Обозначение Big O, часть вторая: космическая сложность

–ü—Ä–∏–º–µ—á–∞–Ω–∏–µ . –ï—Å–ª–∏ –≤—ã –Ω–µ —á–∏—Ç–∞–ª–∏ –Ω–∞—à—É —Å—Ç–∞—Ç—å—é –æ –≤—Ä–µ–º–µ–Ω–Ω–æ–π —Å–ª–æ–∂–Ω–æ—Å—Ç–∏ , —Ä–µ–∫–æ–º–µ–Ω–¥—É–µ—Ç—Å—è –Ω–∞—á–∞—Ç—å —Ç–∞–º. –í–æ –≤—Ç–æ—Ä–æ–π —á–∞—Å—Ç–∏ —ç—Ç–æ–π —Å–µ—Ä–∏–∏ –ø—Ä–µ–¥–ø–æ–ª–∞–≥–∞–µ—Ç—Å—è, —á—Ç–æ –≤—ã –∑–Ω–∞–∫–æ–º—ã —Å —Ä–∞–∑–ª–∏—á–Ω—ã–º–∏ –≤–æ–∑–º–æ–∂–Ω—ã–º–∏ –∑–Ω–∞—á–µ–Ω–∏—è–º–∏ Big O.

–í –Ω–∞—à–µ–π –ø–µ—Ä–≤–æ–π —Å—Ç–∞—Ç—å–µ –æ –Ω–æ—Ç–∞—Ü–∏–∏ Big O –∏ –≤—Ä–µ–º–µ–Ω–Ω–∞—è —Å–ª–æ–∂–Ω–æ—Å—Ç—å , –º—ã –≥–æ–≤–æ—Ä–∏–º –æ —Ç–æ–º, —Å–∫–æ–ª—å–∫–æ –≤—Ä–µ–º–µ–Ω–∏ —Ç—Ä–µ–±—É–µ—Ç—Å—è –¥–ª—è –∑–∞–≤–µ—Ä—à–µ–Ω–∏—è –∞–ª–≥–æ—Ä–∏—Ç–º–∞ –ø—Ä–∏ —É–≤–µ–ª–∏—á–µ–Ω–∏–∏ –µ–≥–æ –≤—Ö–æ–¥–Ω—ã—Ö –¥–∞–Ω–Ω—ã—Ö. –≠—Ç–æ –≤–∞–∂–Ω–æ, –∫–æ–≥–¥–∞ –º—ã –≤–∑–∞–∏–º–æ–¥–µ–π—Å—Ç–≤—É–µ–º —Å –æ—á–µ–Ω—å –±–æ–ª—å—à–∏–º–∏ –Ω–∞–±–æ—Ä–∞–º–∏ –¥–∞–Ω–Ω—ã—Ö. –ë–æ–ª—å—à–æ–π –Ω–∞–±–æ—Ä –¥–∞–Ω–Ω—ã—Ö –≤ —Å–æ—á–µ—Ç–∞–Ω–∏–∏ —Å –ø—Ä–∏–ª–∏—á–Ω–æ–π –≤—Ä–µ–º–µ–Ω–Ω–æ–π —Å–ª–æ–∂–Ω–æ—Å—Ç—å—é –ø—Ä–∏–≤–æ–¥–∏—Ç –∫ –±–æ–ª–µ–µ —ç—Ñ—Ñ–µ–∫—Ç–∏–≤–Ω—ã–º –∞–ª–≥–æ—Ä–∏—Ç–º–∞–º. –û–¥–Ω–∞–∫–æ –µ—Å—Ç—å –µ—â–µ –æ–¥–∏–Ω –∞—Å–ø–µ–∫—Ç –Ω–æ—Ç–∞—Ü–∏–∏ Big O, –∫–æ—Ç–æ—Ä—ã–π –Ω–µ–æ–±—Ö–æ–¥–∏–º–æ —É—á–∏—Ç—ã–≤–∞—Ç—å: —Å–ª–æ–∂–Ω–æ—Å—Ç—å –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞.

–ß—Ç–æ —Ç–∞–∫–æ–µ —Å–ª–æ–∂–Ω–æ—Å—Ç—å –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞?

–°–ª–æ–∂–Ω–æ—Å—Ç—å –≤—Ä–µ–º–µ–Ω–∏ –∏ —Å–ª–æ–∂–Ω–æ—Å—Ç—å –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞ –∞–Ω–∞–ª–æ–≥–∏—á–Ω—ã, –ø–æ—Å–∫–æ–ª—å–∫—É –æ–Ω–∏ —Å–≤—è–∑–∞–Ω—ã —Å –∫–æ–ª–∏—á–µ—Å—Ç–≤–æ –≤—Ö–æ–¥–Ω—ã—Ö –¥–∞–Ω–Ω—ã—Ö, –∫–æ—Ç–æ—Ä—ã–µ –∏–º–µ–µ—Ç –∞–ª–≥–æ—Ä–∏—Ç–º. –ï—Å–ª–∏ –≤—Ä–µ–º–µ–Ω–Ω–∞—è —Å–ª–æ–∂–Ω–æ—Å—Ç—å —Å–≤—è–∑–∞–Ω–∞ —Å –∫–æ–ª–∏—á–µ—Å—Ç–≤–æ–º –æ–ø–µ—Ä–∞—Ü–∏–π, –∫–æ—Ç–æ—Ä—ã–µ –∞–ª–≥–æ—Ä–∏—Ç–º –¥–æ–ª–∂–µ–Ω –≤—ã–ø–æ–ª–Ω–∏—Ç—å –¥–ª—è –∑–∞–≤–µ—Ä—à–µ–Ω–∏—è, —Å–ª–æ–∂–Ω–æ—Å—Ç—å –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞ —Å–≤—è–∑–∞–Ω–∞ —Å –æ–±—â–∏–º –æ–±—ä–µ–º–æ–º –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞, –Ω–µ–æ–±—Ö–æ–¥–∏–º—ã–º –¥–ª—è –∑–∞–≤–µ—Ä—à–µ–Ω–∏—è –∞–ª–≥–æ—Ä–∏—Ç–º–∞. –°–ª–æ–∂–Ω–æ—Å—Ç—å –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞ –≤—ã—Ä–∞–∂–∞–µ—Ç—Å—è –≤ –Ω–æ—Ç–∞—Ü–∏–∏ Big O. & nbsp;

–°–ª–æ–∂–Ω–æ—Å—Ç—å –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞ –≤–∫–ª—é—á–∞–µ—Ç –æ–±—ä–µ–º –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞, –Ω–µ–æ–±—Ö–æ–¥–∏–º–æ–≥–æ –¥–ª—è –≤–≤–æ–¥–∞, –∞ —Ç–∞–∫–∂–µ –≤—Å–ø–æ–º–æ–≥–∞—Ç–µ–ª—å–Ω–æ–µ –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–æ, –Ω–µ–æ–±—Ö–æ–¥–∏–º–æ–µ –¥–ª—è –≤—ã–ø–æ–ª–Ω–µ–Ω–∏—è –∞–ª–≥–æ—Ä–∏—Ç–º–∞. –í—Å–ø–æ–º–æ–≥–∞—Ç–µ–ª—å–Ω–æ–µ –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–æ - —ç—Ç–æ –¥–æ–ø–æ–ª–Ω–∏—Ç–µ–ª—å–Ω–æ–µ –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–æ, –∏—Å–ø–æ–ª—å–∑—É–µ–º–æ–µ –¥–ª—è —Ö—Ä–∞–Ω–µ–Ω–∏—è –≤—Ä–µ–º–µ–Ω–Ω—ã—Ö —Å—Ç—Ä—É–∫—Ç—É—Ä –¥–∞–Ω–Ω—ã—Ö –∏–ª–∏ –ø–µ—Ä–µ–º–µ–Ω–Ω—ã—Ö, –∏—Å–ø–æ–ª—å–∑—É–µ–º—ã—Ö –¥–ª—è —Ä–µ—à–µ–Ω–∏—è –∞–ª–≥–æ—Ä–∏—Ç–º–∞. –ö–∞–∫ –∏ –≤ —Å–ª—É—á–∞–µ —Å –≤—Ä–µ–º–µ–Ω–Ω–æ–π —Å–ª–æ–∂–Ω–æ—Å—Ç—å—é, –±–æ–ª—å—à–æ–µ –û –∞–ª–≥–æ—Ä–∏—Ç–º–∞ —Ä–∞—Å—Å–º–∞—Ç—Ä–∏–≤–∞–µ—Ç –Ω–∞–∏—Ö—É–¥—à–∏–π —Å—Ü–µ–Ω–∞—Ä–∏–π –∏–ª–∏ –∞—Å–∏–º–ø—Ç–æ—Ç–∏—á–µ—Å–∫—É—é –≤–µ—Ä—Ö–Ω—é—é –≥—Ä–∞–Ω–∏—Ü—É.

–û–ø—Ä–µ–¥–µ–ª–µ–Ω–∏–µ –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞, –Ω–µ–æ–±—Ö–æ–¥–∏–º–æ–≥–æ –¥–ª—è –∑–∞–ø—É—Å–∫–∞ –∞–ª–≥–æ—Ä–∏—Ç–º–∞

–ö–æ–≥–¥–∞ –º—ã —Ä–∞—Å—Å—á–∏—Ç—ã–≤–∞–µ–º –ß—Ç–æ–±—ã –æ—Ü–µ–Ω–∏—Ç—å —Å–ª–æ–∂–Ω–æ—Å—Ç—å –∞–ª–≥–æ—Ä–∏—Ç–º–∞ –≤ –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–µ, –æ–±—Ä–∞—Ç–∏—Ç–µ –≤–Ω–∏–º–∞–Ω–∏–µ –Ω–∞ –¥–≤–µ –≤–µ—â–∏: —Ä–∞–∑–º–µ—Ä –≤—Ö–æ–¥–Ω—ã—Ö –¥–∞–Ω–Ω—ã—Ö –∏ –≤—Å–ø–æ–º–æ–≥–∞—Ç–µ–ª—å–Ω–æ–µ –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–æ, –Ω–µ–æ–±—Ö–æ–¥–∏–º–æ–µ –¥–ª—è –∑–∞–ø—É—Å–∫–∞ —Ñ—É–Ω–∫—Ü–∏–∏. –í –±–æ–ª—å—à–∏–Ω—Å—Ç–≤–µ —Å–ª—É—á–∞–µ–≤ –º—ã –Ω–µ —É–º–µ–Ω—å—à–∞–µ–º —Ä–∞–∑–º–µ—Ä –¥–æ –∫–æ–ª–∏—á–µ—Å—Ç–≤–∞ –±–∞–π—Ç–æ–≤ –Ω–∞ –≤—Ö–æ–¥–µ & ndash; –º—ã –ø—Ä–æ—Å—Ç–æ —Å–º–æ—Ç—Ä–∏–º, –∫–∞–∫–æ–π –æ–±—ä–µ–º –ø–∞–º—è—Ç–∏ –Ω–µ–æ–±—Ö–æ–¥–∏–º–æ –∏—Å–ø–æ–ª—å–∑–æ–≤–∞—Ç—å –¥–ª—è –≤–≤–æ–¥–∞ –∏–ª–∏ –≤—Å–ø–æ–º–æ–≥–∞—Ç–µ–ª—å–Ω–æ–≥–æ –ø—Ä–æ—Å—Ç—Ä–∞–Ω—Å—Ç–≤–∞. & nbsp;