{"draftJsState":{"blocks":[{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":70,"offset":0,"style":"ITALIC"}],"text":"Как заменить \"тяжёлую артиллерию\" арифметики на лёгкую кавалерию битов","type":"header-three","key":"ap6il"},{"data":{"image":{"id":"6811a7ba2071087de52b5441"}},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"atomic:image","key":"bog8t"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":8,"offset":31,"style":"BOLD"},{"length":21,"offset":116,"style":"BOLD"}],"text":"Алгоритм работает, но работает медленно?\n\nВ коде много *, /, % и прочих \"тяжёлых\" операций?\n\nДобро пожаловать в мир побитовой оптимизации — старой доброй школы, где даже деление на 2 считается излишеством.","type":"unstyled","key":"b1qjs"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":15,"offset":147,"style":"BOLD"}],"text":"Здесь мы превращаем обычные операции в быстрые, битовые. Плюс — минимум магии, максимум пользы, даже в Python. Да-да, даже в высокоуровневом языке биты — это сила.","type":"unstyled","key":"7mcdi"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83E\uDDE0 Зачем вообще использовать побитовые операции?","type":"header-two","key":"c6kgt"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83D\uDD25 Быстрее: x << 1 почти всегда быстрее, чем x * 2","type":"unordered-list-item","key":"5ajd5"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83E\uDDF5 Легче на CPU: побитовые операции просты для железа","type":"unordered-list-item","key":"5qmsd"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":11,"offset":23,"style":"BOLD"}],"text":"\uD83E\uDDE0 Лучше понимаешь, что под капотом","type":"unordered-list-item","key":"c1g11"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"⚙ Используется в системах реального времени, играх, криптографии и компиляторах","type":"unordered-list-item","key":"6q9rb"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83D\uDE80 10 реальных задач: от простых до боевых","type":"header-two","key":"31u0j"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 1: Умножение на 2, 4, 8","type":"header-three","key":"393os"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"x = 7\nprint(x * 8) # 56\nprint(x << 3) # 56 тоже!","type":"unstyled","key":"4a6ss"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"x << n = x * 2ⁿ — обычный сдвиг влево","type":"unordered-list-item","key":"4m8hi"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"<< 3 = умножение на 8","type":"unordered-list-item","key":"33hea"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":58,"offset":2,"style":"ITALIC"}],"text":"\uD83D\uDCA1 Так можно ускорить циклы, если множители — степени двойки.","type":"unstyled","key":"7mtq8"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 2: Деление на 2, 4, 8","type":"header-three","key":"4bone"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"x = 36\nprint(x // 4) # 9\nprint(x >> 2) # 9","type":"unstyled","key":"92drh"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":13,"offset":32,"style":"BOLD"}],"text":"x >> n = x // 2ⁿ\n\n⚠️ Только для положительных чисел! Отрицательные — отдельная история, Python сохраняет знак.","type":"unordered-list-item","key":"3520p"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 3: Проверка чётности","type":"header-three","key":"ekjee"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"n = 17\nif n & 1 == 0:\n print(\"Чётное\")\nelse:\n print(\"Нечётное\")","type":"unstyled","key":"dg38o"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Последний бит 0 — значит число чётное.","type":"unordered-list-item","key":"9h1gp"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":46,"offset":2,"style":"ITALIC"}],"text":"\uD83D\uDCA1 Это работает даже в условиях, где n % 2 дорог.","type":"unstyled","key":"50deq"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 4: Умножение на 10 — по-умному","type":"header-three","key":"30gvv"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"x = 7\nres = (x << 3) + (x << 1) # 8x + 2x = 10x\nprint(res) # 70","type":"unstyled","key":"76jfg"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Быстрее, чем x * 10, особенно на слабом железе","type":"unordered-list-item","key":"6jetu"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":43,"offset":2,"style":"ITALIC"}],"text":"\uD83E\uDDD9 Так компиляторы иногда оптимизируют внутри.","type":"unstyled","key":"d1765"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 5: Обнулить младший бит","type":"header-three","key":"drpdg"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"x = 77 # 0b1001101\nres = x & ~1\nprint(res) # 76 (0b1001100)","type":"unstyled","key":"aoeb1"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"~1 = 0b...11111110","type":"unordered-list-item","key":"91ugj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"& ~1 = делает последний бит 0 (полезно для выравнивания)","type":"unordered-list-item","key":"cdsln"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 6: Проверка степени двойки","type":"header-three","key":"p0to"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"def is_power_of_two(n):\n return n > 0 and (n & (n - 1)) == 0","type":"unstyled","key":"678tf"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Почему работает?","type":"unstyled","key":"2n6ts"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":12,"offset":40,"style":"BOLD"}],"text":"Степень двойки в двоичном виде — только одна единица","type":"unordered-list-item","key":"8spa"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"n - 1 \"обнуляет\" её и все младшие биты","type":"unordered-list-item","key":"m4gj"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83E\uDDEA Пример:","type":"unstyled","key":"9lbon"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"print(is_power_of_two(8)) # True\nprint(is_power_of_two(10)) # False","type":"unstyled","key":"4pgkf"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 7: Быстрый min(a, b) и max(a, b) без if","type":"header-three","key":"f87pe"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Только для целых чисел — и немного чёрной магии:","type":"blockquote","key":"4gvvd"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"def fast_min(a, b):\n return b ^ ((a ^ b) & -(a < b))\n\ndef fast_max(a, b):\n return a ^ ((a ^ b) & -(a < b))","type":"unstyled","key":"aiqgc"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83D\uDCA5 Используется в DSP и embedded, где if медленно (ветвление = зло)","type":"unstyled","key":"1t4kb"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 8: Сравнение с нулём","type":"header-three","key":"5jg6d"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"n = -5\nprint((n >> 31) & 1) # 1, если n < 0; 0, если n ≥ 0 (на 32 битах)","type":"unstyled","key":"6080g"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"В Python >> 31 для 32-битного представления — не совсем то же самое, но в C/C++ работает так. В Python можно эмулировать:","type":"blockquote","key":"cvgjp"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"sign = int(n < 0)","type":"unstyled","key":"altr4"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 9: Быстрое округление вниз до ближайшей степени двойки","type":"header-three","key":"3grbk"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"def round_down_pow2(n):\n p = 1\n while p << 1 <= n:\n p <<= 1\n return p","type":"unstyled","key":"9c6sa"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"⏱️ Эффективнее при больших n, чем логарифм или math.pow","type":"unstyled","key":"7unpr"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"✅ Задача 10: Обмен значений без временной переменной","type":"header-three","key":"fspf6"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"a, b = 5, 9\na = a ^ b\nb = a ^ b\na = a ^ b\nprint(a, b) # 9, 5","type":"unstyled","key":"3f9kr"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83D\uDCA1 Работает через свойство XOR: a ⊕ b ⊕ b = a","type":"unstyled","key":"fdl64"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83D\uDEE0 Побитовая таблица \"быстрых замен\"","type":"header-two","key":"7706p"},{"data":{"image":{"id":"6811a9bbeaab1b4f8c839786"}},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"atomic:image","key":"98pc9"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"⚙️ А стоит ли вообще это использовать в Python?","type":"header-two","key":"f93gk"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[{"length":19,"offset":163,"style":"BOLD"}],"text":"✔ Если пишете библиотеки, которые требуют скорости\n\n✔ Если работаете с бинарными протоколами\n\n✔ Если хотите тренировать «мышцы алгоритмиста»\n\n✔ Если оптимизируете критические участки кода (напр. в NumPy, Cython, Numba)\n\n❌ Но не стоит злоупотреблять, если понятность важнее микросекунд","type":"blockquote","key":"7dhg8"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83D\uDCCC Заключение","type":"header-two","key":"2pf8l"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Побитовые операции — не только для олимпиадников и системщиков. Это:","type":"unstyled","key":"b1o9j"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83D\uDCC8 Инструмент для оптимизации","type":"unordered-list-item","key":"21d2t"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83E\uDDE0 Способ тренировать мозг","type":"unordered-list-item","key":"e1f7o"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"\uD83E\uDDF0 Реальный способ улучшить работу алгоритма","type":"unordered-list-item","key":"a1neo"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"Биты — это просто. Главное — начать сдвигаться в нужную сторону. \uD83D\uDE09","type":"blockquote","key":"4pttm"},{"data":{},"depth":0,"entityRanges":[],"inlineStyleRanges":[],"text":"","type":"marker","key":"ykjFQ8bX96HmMi8n3dpj"}],"entityMap":{}},"mentions":[]}