84;
представлеl=
5;ии
алгоритмов) =
080;
на учебном
алгоритмичk=
7;ском
языке
ветвление
представляk=
7;тся
так:
=
&nb=
sp; =
=
&nb=
sp; Если(усло
=
74;ие)
то (версия
1) иначе
(серия 2) конец=
<=
/p>
Здесь
(серия 1) и
(серия 2)-это в
общем случа
=
77;
некоторые
последоватk=
7;льности
на продолжи
=
90;ельной
ветви (да) и
отрицательl=
5;ой
ветви (нет)
ветвления.=
Вот
пример
использоваl=
5;ия
ветвления в
бытовой сит
=
91;ации.
Если
на улице иде=
090;
=
Дождь тl=
6;
надеть
сапоги
Иначе
надеть туфл
=
80;
=
Конец
ветвления.=
Выйти иk=
9;
дома
Да &n=
bsp;  =
; &n=
bsp;  =
; &n=
bsp;
нет
|
<=
/p>
Если же
на ветви (нет)
отсутствуеm=
0;
последоватk=
7;льность
команд, т. е.
(серия 2)
отсутствуеm=
0;,
то такое
ветвление
называется
неполным. Во=
090;
пример непо&=
#1083;ного
ветвления и=
з
той же
бытовой
серии:
&n=
bsp;
Да &n=
bsp;  =
; &n=
bsp;
нет
&n=
bsp;
|
<=
/p>
=
Если на улиц
=
77;
идет дождь=



То взятn=
0;
зонт
=
Конец
ветвления<=
/span>
Вый
=
90;и
из дома
<=
/p>
простым=
;и
командами
являются
команды при
=
89;ваивания,
ввода и
вывода. В
качестве
условия в ве=
090;влении
используетl=
9;я
логическое
выражение.=
Пример.
Дано х
- значение
аргумента.=
Найти у R=
11;
значение
функции.
Связ=
ь у=3D {х,
если х>-0
{x, если х<0.
На
алгоритмичk=
7;ском
языке
алгоритм
выглядит та
=
82;:
Алг. Модуль
=
Вещ. X, =
y,
Нач. ввод x
=
Если x>_0
=
То y:=3D-x
=
Конец
ветвления =

Вывод <=
u>y
Кон.
Эту же
самую задач
=
91;
можно решит=
00;
путем испол=
00;зования
неполной
формы
ветвления.
&n=
bsp;  =
; &n=
bsp;  =
;
Да
&n=
bsp;
&n=
bsp;  =
; Не=
;т
|
<=
/p>
Если на
ветвях
развилки в
свою очеред=
00;
находятся
ветвления, т=
086;
говорят, что
такой алгор
=
80;тм
имеет
структуру в&=
#1083;оженных
ветвлений. <=
/o:p>
Пример.=
Дано:A, D, =
C.
Найти: D =3Dmax =
(A, B, C). =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Цикличе=
;ские
алгоритмы.
Команда
повторения.
1. Алгорит=
;м
- понятное и
точное
предписаниk=
7;
исполнителn=
2;
выполнить
коночную
последоватk=
7;льность
команд,
приводящую
от исходных
данных к
искомому
результату.
Всяки=
й
алгоритм
составляетl=
9;я
из простых
команд,
команд- обращ=
;ений
к
вспомогатеl=
3;ьным
алгоритмам
=
80;
структурныm=
3;
команд. К “ структурны=
м
“ относятся
команда
ветвления и
команда
цикла.
Цикл-это
команда
исполнителn=
2;
многократнl=
6;
повторить
указанную
последоватk=
7;льность
команд.
Однако
слово “
многократнl=
6;”
не значит “д=
086;
бесконечноl=
9;ти”.
Организациn=
3;
циклов,
никогда не
приводящая
=
82;
остановке в
выполнении
алгоритма,
является
нарушением
требования
его результ
=
72;тивности-
получения
результата
за конечное
число шагов.
&n=
bsp;  =
; &n=
bsp;
P
&n=
bsp;  =
;
Да &n=
bsp;  =
; &n=
bsp;
нет
|
Рассмотриl=
4; графичесl=
2;ое
представлеl=
5;ия
циклическоk=
5;о
алгоритма. В
него входят =
074;
качестве
базовых
следующие
структуры:
блок
проверки
условия P и блок S,
называемый &=
#1090;елом
цикла, Если
тело цикла S расположен=
;о
после
проверки
условий P (цикl=
3;
с предусло
=
74;ием).
То может
=
89;лучится,
что при
определеннm=
9;х
условиях
блок =
S не выпо
=
83;нится
ни разу.
Такой
вариант
организациl=
0;
цикла,
управляемыl=
1;
предусловиk=
7;м,
называетсn=
3; &=
#1094;икл
- пока.
=
Пока P повторить=
;
S
Конец=
цикла=
;
=
=
=
=

Если
условие P н=
е
выполняетсn=
3;,
то
происходит
выход из
цикла на
команду, зап=
080;санную
после строк
=
80; “конец
цикла “,
Здесь
условие P –
это условие
на
продолжениk=
7;
цикла.
<=
/p>
Возможе=
;н
другой
случай, когд=
072;
тело цикла S
Выполня=
;ется
по крайней
один раз и
будет
повторя=
;тся
до тех пор,
пока не
станет исти
=
85;ным
условие=
; P.такая
организациn=
3;
цикла, когда
его
тело
расположенl=
6;
перед
проверкой
условия P,
носит
название
цикла с
постусловиk=
7;м,
или
цикла – до.
Истинность
условия P в этом
случае-
условие
окончания
цикла.
Отметим=
;,
что возможн
=
72;
ситуация с
постусловиk=
7;м
и при
организациl=
0;
цикла –пока.
Итак, цикла –до=
завершаетl=
9;я,
когда
условие P с=
тановится
истинным, а
цикл –пока
–когда P
становился
ложным.
Другими
словами,
цикл-до
выполнятся R=
21;до”
истинности
условия, а
цикл – пока
выполняетсn=
3;,
указанное
логическое
выражение
остается
истинным. Со=
074;ременные
языки
программирl=
6;вания
имеют
достаточныl=
1;
набор
операторов,
реализующиm=
3;
как цикл-=
087;ока,
так и цикл – до.
Отметим
основное
отличительl=
5;ое
свойство
циклическиm=
3;
алгоритмов;
количество
действий,
исполняемы
=
74;
процессе
работы
такого
алгоритма,
может сущес
=
90;венно
повышать
количество
команд, сост=
072;вляющих
тело цикла.
В блок - схемах
алгоритмов
(графическо
=
84;
представлеl=
5;ие
алгоритмов) =
080;
на учебном
алгоритмичk=
7;ском
языке цикла
пока
представляk=
7;тся
так:
<=
/p>
<=
![if !vml]>
|
|
Да &n=
bsp;  =
; &n=
bsp;  =
; &n=
bsp;
не
=
90;
&n=
bsp;
|
|
<=
/p>





Цикл –=
; до
представляk=
7;тся
аналогичнl=
6;.
Пример.=
Зад
=
72;ча
построить
таблицу
значений =
Функции=
; y=3Dtg x
на
отрезке [A, B] с
шагом
H.
Дано: A- начk=
2;льное
значение
аргумента,=
B- l=
2;онечное
значение
аргумента,

H- шаг
изменения
аргумента.=
Найти: Y- знаm=
5;ение
функции.
Связь: y=3D t g x,
где x=3D a, a+ =
h, …, B.<=
o:p>
Здесь
тело цикла
состоит из
двух команд:
вычисление
=
91;
и печать
значения
аргумента х и
соответствm=
1;ющего
ему значени=
03;
функции m=
1;.
Коман&=
#1076;а
x=3D x+ h осуществ=
;ляется
переход к
следующему
значению
аргумента х.
Проверка
условий, сто=
103;щая
после
выполнения
цикла (X> b),
показывает,
что это цикл
– до.
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