From 50a2ade2ca034634d83848e188f05790d020eb18 Mon Sep 17 00:00:00 2001 From: egorzhurov Date: Mon, 13 May 2024 20:32:32 +0300 Subject: [PATCH] Move 45 article to markdown format --- .../java-core/045/Algorithms Complexity.md | 156 ++++++++++++++++++ lessons/java-core/045/schedule.png | Bin 0 -> 111243 bytes lessons/java-core/045/timeComplexity.png | Bin 0 -> 692450 bytes 3 files changed, 156 insertions(+) create mode 100644 lessons/java-core/045/Algorithms Complexity.md create mode 100644 lessons/java-core/045/schedule.png create mode 100644 lessons/java-core/045/timeComplexity.png diff --git a/lessons/java-core/045/Algorithms Complexity.md b/lessons/java-core/045/Algorithms Complexity.md new file mode 100644 index 0000000..443d2d0 --- /dev/null +++ b/lessons/java-core/045/Algorithms Complexity.md @@ -0,0 +1,156 @@ +# Сложность алгоритмов. Первое знакомство + +**Сложность алгоритмов** (или **вычислительная сложность алгоритмов**) – математическая функция, демонстрирующая +примерную зависимость **времени выполнения** алгоритма (или **потребляемой памяти**) в зависимости от числа элементов. + +Данная тема достаточно важна для того, чтобы сравнивать различные алгоритмы между собой. Сюда же можно отнести выбор +структуры данных (в нашем случае – актуально при выборе коллекций, в первую очередь) в зависимости от задачи – поскольку +определенные структуры данных используют определенные алгоритмы для вставки, удаления и поиска значений – можно сделать +сравнительный анализ сложности используемых ими алгоритмов и руководствоваться таким анализом при выборе конкретной +структуры данных. + +Я не могу сказать, что данную тему стоит изучать досконально на ранних этапах, но общее представление о ней стоит иметь. +Как минимум, чтобы знать о том, что такие подходы существуют и их можно использовать при необходимости. + +В рамках данного урока мы разберем классические примеры операций, по использованию которых можно оценить сложность +алгоритма (преимущественно, временную) и рассмотрим сложность операций в различных типах коллекций в Java. + +Поскольку тема сложности алгоритмов достаточно востребована различными специалистами (включая разработчиков +безотносительно используемого ими ЯП), материалов, в т.ч. русскоязычных, достаточно много. Поэтому вы можете +воспользоваться как предлагаемыми мной ссылками, так и найти иные источники, которые вам покажутся доступными (если +таковые будут – не стесняйтесь делиться в комментах). + +Начать предлагаю со [статьи](https://tproger.ru/articles/computational-complexity-explained/) + +Очень короткая и очень простая статья, не дающая полного представления, но очень удачная, чтобы начать свой путь в теме +сложности алгоритмов. + +Из нее рекомендую отметить следующие моменты: + +- Сложность алгоритма не дает информацию о затрачиваемом времени (или памяти) в абсолютным величинах. Впрочем, этого + обычно и не требуется; +- Что такое **О-нотация**. Рекомендую ознакомиться отдельно, если этот термин незнаком. Хотя бы на Википедии или в + другом источнике на ваш выбор; +- _n_ – количество элементов, обрабатываемых алгоритмом; +- Конечная сложность алгоритма, может быть представлена как в виде нескольких слагаемых (например, _log(n) + n2_), так и + в виде какого-то константного коэффициента в функции (скажем, _7log(n)_) и прочих вариациях на тему. За редким + исключением (например, _nlog(n)_), все «вторичные» элементы выражения игнорируются, оставляя лишь то, что в большей + степени влияет на сложность: (_log(n) + n2) → n2_, _7log(n) → log(n)_; +- Примеры. Они описывают лишь **линейную**, **квадратичную** и **логарифмическую сложность**, но вполне доступны. + Алгоритмы, приводимые в пример – просты и их легко разобрать, даже если ранее они вам не встречались. Единственное, + для квадратичной сложности я бы привел в пример **сортировку пузырьком**. Она имеет ту же сложность, но чаще известна + новичкам. + +В целом, рекомендую запомнить следующие варианты сложности алгоритмов и общий сценарий их возникновения: + +1. _О(1)_. Сложность алгоритма не зависит от числа элементов. Получение длины массива, например; +2. _О(n)_. **Линейная сложность**. Например, обход массива циклом; +3. _O(n²)_. В общем случае можно представить как _O(nᵐ)_ (да простят меня за такие обобщения). Классический пример – + вложенные циклы с полным перебором. Как пример квадратичной сложности – упомянутая выше сортировка пузырьком, в общем + случае – сложность алгоритма будет зависеть от числа вложенных циклов: при полном перебора элементов в 4 вложенных + друг в друга циклах, _m = 4_, сложность алгоритма – _О(n⁴)_; +4. _О(log(n))_. **Логарифмическая сложность**. Пример алгоритма – бинарный поиск в массиве, приводился в статье по + ссылке выше. Альтернативный пример – поиск элемента в бинарном дереве поиска. По сути, каждая итерация алгоритма + будет вызвана на _n/2 (3, 10, m)_ множестве данных, в сравнении с предыдущей. Где _2 (3, 10, m)_ будет основанием + логарифма, но обычно им пренебрегают (в целом, почти всегда – 2); +5. _O(nlog(n))_. Все то, что вы сможете нагуглить по фразе «разделяй и влавствуй» в алгоритмизации. Сюда можно отнести + большинство эффективных сортировок: **quicksort** (исключая худший случай), **merge sort** и т.д. Суть сводится к + рекурсивной обработке массива данных с уменьшением этого массива в _2 (3, 10, m)_ раз, указывающем на основание + логарифма, но, в отличии от алгоритмов поиска, с перебором элементов на каждой итерации. В наиболее общем случае + можно представить как совокупность рекурсивных вызовов(каждый вызов порождает _2 (3, 10, m)_ новых) и цикла (или + нескольких циклов, но без вложенности). + +Факультативно могу предложить рассмотреть заодно: + +- _О(2ⁿ)_. В более общем случае, можно представить как _mⁿ_. **Экспоненциальная сложность**. Пример – рекурсивный поиск + чисел Фибоначчи. Или полный перебор возможных значений строк заданной длины. _m_ – количество возможных символов, + _n_ – длина строки. В общем, весь возможный спектр алгоритмов, где каждая итерация увеличивает обрабатываемое + множество данных в _2 (3, 10, m)_ раз; +- _О(n!)_. **Факториальная(?) сложность**. Классических примеров в контексте алгоритмов, честно говоря, не знаю, но + логика подсказывает думать в сторону комбинаторики. Вики подсказывает + решение [задачи коммивояжера](https://ru.wikipedia.org/wiki/Задача_коммивояжёра) методом полного перебора. + +Последние два пункта вряд ли понадобятся вам на практике, но ярко демонстрируют, насколько затратные алгоритмы можно +реализовать. + +> !NB: Уже написав большую часть урока наткнулся на неплохую +> [статью](https://techrocks.ru/2020/07/15/big-o-explanation-for-newbies/) с примерами + +В качестве визуализации – график роста О-большого для алгоритмов разной сложности. +[Источник](https://habr.com/ru/post/188010/) + +![img.png](schedule.png) + +Не уверен, что стоит погружаться тем, кто впервые познакомился с темой, но некоторые графические материалы там довольно +интересны. Так что советую посмотреть, но не переживать, если что-то будет непонятно. + +[Бесплатный бонус](https://tproger.ru/translations/algorithms-and-data-structures/). +Еще одна статься для начинающих. Тоже общие термины, классические примеры. Бонусом - понятие наилучшего, среднего и +наихудшего случаев. Чуть ниже мы его коснемся. + +В целом - советую изучить все представленные ссылки. Тема тяжела для восприятия, если ранее с ней не были знакомы. +Повторенье - мать ученья:) + +## О наших баранах и Java + +Как уже было сказано, сложность алгоритма может быть применена в отношении потребляемой памяти или в отношении +затрачиваемого времени. Мой опыт говорит, что временная сложность имеет большее значение в современной Java-разработке, +поскольку дефицита памяти на горизонте не видно. Но в данном случае на истину не претендую. + +Также стоит отметить, что оценка сложности, как правило, проводится для худшего и среднего случаев (где это имеет +смысл). Иногда – еще и для лучшего. И это имеет смысл. + +Скажем, для лучшего случая (сортировки уже отсортированного массива) сортировки пузырьком, временная сложность будет +_O(n)_, а вот для классической реализации quicksort временная сложность в лучшем и среднем случае – _O(nlog(n))_. + +Соответственно, в ситуации, когда в вашу функцию сортировки в 90% случаев приходит уже отсортированный ранее массив и +лишь в 10% случаев – не отсортированный, возможно, стоит использовать именно сортировку пузырьком:) + +Касательно сложности операций в различных java-коллекциях – предлагаю картинку ниже: + +![img.png](timeComplexity.png) + +Она уже знакома тем, кто читает чаты, но может быть в новинку для остальных. + +Опираясь на нее, можно, например, сделать вывод, что `TreeMap` – лучший выбор, если вы предполагаете частый (в сравнении +с операциями вставки и удаления) перебор всех значений в отсортированном виде - именно тогда может иметь значение +порядок элементов. Но, для ситуаций, когда вставка/удаление значений происходит чаще, чем подобные операции – выгоднее +использовать `HashMap`. + +К слову, в отношении последней (а также ее наследников и связанных _Set_’ов) советую особо не переживать насчет худших +показателей – они представлены для некорректно определенных хэшкодов – по сути, для ситуации, когда все значения (пары) +оказались в одном бакете и представляют собой связный список. + +## В качестве заключения + +Сложность алгоритмов – достаточно серьезная тема. Но главное, что стоит помнить о ней – она показательна на объемах +данных, стремящихся к бесконечности. И абсолютные затраты времени на малых объемах данных могут быть выгоднее в +алгоритмах, которые на большом объеме совершенно неэффективны. + +Вторым важным пунктом стоит отметить, что сравнивать различные алгоритмы (особенно – эффективность различных структур +данных) стоит тогда, когда с выбранной структурой будет производиться множество операций. Иными словами – помните о +накладных расходах. + +Скажем, нет смысла превращать ваш `ArrayList` в `TreeSet` ради единичной операции поиска – создание новой структуры +(с _N_ вставками) будет куда дороже, чем потенциальный выигрыш от более эффективного поиска. Зато это может иметь +смысл, если структура будет инициализирована единожды, в количество проверок на вхождение будет многократно превышать +число элементов в ней. + +К сожалению, это очевидно на банальных примерах, но не всегда очевидно на практике. + +#### На сегодня все! + +Урок теоретический. В качестве практики могу предложить воспроизведение основных операций для различных коллекций – +посмотрите, на каких объемах данных выигрыш у различных коллекций станет ощутим. Самый простой способ измерить разницу +во времени – использовать `System.nanoTime()` или `System.currentTimeMillis()` до и после замеряемых операций и считать +их разность. + +![img.png](../../../commonmedia/justTheoryFooter.png) + +> Если что-то непонятно или не получается – welcome в комменты к посту или в лс:) +> +> Канал: https://t.me/ViamSupervadetVadens +> +> Мой тг: https://t.me/ironicMotherfucker +> +> **Дорогу осилит идущий!** \ No newline at end of file diff --git a/lessons/java-core/045/schedule.png b/lessons/java-core/045/schedule.png new file mode 100644 index 0000000000000000000000000000000000000000..267c6b6ebca17ce646ea20af38d5a7539d3f85e0 GIT binary patch literal 111243 zcmeFZRa9M1&^;L3-QC^&;z0tz-5r7ig1hUzxP%ZO1b25QxCSSAh#RBf4&#A7is@{87AHtOtrBM(G5#POgha&S)QuW@EmzghiT%6#4kG4y|14|@3#0( z=l3{b>dkySzuWdCn{OzdE;~+iR?=E7Mtd*$?-C8`{1Ntc?eXBJhX4D~F!=xfFf8o< z#UXnc?-78xq^{H3g@r{DIr0p|S@n4#rEP@Y^YZ8!7^P%nV2X+I;!5PFm`c-ymz&-vzDrn 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