From d4d1e44cff51ceff63df491a31ce74f553675f10 Mon Sep 17 00:00:00 2001 From: Aleksey Lobanov Date: Tue, 9 Aug 2016 22:39:48 +0300 Subject: [PATCH] Added compression --- .gitignore | 1 + archives.html | 55 +- archives.html.gz | Bin 0 -> 1464 bytes author/aleksei-lobanov.html | 167 +----- author/aleksei-lobanov.html.gz | Bin 0 -> 3339 bytes authors.html | 41 +- authors.html.gz | Bin 0 -> 1054 bytes categories.html | 42 +- categories.html.gz | Bin 0 -> 1042 bytes category/misc.html | 111 +--- category/misc.html.gz | Bin 0 -> 2509 bytes category/proekty.html | 108 +--- category/proekty.html.gz | Bin 0 -> 2167 bytes category/project-euler.html | 80 +-- category/project-euler.html.gz | Bin 0 -> 1743 bytes feeds/all.atom.xml.gz | Bin 0 -> 2320 bytes feeds/all.rss.xml.gz | Bin 0 -> 2368 bytes feeds/feed.atom.xml.gz | Bin 0 -> 2319 bytes feeds/feed.rss.xml.gz | Bin 0 -> 2368 bytes feeds/misc.atom.xml.gz | Bin 0 -> 1475 bytes feeds/proekty.atom.xml.gz | Bin 0 -> 1043 bytes 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Archives for Блог 529

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Пт 22 Июль 2016
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Нахождение суммы k-ых степеней
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Чт 17 Март 2016
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Wallabag и реальная жизнь
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Вс 10 Январь 2016
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Как я шахматного бота писал
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Вс 02 Август 2015
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CrossGen v1.0
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Пт 17 Июль 2015
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Моё решение задачи 60
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Пт 03 Июль 2015
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Ещё одно вычисление выражений
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Пт 17 Апрель 2015
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Мой первый пост
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- - - - - \ No newline at end of file + \ No newline at end of file diff --git a/archives.html.gz b/archives.html.gz new file mode 100644 index 0000000000000000000000000000000000000000..c32767d62ba72e19da17b3bf03072ca56dd278a1 GIT binary patch literal 1464 zcmV;p1xNZHiwFP!000021GQIMZ`4KsBDBwhEza}KUs$mCa^mz4k ztooX(wNdNPG8G}~u3)?!Z9LQgqJ1FDv4e!!%Re%s5O$%xi+|~e@ebz-iITATSw1Gz z5ER5jX=?mhX1W+SzhjP#Nin^avA$pX7GIjj3o=QGVI59uD3HQX0lsG!eHuoz9>hu} z)NhW5G0bq<&L8D3^UeGzIy!T_^`yDIa#l!n?PoV&!x#J!&ITJ=6P zlBUoe#2!D-+NMieNrG@gl^_NVetCZV+W4VH^ROG8hQKxC{SP8a>%Dk@>EJZJzHng| z7L}$Tt%B{;UDaM61X3z5ks*X+s|wG!v+hh;3oD~7ukstor?;)2t&R+bWAWdeH*YPa zHQkcuN*}ul#H-f6EHgwDMVV$ILPP*dqoj!1GBY8(UkLEk0_rF^&{Vl-3A$8M)FL}m zTG?Yr+OTZkT02W4MM8>(GE-abEswO3RPT8Y27}QFsJeffq<2cukSQ7%->3{YlfbY( za6@Ox{b-@wi%#3kWq2bIOHw8KBWQX(rHWAzP`Bl!;~5(pPTQ*?>mwF|iYs^*s-UA= zakD+If|&KGMqOaPbCQ5{VxkrDQCULM&L0=I(98_Ve=UB>Ul#Y#Orts5^1`huhGF|{ z0$eYZ+JM}XUMyGRkP1ez&XQz^dwAH3u{JcNf-=Zx{ztx6+yUel`Lq0a{yJaJpQGYt zaXWvNzbfvb9xm<`cMgk=PEW$}E!gv>-1j`+u&DtG;TX$5fn{?J<-bGJ85vFBtSI4vFoIWOwkm+#HzOO$*HLi;FxTw61NvI=pyC9)*Ykh!*Twx^*!*1FM9l`u z{{oLEC8Go7tw(woNaz^y2S-}SNaBt(1cQc?&?GfcYlM z|IRnzac#u#O}<{-w9NNl*np}&1b$D8+cv|N;n95<21;rjQGxr-2Jl(1k7uZ;0Q*h1 zu?y7WQEA2+Xg`=lG6_WiiMAcINwc>8RUXhvI zi%R3jM^OP1fGx2M;WF4C!f(w>R{fzOtCnEd&A${s0xPJ)Gg}RmKY{MOTju}e7Rgan ztmOu^Ou*MD{%jr4+04{2dD19O?Gys0Su4K;ij`v2fI-u=q-_m+FPZw zvU0KvG1<*TV8_s8ST|GO*@%%Jx&fR(Ll-#=5@9CIR9(YjM9pYLe=)pBqH~~%U|VjC zVnwbUK$GR&L!WSbpUY~*xuBRv29lqG8`YBNBWcD&5I!_4sIDjxfeGbQ zVYQpW91-Rmj4_u9Pg2@E+4i9!Sza%88;8{l S1P!+TbNvUH#uyfZ4FCXD9K>M& literal 0 HcmV?d00001 diff --git a/author/aleksei-lobanov.html b/author/aleksei-lobanov.html index 34ee137..bf7e023 100644 --- a/author/aleksei-lobanov.html +++ b/author/aleksei-lobanov.html @@ -1,66 +1,7 @@ - - - - - - - - Блог 529 - Алексей Лобанов - - - - - - - - - - - - - - - - - - - Блог 529 - Алексей Лобанов - -
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  1. -
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    Нахождение суммы k-ых степеней

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    Как придумать формулу для суммы \(1^5 + 2^5 + 3^5 + \ldots + n^5\) и есть ли она вообще?

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    Wallabag и реальная жизнь

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    Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

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    CrossGen v1.0

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    Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

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    Моё решение задачи 60

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    Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

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    Ещё одно вычисление выражений

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    На хабре когда-то увидел статью про то, что в Яндексе двум сотрудникам дали задачу на написание приложения, для вычисления выражений. Менеджер справился за 4 часа, а программист за два. Я решил попробовать свои силы.

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  • Wallabag и реальная жизнь

    Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

  • CrossGen v1.0

    Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

  • Моё решение задачи 60

    Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

  • Ещё одно вычисление выражений

    На хабре когда-то увидел статью про то, что в Яндексе двум сотрудникам дали задачу на написание приложения, для вычисления выражений. Менеджер справился за 4 часа, а программист за два. Я решил попробовать свои силы.

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    Authors on Блог 529

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      Нахождение суммы k-ых степеней

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      Как придумать формулу для суммы \(1^5 + 2^5 + 3^5 + \ldots + n^5\) и есть ли она вообще?

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      Wallabag и реальная жизнь

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      Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

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  • Wallabag и реальная жизнь

    Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

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      CrossGen v1.0

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      Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

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      Ещё одно вычисление выражений

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      На хабре когда-то увидел статью про то, что в Яндексе двум сотрудникам дали задачу на написание приложения, для вычисления выражений. Менеджер справился за 4 часа, а программист за два. Я решил попробовать свои силы.

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      Моё решение задачи 60

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      Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

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      Нахождение суммы k-ых степеней

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      Как придумать формулу для суммы \(1^5 + 2^5 + 3^5 + \ldots + n^5\) и есть ли она вообще?

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      Wallabag и реальная жизнь

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      Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

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      CrossGen v1.0

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      Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

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      Моё решение задачи 60

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      Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

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      Ещё одно вычисление выражений

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      На хабре когда-то увидел статью про то, что в Яндексе двум сотрудникам дали задачу на написание приложения, для вычисления выражений. Менеджер справился за 4 часа, а программист за два. Я решил попробовать свои силы.

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  • Wallabag и реальная жизнь

    Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

  • CrossGen v1.0

    Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

  • Моё решение задачи 60

    Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

  • Ещё одно вычисление выражений

    На хабре когда-то увидел статью про то, что в Яндексе двум сотрудникам дали задачу на написание приложения, для вычисления выражений. Менеджер справился за 4 часа, а программист за два. Я решил попробовать свои силы.

    • Page 1 / 1
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    Здравствуйте, я Алексей Лобанов

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    В данный момент студент ВМК МГУ. Немного занимаюсь фрилансом.

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    В основном программирую на Python и C++, есть также знания HTML, CSS, Delphi, Bash. Разрабатываю прикладные приложения (в том числе графические под Win/MacOS/Linux), парсеры (с использованием scrapy), скрипты автоматизации -Есть опыт разработки веб-приложений с использованием микрофреймворка Flask.

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    - Powered by Pelican. -

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      Мои проекты

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      Значительная часть моих проектов есть на GitHub или BitBucket вместе с открытым исходным кодом.

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      CrossGen

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      alt text

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      Что использовалось

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      Что реализовано

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      1. Графический интерфейс
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      2. Автоматическая локализация всего интерфейса на русский и английский языки
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      3. Быстрая генерация кроссворда по заданной сетке с использованием эвристики
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      4. Автоматический бенчмарк для измеренеия производительноти генерации -Подробнее я писал тут
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      За подробностями пишите мне на почту

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      CrossGen v1.0

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      Начать, наверное, нужно с того, что реальную практическую значимость я осознал после того, как реализовал 90% того, что есть сейчас. Сейчас мне кажется, что единственное применение данного приложения лишь в том, чтобы создавать кроссворды очень сложной или необычной формы. Зачем это надо обычному человеку я вообще не знаю.

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      Собственно, алгоритм генерации изначально был примитивным: простой рекурсивный поиск с отсечением. Скорость генерации более-менее сложных сеток была ужасной (для перцентиля 30% это примерно 40 минут на этой сетке, в общем случае, время генерации непредсказуемо.

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      В дальнейшем были выполнены некоторые оптимизации. Первой более-менее значимой стала замена передачи сетки в юникоде (во внутреннем цикле) на передачу сетки в однобайтовой кодировке, таким образом, языки с алфавитом больше ~200 букв пролетают. Впрочем, мне кажется, что им не слишком сильно требуются кроссворды. Такая оптимизация дала ~35% прироста при значимом времени перебора (больше секунды).

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      В какой-то момент, мне показалось, что оптимизация структуры данных для хранения сетки тоже могла сильно увеличить производительность, но это будет заметно только на разряженных сетках, которые и так достаточно быстро генерируются. На сложных же плотных сетках, прирост скорости может быть минимальным, вплоть до отрицательного. Таким образом, используются просто двумерный массив.

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      Наибольший прирост, как и ожидалось, дало упорядочивание словаря по некоторому критерию. Таким образом, при переборе, “плохие” варианты будут попадаться редко. На это ушло немногим больше дня. В конечном итоге, целевой функцией, которая стала критерием сортировки, стала такая \(\sqrt[n]{\prod_{i=1}^{n}{f\left( a_i \right)}}\) (иначе говоря, среднее геометрическое отлично подошло), где \(n\) — количество букв в слове, \(a_i\) — буквы слова, а \(f \left( x \right)\) есть вероятность появления буквы \(x\). Я отсекаю примерно половину самых “плохих” слов, а из того, что осталось я составляю кроссворд. Производительность, в среднем, увеличилась в ~1000 раз. На тестовых сетках для перцентиля 90% длительность работы около секунды.

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      Что реализовано

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      • Прозрачная интернационализация (пока только русский и английский языки)
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      • Быстрая генерация
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      • Простая смена словаря
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      Что может быть реализовано

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      • Визуальный редактор сетки
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      • Экспорт в HTML, PDF, Markdown
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      Скриншоты

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      • Версия для Xubuntu: -alt text
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      Ещё одно вычисление выражений

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      Задачка кажется не очень сложной, даже, если не знать как её делать (я не знал). Целью является быстрое вычисление чего-то типа 4 * ( 5 + 7 ^ 4). Для это я парсил исходную строку в список токенов, а затем непосредственно вычислял, что получится.

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      Я решил, что проще всего будет реализовать (а мне потом и понять) алгоритм, когда после каждого действия будет выполняться некий “хороший” инвариант. Первое что приходит в голову — это то, что истинность выражение после выполнения операции не меняется (TITO соблюдается). То есть выражение 3 + 5 можно заменить на 8 или хотя бы на 4 * 2.

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      Непосредственно сама обработка является несколькими проходами, так что в каждом проходе мы избавляемся от операций одного приоритета. 4 + 5 * 3 заменяется на 4 + 15, 7 - 5 * 2^3 заменяется на 7 - 5*8. Таким образом, каждый цикл тривиален, и легко задавать приоритеты операций.

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      Если использовать один список как контейнер для токенов и при работе изменять непосредственно его, сохраняя указанные инварианты, то сложность получается \(O\left( N \right)\), где \(N\) — число токенов.

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      Времени на непосредственно кодирование ушло часа три-четыре, но в это время не входит продумывание мелких деталей.

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      Всё написано на C++11. Исходники лежат на GitHub и BitBucket.

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      Как я шахматного бота писал

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      Лет 5 назад я достаточно активно играл в “живые” шахматы. Потом времени на это стало не хватать и постепенно перешёл на редкие партии в онлайне. Сейчас для игры я использую одно из самых популярных приложений вк. Это проще, чем использовать, к примеру, FICS. Предмет обсуждения появился из-за того, что я как-то раз встретился с соперником, который на все ходы потратил порядка 10 секунд, при этом не допустив значимых ошибок. Тогда я решил написать своего бота, чтобы узнать что с ним будет и столкнусь ли я с какими-нибудь подводными камнями.

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      Целью было максимально быстрое написание максимально простого решения. Поэтому от разбора протокола я сразу отказался, тем более у меня не было подобного опыта ранее. Была мысль работать с FICS (у меня есть библиотека для работы с их протоколом), но поскольку я там не играю, то и результаты были бы не так интересны, во всяком случае, для меня. Таким образом, я писал простого кликера для приложения вк.

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      Изначально хотелось найти доску и определить положения всех фигур, это было бы достаточно универсально, хотя и привязало бы меня к OpenCV. Тем не менее, решил не усложнять: можно определять только последний ход, а это можно сделать, проверяя цвет только одного пикселя.

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      В самом скрипте около 200 строк на python. Очень сильно помогла библиотека chess, которая взяла на себя общение с движком (я использовал stockfish), проверку на допустимые ходы и определение мата. Некоторое время я уделил тому, чтобы сделать бота максимально похожим на человека, чтобы было невозможно выявить, что это бот полностью автоматическими средствами. По пунктам:

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      • Клик по полю в случайном месте, с распределением по Гауссу, центр которого не совпадает с центром клетки
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      • Случайное время хода, длительность которого распределена по Гауссу, причём средняя длительность хода изменяется, в зависимости от номера текущего хода.
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      • Прокладываются дополнительные точки, с распределением по Гауссу, при перемещении курсора от точки к точке.
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      По факту, всё это было лишним, бан получить не удалось даже при простом клике из начальной точки в конечную.

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      Примеры работы скрипта можно посмотреть тут и тут, анализы двух сыгранных игр лежат тут и тут (оппонент имеет рейтинг около 2100).

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      На момент публикации аккаунт вполне жив. Рейтинг достиг некоторого потолка (около 2200), после которого найти игроков примерно равного рейтинга, не являющихся ботами, очень сложно. Сражаться же с ботами сильно сложнее, такую цель я не ставил. Интересно, хоть и ожидаемо, что при наборе рейтинга было достаточно личностей, для которых возможность того, что их нагло обманули, и они играли с ботом была столь неприятна, что они не могли сдерживаться. Например: -alt text

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      p.s. Уже после создания рабочей версии от одного из оппонентов узнал про lichess.org. Это отличный ресурс на котором кроме, собственно, платформы для игры в шахматы (поддерживается большое количество их вариантов), есть тренировки по дебютам, анализ игр. Самое интересное — ресурс полностью открытый, все исходники есть на github.

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      В процессе подготовки данного материала узнал про InternetChessKiller, который делает, фактически, тоже самое, что и мой скрипт, но без привязки к какой-то одной игровой площадке. Исходники старых версий можно найти, например, в этом репозитории.

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      p.p.s. Боты на серверах, предназначенных для людей, играющие в игры, которые предназначены для людей очень сильно мешают людям. Тем не менее, проверять, насколько сильно они мешают не нужно!

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      Мой первый пост

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      Главная причина появления заключается в том, что мне захотелось использовать хоть как-то купленный домен (я купил его только ради почты). Плюс мне бы хотелось проще давать контактные данные, а адрес сайта достаточно простой.

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      Пока я планирую публиковать свои, возможно не лучшие, но рабочие решения для задач из Project Euler (projecteuler.net). На самом деле, решения значительного числа задач уже есть в Сети, но на английском. Хотя, это и не есть большая проблема.

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    - -comments powered by Disqus - - - \ No newline at end of file + \ No newline at end of file diff --git a/posts/moi-pervyi-post/index.html.gz b/posts/moi-pervyi-post/index.html.gz new file mode 100644 index 0000000000000000000000000000000000000000..7b4aafd157c299742cd007572585167e307f60e5 GIT binary patch literal 2280 zcmV{F?jZaKN`dcb*ZxvzERvAa1Rw46V9H!gcuM3Pa>J27)eC{oQ**!$6X zi$y)w2>VhbthG7|qq&ZmId1Xy;&t(y6h9UFqx;2^(WBz||NaG|*P{oc?WJa5CFcmF z6abxwsZjDvbCJ%dbruT`INQpE)H9M>JktGE#0ETMo*B&SHTz?p-XW63El25L%v7H- z0O(8BZ8^Rlz<=Fm2@67{f>g+a#{6^U!)TU-0Wo`AG~9(C=mG=f_k`%hjAmTk=$RT|EiFA zGS>V{b-r2MCu)nv(XV`_8=XAW`SR~YDt={68`qbw(Nw*?mQw~A>i6gtQ;=1D!qbKE zc1o;-PWCUo_2y12dNa!3YHyG0e%?7gRh-h;F~7qSs{6jogDzu{3TPbrRExyFm&A@W zsYA02B9vk!2ykuLtQjga)=Z{ULuE3hq~#QUDGs6L{6NmFy-zNKG`R}E4hen+5vkO1 zJYebcG(Np{Z2=2g-iVT6)quBEFn}s9WRQpmVEO0LTl3%b*GxEIt#1Z)Z|Rv}TI8D@ z5e;W_%wLMt0+@~O5L?8%5^AZ_{!HYAN=9JaXE3){``1WGHeu-rfvon+SPi_tw@{nTR$CrzC?*l0{sy zP`9+qfin#?9{@Mo8^KS73wC#=_ zBjF}w;;D9Lw8vDC*)u2~8zR8NZUYYT6Z9HDzj!g)9zFUQu(SiAKF0iKu}6?3nC3O$ z?!OhDttI$(TGiU7D&gEwsAiDIV~ZOjH@iaUNtl86c-j@?pqh!>4Y9=_CrD>VHW*f^ z)GuK`s2Nz4wk;L#WvLR?nNZrp#tH6=YEX)JDiCv}kG4sTUeHLtlXg^gaokLUYgel|UnMqn{NiN=Sp?Tw#hhg)eUb~ZxfHgkcQD#1 z4se1Pa*tv45UlqK7C_<|h`#_+eg{&!aGGsk57SQwCRp*ZK}I|HjTA3o$G(vteGM?% z=m2xpZ=qU^9w4?URnOq_2?%Y&f|W#x7pTUwNH0bYLE3V7g{C9LQ`ChMq=wq9#6fXL zVD1OlW5^)-3mn`Bu&1W70Q?SCmAVh%VNUU2!gO!+h#aMAiqYtgDDc!+YIjWVHITu2 z3uVgCDkUt({RTk;f?f-`&u4JT*Ts*hirC{G!tR~XH?R%4z8c$U z&oF{XVu*h;_54%VQU(B=bF>3)ES}BXL$yj1pr8vVYdphcKV^^~?fEGTdvwS@@Pue4 zr1}ySq91_WJd z00k}i96->TFM-y7O-w!p8h^6!cu-n!0=H*_4Jbkq&3e-KWgpJ7TWwRSxm{-Oan)4@ z$E;9nR4O@-PwF=${NGH}nJh86{`kUtS%Vgt^@JP-30GlxjpA2(-DM}k|HnWd90Ap| zXP+eHwY+EB9mH&q6KrG7c#>tzEjaFjMUp_to4k3(7i7fM-CW($K!`@zaKS<;Qg-q7 zgIoLPo&9!>n`bCuUkrXPKqvhIFs)lI@%h*9*tmwg2c$VPSAaKd@QRd6U_3fl- z%~{fc4(GOVt2ng@%^uSwNAl;43(u9XfH1b;*#@CG~b5SckCJUqI$#%NA^ z955uC_Fo@bX&dbm#Y>g@{|NBp?EnYzIuiTn#pq3y(aAjx`5-(C;t4Hs)Zr*fnDW)%np~zG1HryMRy?57EplLdL z-dlAy8?de=4ex9~r;P@8H#e=vrePm7bo~oN?6sn~0N3?~g2{y;qA@xwRu99sRdekf z;R(O5y)nr{h{kFpzUk#}ezIBg# - - - - - - - - Моё решение задачи 60 - - - - - - - - - - - - - - - - - - - - Моё решение задачи 60 - -
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      Моё решение задачи 60

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      Необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число. Здесь под процедурой “склеивания” чисел \(a\) и \(b\) подразумевается получения из \(a = \overline{a_1 a_2 \ldots a_n}\) и \(b = \overline{b_1 b_2 \ldots b_m}\) некоторого \(c\) так, что \(c = \overline{a_1 a_2 \ldots a_n b_1 b_2 \ldots b_m}\).

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      Полное условие можно найти тут

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      Для начала, можно понять, что непосредственный перебор “в лоб” слишком медленный и нужного результата не даст. Поэтому хочется уйти от, как мне кажется, не самого формализуемого условия к чему-то более простого, с чем проще работать. Давайте сначала поймём, какие вообще числа могут быть в одном множестве. Для этого достаточно перебрать все разбиения на два подчисла всех простых чисел. Это достаточно быстро, порядка \(O\left( N \right)\) операций. Важно не забыть, что мы можем разбивать число \(p\) только на \(\overline{p_1 p_2}\), между числами не может быть нулей! То есть если число 37 разбивается на 3 и 7, то 307 нет.

      -

      Пусть мы получили набор таких разбиений, то есть набор пар вида \(\left( p, q \right)\). Давайте составим из них граф, где вершинки это простые числа, а ориентированное ребро из \(p\) в \(q\) означает, что есть пара \(\left( p, q \right)\). Из того, что порядок склеивания чисел произвольный сразу следует, что рассматриваемый граф должен быть неориентированным. Таким образом, все пары \(\left( p, q \right)\) для которых нет пары \(\left( q, p \right)\) необходимо выкинуть, а из оставшихся построить граф.

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      Теперь задача стало гораздо понятнее: достаточно выбрать клику размера 5, что сумма значений её вершин минимальна. В общем случае, это достаточно ресурсоёмкая(как мне кажется) задача, но в реальном графе количество рёбер не слишком большое. В худшем случае, по теореме Турана, количество рёбер в графе лишь с одной такой кликой примерно на 10% меньше числа рёбер в полном графе.

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      Непосредственно сам поиск такой клики можно реализовать тривиально. Ниже мой код на C++11 с использованием библиотеки Boost Graph Library (BGL).

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      #include <iostream>
+        
      1. Моё решение задачи 60
        Необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число. Здесь под процедурой “склеивания” чисел \(a\) и \(b\) подразумевается получения из \(a = \overline{a_1 a_2 \ldots a_n}\) и \(b = \overline{b_1 b_2 \ldots b_m}\) некоторого \(c\) так, что \(c = \overline{a_1 a_2 \ldots a_n b_1 b_2 \ldots b_m}\).
        Полное условие можно найти тут
        Для начала, можно понять, что непосредственный перебор “в лоб” слишком медленный и нужного результата не даст. Поэтому хочется уйти от, как мне кажется, не самого формализуемого условия к чему-то более простого, с чем проще работать. Давайте сначала поймём, какие вообще числа могут быть в одном множестве. Для этого достаточно перебрать все разбиения на два подчисла всех простых чисел. Это достаточно быстро, порядка \(O\left( N \right)\) операций. Важно не забыть, что мы можем разбивать число \(p\) только на \(\overline{p_1 p_2}\), между числами не может быть нулей! То есть если число 37 разбивается на 3 и 7, то 307 нет.
        Пусть мы получили набор таких разбиений, то есть набор пар вида \(\left( p, q \right)\). Давайте составим из них граф, где вершинки это простые числа, а ориентированное ребро из \(p\) в \(q\) означает, что есть пара \(\left( p, q \right)\). Из того, что порядок склеивания чисел произвольный сразу следует, что рассматриваемый граф должен быть неориентированным. Таким образом, все пары \(\left( p, q \right)\) для которых нет пары \(\left( q, p \right)\) необходимо выкинуть, а из оставшихся построить граф.
        Теперь задача стало гораздо понятнее: достаточно выбрать клику размера 5, что сумма значений её вершин минимальна. В общем случае, это достаточно ресурсоёмкая(как мне кажется) задача, но в реальном графе количество рёбер не слишком большое. В худшем случае, по теореме Турана, количество рёбер в графе лишь с одной такой кликой примерно на 10% меньше числа рёбер в полном графе.
        Непосредственно сам поиск такой клики можно реализовать тривиально. Ниже мой код на C++11 с использованием библиотеки Boost Graph Library (BGL).
        #include <iostream>
 #include <algorithm>
 #include <vector>
 #include <set>
@@ -232,12 +166,7 @@
         cout << "Result is " << min_element(good_sums.begin(),good_sums.end(), [](pair<size_t, size_t> a, pair<size_t, size_t> b){return a.first < b.first;})->first << endl;
     return 0;
 }
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        Ответ: 26033
        
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        UPD. Кажется, getNeedSet можно было реализовать гораздо проще, использую BGL посетителей (Visitors). Но, к сожалению, на этапе написания кода я про это забыл.
        
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      Нахождение суммы k-ых степеней

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      Давайте сразу обобщим задачу до нахождения \(f_k\left( n \right)\), что

      $$f_k\left( n \right) = 1^k + 2^k + \ldots + n^k$$
      -Для \(k=1\) формула известна всем школьникам: \(f_1\left( n \right) = \frac{n\left(n+1 \right)}{2}\). Формулу для \(k=2\) знают уже не все, но всё же в школе её найти можно (я видел на обложке учебника по алгебре): \(f_2\left( n \right) = \frac{n\left(n+1 \right) \left( 2n + 1 \right)}{6}\)

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      Интуиция может подсказать, что \(f_k \left( n \right)\) есть некий полином со степенью \(k+1\). Если это так, то его нахождение тривиально. Например, можно посчитать его в явном виде, используя полином Лагагранжа. -Осталось показать, что наша функция представима в таком виде.

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      Для начала введём обозначение. “Нижней степенью”, \(x^{\underline{k}}\), будем обозначать такое выражение:

      $$x^{\underline{k}} = x(x-1)\cdot \ldots \cdot (x-k+1)$$
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      Далее, заметим следующее, если \(a_i = A_{i+1} - A_i\), где \(\lbrace a_i \rbrace\) и \(\lbrace A_i \rbrace\) — некие последовательности, то \(\sum_{i=1}^n = A_{n+1}-A_1\) (телескопирование, можно посмотреть тут, с. 6).

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      Теперь посчитаем сумму \(\sum_{i=1}^n i^{\underline{k}}\). Для этого достаточно понять, что \(\left( x+1 \right)^{\underline{k+1}} - \left(x \right)^{\underline{k+1}} = \left( k+ 1 \right)x^{\underline{k}}\). Отсюда сразу получаем, что -

      $$\sum_{i=1}^n i^{\underline{k}} = \frac{\left( n+1 \right)^{\underline{k+1}}}{k+1}$$
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      Осталось показать, что “нормальные” степени выражаются через нижние. Начнём со степени \(k=1\), тут всё просто: -

      $$x = x^{\underline{1}}$$
      -С бОльшими степенями сделаем следующее: считая, что все степени, меньше, чем \(k\) мы выражать умеем, раскроем скобки в определении нижней степени. Теперь поймём, что старший коэффициент \(1\): \(x^{\underline{k}} = x^k + \sum_{i=1}^k a_ix^i\) или \(x^k = \sum_{i=1}^k a_ix^i - x^{\underline{k}}\). Осталось понять, что каждое из слагаемых вида \(a_ix^i\) мы умеем выражать через нижние степени. Таким образом, можно получить следующее: -
      $$ \sum_{i=1}^{n} i^k = \sum_{i=1}^{n} \sum_{j=1}^{k} a_j i^{\underline{k}} = \sum_{j=1}^{k} \sum_{i=1}^{n} a_j i^{\underline{k}} = \sum_{j=1}^{k} \frac{a_j \left(n+1 \right)^{\underline{k+1}}}{k+1}$$
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      Кстати, формула для суммы в самом начале такая: -

      $$ \sum_{i=1}^n i^5 = \frac{1}{12} n^2 \left(n+1 \right)^2 \left(2n^2 + 2n-1 \right) $$
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      Wallabag и реальная жизнь

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      Начать следует с того, что Wallabag действительно является самым популярным среди открытых приложений для отложенного чтения. Можно взять, например, alternativeto:

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      Первый релиз вышел почти два года назад. Тем не менее, мне сложно назвать продукт зрелым. Последняя, на момент написания, версия 2.0.0-beta.2 не может похвастаться простым процессом установки. Вариант просто выполнить команды из мануалов по очереди у меня не получился. В этом соперничать с тем же Pocket, очевидно, бессмысленно.

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      Стандартная тема, material, ужасно выглядит на моём ноутбуке с разрешением 1366x768, элементы явно рассчитаны на большую диагональ. Ещё часть места отъедает неубирающаяся плашка внизу страницы, предупреждающая о том, что баги в бета версии не есть что-то плохое. Официальное Android приложение упорно не может найти сервер.

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      После волевого решения перейти на стабильную версию (то есть откатиться в равзвитии на полгода назад), дела улучшились, но не сильно. Количество настроек минимально, если не сказать, что их вообще нет. Но оно работает, вроде.

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      Сложности, впрочем, только начались. Обещанная синхронизация с Pocket работает, мягко говоря, неоптимально. После загрузки экспортированного html файла со ссылками, wallabag почти час выкачивал мои 750 статей. Где-то на 500-й статье он выделил слишком много памяти и упал с ошибкой. После этого пришлось руками искать потенциально проблемные статьи и удалять их по одной — удалить сразу несколько элементов невозможно. Затем надо было выкачивать ещё 250 статей, периодически посматривая, чтобы ничего снова не упало.

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      Кажется, что все проблемы закончились, но нет. Дальше синхронизация с телефоном. Она заняла почти столько же времени, при этом, начальное очевидное предположение о том, что токен безопасности вбивать не нужно (он сам заполняется в приложении) стоило где-то 15 минут поиска. Но и это не всё. После того, как база загрузилась, небольшие изменения на телефоне (такие как удаление статьи) синхронизировались больше минуты!

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      Резюме: пользоваться можно, но советовать кому-либо это использовать я точно не стану.

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      Этого бы поста не было бы, если бы я сказал, что Wallabag плохой, а OTHER_PRODUCT хороший и можно пользоваться им. Но я так написать не могу. Ни я, ни alternativeto других решений не знают. Значит нужно их создать. На моём слабеньком VPS уже почти год трудится Syncthing, управляя значительным количеством файлов с минимальной нагрузкой на ЦП. Поэтому мне кажется, что Go подойдёт идеально.

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      Если написать подобный продукт на Go, то многие проблемы даже не появятся:

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      • не нужно разрешать большое количество зависимостей — достаточно одного бинарника
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      • скорость генерации контента (например, создание pdf, epub) будет значительно выше
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      • небольшой оверхед позволит всё хранить в памяти
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      • работа почти на чём угодно
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      В совокупности, будет достигнуто, как мне кажется, самое главное — удобство для обычного пользователя, который сможет без проблем развернуть это на любом VPS.

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      Моё решение задачи 60

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      Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

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      CrossGen v1.0

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      Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

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      Моё решение задачи 60

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      Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

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      Wallabag и реальная жизнь

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      Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

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      Нахождение суммы k-ых степеней

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      Как придумать формулу для суммы \(1^5 + 2^5 + 3^5 + \ldots + n^5\) и есть ли она вообще?

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      Wallabag и реальная жизнь

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      Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

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      CrossGen v1.0

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      Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

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      Ещё одно вычисление выражений

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      На хабре когда-то увидел статью про то, что в Яндексе двум сотрудникам дали задачу на написание приложения, для вычисления выражений. Менеджер справился за 4 часа, а программист за два. Я решил попробовать свои силы.

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      Моё решение задачи 60

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      Краткое условие: необходимо найти множество из пяти простых чисел с минимальной суммой такое, что после “склеивания” в любом порядке любых двух чисел из него тоже будет простое число.

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      Wallabag и реальная жизнь

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      Как я устанавливал известнейшее свободное решение для отложенного чтения, и что из этого получилось.

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      CrossGen v1.0

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      Читая хабр, случайно натолкнулся на идею сделать программу, которая по заданной кроссвордной сетке находит способ её заполнить. В этом посте вкратце напишу про моё решение и первую версию приложения.

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    Tags for Блог 529

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text-decoration: none; } - -#site-title { - font-family: "Philosopher", sans-serif; - font-size: 2em; - -webkit-transition: all 0.3s; - -moz-transition: all 0.3s; - -ms-transition: all 0.3s; - -o-transition: all 0.3s; - transition: all 0.3s; } - #site-title:hover { - color: #38c5c5; } - -#site-desc { - font-size: 1.3em; - padding: 0 6px; } - -#post-container { - position: relative; - margin-left: 27%; - max-width: 800px; - overflow-wrap: break-word; } - -#nav-links { - list-style: none; - padding: 0; - font-family: "Philosopher", sans-serif; - font-size: 2em; - font-variant: bold; } - #nav-links li { - margin: 12px 12px; } - #nav-links a { - padding: 0 24px; - border-radius: 24px; - display: inline-block; - border: 3px solid #eeeeee; - line-height: 1.8em; - -webkit-transition: all 0.3s; - -moz-transition: all 0.3s; - -ms-transition: all 0.3s; - -o-transition: all 0.3s; - transition: all 0.3s; } - #nav-links a:hover { - border-color: #38c5c5; - color: #38c5c5; } - -#post-list { - list-style: none; } - -.post-entry { - margin: 3em 0; } - -.entry-header { - font-family: "Forum", sans-serif; - font-variant: bold; } - .entry-header a { - color: #272822; - text-decoration: none; } - .entry-header a:hover { - color: #38c5c5; - text-decoration: none; } - .entry-header time { - color: #8e927e; } - .entry-header h1 { - margin: 0.5em 0; } - -.post-content a { - color: #38c5c5; } -.post-content img { - display: block; - margin: 0 auto; - max-width: 80%; } -.post-content blockquote { - font-style: italic; } -.post-content pre { - font-size: 14px; - background-color: #e6e6e6; - padding: 10px; - margin: 10px; - overflow: auto; - font-family: "Ubuntu Mono", monospace; } - -.post-meta a { - font-style: italic; - color: #38c5c5; } - -.paginator { - text-align: center; - padding: 12px; - font-size: 1.4em; - font-family: "Oswald", sans-serif; } - .paginator a { - color: #272822; - text-decoration: none; } - .paginator a:hover { - color: #38c5c5; } - -/* ========================================================================== - EXAMPLE Media Queries for Responsive Design. - Theses examples override the primary ('mobile first') styles. - Modify as content requires. - ========================================================================== */ -@media only screen and (max-width: 800px) { - /* Style adjustments for viewports that meet the condition */ - #sidebar { - position: static; - width: 100%; - padding: 0; } - - #post-container { - width: 100%; - position: static; - margin: 0; - padding: 0px; } - - #post-list { - padding: 0; } - - #nav-links { - text-align: center; - padding: 0; - font-size: 1.8em; } - #nav-links li { - display: inline; - margin-top: 6px; } - #nav-links a { - display: inline-block; } - - #site-title h1 { - margin-top: 0; } - - #site-header { - margin-left: 18px; } - - .side-shadow { - -webkit-box-shadow: 0 3px 12px 3px #8e927e; - -moz-box-shadow: 0 3px 12px 3px #8e927e; - box-shadow: 0 3px 12px 3px #8e927e; } - - .post-entry { - padding: 0 12px; } } -@media only screen and (max-width: 640px) { - #nav-links { - font-size: 1.1em; } - - #site-desc { - font-size: 1em; } - - #site-title h1 { - font-size: 1.3em; - margin: 0.1em 0px; } - - #site-info { - font-size: 0.6em; } } +body{color:#272822;background-color:#eee;font-family:"PT Sans",sans-serif}#sidebar{background:url("../img/stressed_linen/stressed_linen.png") repeat;position:fixed;left:0;bottom:0;right:auto;top:0;width:25%;min-width:200px;padding-left:8px;padding-right:8px;color:#eee}#sidebar a{color:#eee;text-decoration:none}#site-title{font-family:"Philosopher",sans-serif;font-size:2em;-webkit-transition:all .3s;-moz-transition:all .3s;-ms-transition:all .3s;-o-transition:all .3s;transition:all .3s}#site-title:hover{color:#38c5c5}#site-desc{font-size:1.3em;padding:0 6px}#post-container{position:relative;margin-left:27%;max-width:800px;overflow-wrap:break-word}#nav-links{list-style:none;padding:0;font-family:"Philosopher",sans-serif;font-size:2em;font-variant:bold}#nav-links li{margin:12px 12px}#nav-links a{padding:0 24px;border-radius:24px;display:inline-block;border:3px solid #eee;line-height:1.8em;-webkit-transition:all .3s;-moz-transition:all .3s;-ms-transition:all .3s;-o-transition:all .3s;transition:all .3s}#nav-links a:hover{border-color:#38c5c5;color:#38c5c5}#post-list{list-style:none}.post-entry{margin:3em 0}.entry-header{font-family:"Forum",sans-serif;font-variant:bold}.entry-header a{color:#272822;text-decoration:none}.entry-header a:hover{color:#38c5c5;text-decoration:none}.entry-header time{color:#8e927e}.entry-header h1{margin:.5em 0}.post-content a{color:#38c5c5}.post-content img{display:block;margin:0 auto;max-width:80%}.post-content blockquote{font-style:italic}.post-content pre{font-size:14px;background-color:#e6e6e6;padding:10px;margin:10px;overflow:auto;font-family:"Ubuntu Mono",monospace}.post-meta a{font-style:italic;color:#38c5c5}.paginator{text-align:center;padding:12px;font-size:1.4em;font-family:"Oswald",sans-serif}.paginator a{color:#272822;text-decoration:none}.paginator a:hover{color:#38c5c5}@media only screen and (max-width:800px){#sidebar{position:static;width:100%;padding:0}#post-container{width:100%;position:static;margin:0;padding:0}#post-list{padding:0}#nav-links{text-align:center;padding:0;font-size:1.8em}#nav-links li{display:inline;margin-top:6px}#nav-links a{display:inline-block}#site-title h1{margin-top:0}#site-header{margin-left:18px}.side-shadow{-webkit-box-shadow:0 3px 12px 3px #8e927e;-moz-box-shadow:0 3px 12px 3px #8e927e;box-shadow:0 3px 12px 3px #8e927e}.post-entry{padding:0 12px}}@media only screen and (max-width:640px){#nav-links{font-size:1.1em}#site-desc{font-size:1em}#site-title h1{font-size:1.3em;margin:.1em 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