Рекурсия Python: Руководство

Michael Zippo 27.11.2021

–ö–∞–∫ –∏—Å–ø–æ–ª—å–∑–æ–≤–∞—Ç—å —Ä–µ–∫—É—Ä—Å–∏—é Python

–†–µ–∫—É—Ä—Å–∏—è Python - —É—Å—Ç—Ä–∞—à–∞—é—â–∞—è —Ç–µ–º–∞ –¥–ª—è –Ω–æ–≤–∏—á–∫–æ–≤. –î–∞–≤–∞–π—Ç–µ —Ä–∞–∑–≤–µ–µ–º –º–∏—Ñ –æ —Ç–æ–º, —á—Ç–æ —Ä–µ–∫—É—Ä—Å–∏—è —Ç—Ä—É–¥–Ω–∞, –ø—É—Ç–µ–º –µ–µ –æ–ø—Ä–µ–¥–µ–ª–µ–Ω–∏—è. –†–µ–∫—É—Ä—Å–∏—è - —ç—Ç–æ –º–µ—Ç–æ–¥ –ø—Ä–æ–≥—Ä–∞–º–º–∏—Ä–æ–≤–∞–Ω–∏—è, –ø—Ä–∏ –∫–æ—Ç–æ—Ä–æ–º —Ñ—É–Ω–∫—Ü–∏—è –≤—ã–∑—ã–≤–∞–µ—Ç —Å–∞–º–∞ —Å–µ–±—è.

–ó–≤—É—á–∏—Ç –ø—Ä–æ—Å—Ç–æ, –ø—Ä–∞–≤–¥–∞? –ö–æ–≥–¥–∞ –≤—ã –æ—Å–≤–æ–∏—Ç–µ—Å—å, —Ä–µ–∫—É—Ä—Å–∏—è - –Ω–µ —Å–ª–æ–∂–Ω–∞—è –∫–æ–Ω—Ü–µ–ø—Ü–∏—è.

–í —ç—Ç–æ–º —Ä—É–∫–æ–≤–æ–¥—Å—Ç–≤–µ –ø–æ Python –º—ã –ø–æ–≥–æ–≤–æ—Ä–∏–º –æ —Ä–µ–∫—É—Ä—Å–∏–∏ –∏ –æ —Ç–æ–º, –∫–∞–∫ –æ–Ω–∞ —Ä–∞–±–æ—Ç–∞–µ—Ç. –ú—ã —Ä–∞—Å—Å–º–æ—Ç—Ä–∏–º –ø—Ä–∏–º–µ—Ä —Ä–µ–∫—É—Ä—Å–∏–∏ —Å –∏—Å–ø–æ–ª—å–∑–æ–≤–∞–Ω–∏–µ–º —Ñ–∞–∫—Ç–æ—Ä–∏–∞–ª—å–Ω—ã—Ö —Ñ—É–Ω–∫—Ü–∏–π, —á—Ç–æ–±—ã –ø–æ–º–æ—á—å –≤–∞–º –Ω–∞—á–∞—Ç—å —Ä–∞–±–æ—Ç—É —Å —ç—Ç–∏–º –º–µ—Ç–æ–¥–æ–º –ø—Ä–æ–≥—Ä–∞–º–º–∏—Ä–æ–≤–∞–Ω–∏—è.

–ß—Ç–æ —Ç–∞–∫–æ–µ —Ä–µ–∫—É—Ä—Å–∏—è?

–†–µ–∫—É—Ä—Å–∏—è - —ç—Ç–æ —Ç–æ, –≥–¥–µ –≤—ã –æ–ø—Ä–µ–¥–µ–ª—è–µ—Ç–µ —á—Ç–æ-—Ç–æ –≤ —Ç–µ—Ä–º–∏–Ω–∞—Ö —Å–∞–º–∞.

–†–µ–∫—É—Ä—Å–∏–≤–Ω–∞—è —Ñ—É–Ω–∫—Ü–∏—è —Ä–µ—à–∞–µ—Ç –ø—Ä–æ–±–ª–µ–º—ã, –≤—ã–∑—ã–≤–∞—è —Å–µ–±—è —Å–Ω–æ–≤–∞. –¢–∞–∫–æ–µ –ø–æ–≤–µ–¥–µ–Ω–∏–µ –ø–æ–¥–¥–µ—Ä–∂–∏–≤–∞–µ—Ç—Å—è –±–æ–ª—å—à–∏–Ω—Å—Ç–≤–æ–º –æ—Å–Ω–æ–≤–Ω—ã—Ö —è–∑—ã–∫–æ–≤ –ø—Ä–æ–≥—Ä–∞–º–º–∏—Ä–æ–≤–∞–Ω–∏—è, –Ω–∞–ø—Ä–∏–º–µ—Ä Python. –û–Ω–∏ —è–≤–ª—è—é—Ç—Å—è –≤–∞–∂–Ω–æ–π —á–∞—Å—Ç—å—é –∏–Ω—Ñ–æ—Ä–º–∞—Ç–∏–∫–∏ –∏ –Ω–∞—É–∫–∏ –æ –¥–∞–Ω–Ω—ã—Ö.

–†–µ–∫—É—Ä—Å–∏—è –ø–æ–ª–µ–∑–Ω–∞, –∫–æ–≥–¥–∞ —Ä–µ—à–µ–Ω–∏–µ –ø—Ä–æ–±–ª–µ–º—ã –º–æ–∂–Ω–æ –Ω–∞–π—Ç–∏, —Ä–∞–∑–±–∏–≤ –µ–µ –Ω–∞ –±–æ–ª–µ–µ –º–µ–ª–∫–∏–µ –∑–∞–¥–∞—á–∏, –∏—Å–ø–æ–ª—å–∑—É—é—â–∏–µ –æ–¥–Ω—É –∏ —Ç—É –∂–µ —Ñ–æ—Ä–º—É–ª—É. –ü—Ä–æ–±–ª–µ–º—ã —Ç–∞–∫–æ–≥–æ —Ç–∏–ø–∞ —á–∞—Å—Ç–æ –Ω–∞–∑—ã–≤–∞—é—Ç "—Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–º–∏ –∞–ª–≥–æ—Ä–∏—Ç–º–∞–º–∏". –ö–ª—é—á –∫ –∏—Ö —Ä–µ—à–µ–Ω–∏—é - –≤ –Ω–∞–∑–≤–∞–Ω–∏–∏!

–ò—Ç–µ—Ä–∞—Ç–∏–≤–Ω—ã–π –∏ —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–π

–ï—Å—Ç—å –¥–≤–∞ —Å–ø–æ—Å–æ–±–∞ —Ä–µ—à–∏—Ç—å –∞–ª–≥–æ—Ä–∏—Ç–º: –∏—Ç–µ—Ä–∞—Ç–∏–≤–Ω–æ –∏–ª–∏ —Ä–µ–∫—É—Ä—Å–∏–≤–Ω–æ.

–ò—Ç–µ—Ä–∞—Ü–∏–æ–Ω–Ω—ã–µ —Ä–µ—à–µ–Ω–∏—è –∞–ª–≥–æ—Ä–∏—Ç–º–æ–≤ —Å—á–∏—Ç–∞—é—Ç—Å—è "–º–æ—â–Ω—ã–º–∏, –Ω–æ —É—Ä–æ–¥–ª–∏–≤—ã–º–∏". –û–Ω–∏ –≤—ã–ø–æ–ª–Ω—è—é—Ç —Å–≤–æ—é —Ä–∞–±–æ—Ç—É, –Ω–æ –Ω–µ –¥–µ–ª–∞—é—Ç –µ–µ —Å–∞–º—ã–º —ç–ª–µ–≥–∞–Ω—Ç–Ω—ã–º —Å–ø–æ—Å–æ–±–æ–º. –ß—Ç–æ–±—ã –ø—Ä–∞–≤–∏–ª—å–Ω–æ –ø–æ–Ω—è—Ç—å —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–µ –∞–ª–≥–æ—Ä–∏—Ç–º—ã, –Ω–∞–º –Ω—É–∂–Ω–æ –≤–∑–≥–ª—è–Ω—É—Ç—å –Ω–∞ –∏—Ç–µ—Ä–∞—Ç–∏–≤–Ω—ã–µ —Ñ—É–Ω–∫—Ü–∏–∏.

81% —É—á–∞—Å—Ç–Ω–∏–∫–æ–≤ –∑–∞—è–≤–∏–ª–∏, —á—Ç–æ –æ–Ω–∏ –ø–æ—á—É–≤—Å—Ç–≤–æ–≤–∞–ª–∏ —Å–µ–±—è –±–æ–ª–µ–µ —É–≤–µ—Ä–µ–Ω–Ω—ã–º–∏ –≤ —Å–≤–æ–∏—Ö –ø–µ—Ä—Å–ø–µ–∫—Ç–∏–≤–∞—Ö —Ç—Ä—É–¥–æ—É—Å—Ç—Ä–æ–π—Å—Ç–≤–∞ –≤ —Ç–µ—Ö–Ω–∏—á–µ—Å–∫–∏—Ö –æ–±–ª–∞—Å—Ç—è—Ö –ø–æ—Å–ª–µ –ø–æ—Å–µ—â–µ–Ω–∏—è —É—á–µ–±–Ω–æ–≥–æ –∫—É—Ä—Å–∞. –ü—Ä–æ–π–¥–∏—Ç–µ –∫—É—Ä—Å –æ–±—É—á–µ–Ω–∏—è —Å–µ–≥–æ–¥–Ω—è.

–°—Ä–µ–¥–Ω–∏–π –≤—ã–ø—É—Å–∫–Ω–∏–∫ —É—á–µ–±–Ω–æ–≥–æ –ª–∞–≥–µ—Ä—è –ø–æ—Ç—Ä–∞—Ç–∏–ª –º–µ–Ω–µ–µ —à–µ—Å—Ç–∏ –º–µ—Å—è—Ü–µ–≤ –Ω–∞ –ø–µ—Ä–µ—Ö–æ–¥–Ω—É—é –∫–∞—Ä—å–µ—Ä—É, –æ—Ç –Ω–∞—á–∞–ª–∞ —É—á–µ–±–Ω–æ–≥–æ –ª–∞–≥–µ—Ä—è –¥–æ –ø–æ–∏—Å–∫–∞ —Å–≤–æ–µ–π –ø–µ—Ä–≤–æ–π —Ä–∞–±–æ—Ç—ã.

–ò—Ç–µ—Ä–∞—Ç–∏–≤–Ω–∞—è function - —ç—Ç–æ —Ñ—É–Ω–∫—Ü–∏—è, –∫–æ—Ç–æ—Ä–∞—è —Ä–µ—à–∞–µ—Ç –ø—Ä–æ–±–ª–µ–º—É —Å –ø–æ–º–æ—â—å—é —Ü–∏–∫–ª–∞. –û–Ω –±—É–¥–µ—Ç –≤—ã–ø–æ–ª–Ω—è—Ç—å –∫–æ–¥ –≤–Ω—É—Ç—Ä–∏ —Ü–∏–∫–ª–∞, –ø–æ–∫–∞ —ç—Ç–æ—Ç —Ü–∏–∫–ª –Ω–µ –±—É–¥–µ—Ç –∑–∞–≤–µ—Ä—à–µ–Ω. –†–µ–∫—É—Ä—Å–∏–≤–Ω–∞—è —Ñ—É–Ω–∫—Ü–∏—è - —ç—Ç–æ —Ñ—É–Ω–∫—Ü–∏—è, –∫–æ—Ç–æ—Ä–∞—è —Ä–∞–∑–±–∏–≤–∞–µ—Ç –ø—Ä–æ–±–ª–µ–º—É –Ω–∞ –±–æ–ª–µ–µ –º–µ–ª–∫–∏–µ —á–∞—Å—Ç–∏ –∏ —Ä–µ—à–∞–µ—Ç –∫–∞–∂–¥—É—é —á–∞—Å—Ç—å, –≤—ã–∑—ã–≤–∞—è —Å–µ–±—è.

–§–∞–∫—Ç–æ—Ä–∏–∞–ª—ã: –∏—Ç–µ—Ä–∞—Ç–∏–≤–Ω—ã–π –ø—Ä–∏–º–µ—Ä

–§–∞–∫—Ç–æ—Ä–∏–∞–ª—ã - —Ö–æ—Ä–æ—à–∏–π —Å–ø–æ—Å–æ–± –ø—Ä–æ–¥–µ–º–æ–Ω—Å—Ç—Ä–∏—Ä–æ–≤–∞—Ç—å —Ä–µ–∫—É—Ä—Å–∏—é –∏ –∏—Ç–µ—Ä–∞—Ç–∏–≤–Ω–æ–µ –º—ã—à–ª–µ–Ω–∏–µ. –í –º–∞—Ç–µ–º–∞—Ç–∏–∫–µ —Ñ–∞–∫—Ç–æ—Ä–∏–∞–ª—ã - —ç—Ç–æ —Å—É–º–º–∞ —á–∏—Å–ª–∞ –∏ –∫–∞–∂–¥–æ–≥–æ —á–∏—Å–ª–∞ –¥–æ –µ–≥–æ —É–º–Ω–æ–∂–µ–Ω–∏—è.

–§–∞–∫—Ç–æ—Ä–∏–∞–ª 5 —Ä–∞–≤–µ–Ω 5 * 4 * 3 * 2 * 1. –§–∞–∫—Ç–æ—Ä–∏–∞–ª 2 —Ä–∞–≤–µ–Ω 2 * 1.

–ß—Ç–æ–±—ã –≤—ã—á–∏—Å–ª–∏—Ç—å factorial, –º—ã –º–æ–∂–µ–º –Ω–∞–ø–∏—Å–∞—Ç—å –∏—Ç–µ—Ä–∞—Ç–∏–≤–Ω—É—é —Ñ—É–Ω–∫—Ü–∏—é:

–≠—Ç–∞ —Ñ—É–Ω–∫—Ü–∏—è –∏—Å–ø–æ–ª—å–∑—É–µ—Ç —Ü–∏–∫–ª for –¥–ª—è –ø–µ—Ä–µ–±–æ—Ä–∞ –≤—Å–µ—Ö —á–∏—Å–µ–ª –≤ –¥–∏–∞–ø–∞–∑–æ–Ω–µ –æ—Ç 1 –∏ —á–∏—Å–ª–∞, –∫–æ—Ç–æ—Ä–æ–µ –º—ã —É–∫–∞–∑–∞–ª–∏ –ø–ª—é—Å 1. –î–ª—è –∫–∞–∂–¥–æ–π –∏—Ç–µ—Ä–∞—Ü–∏–∏ —á–∏—Å–ª–æ, –∫–æ—Ç–æ—Ä–æ–µ –ø–æ–≤—Ç–æ—Ä—è–µ—Ç—Å—è —Ü–∏–∫–ª, —É–º–Ω–æ–∂–∞–µ—Ç—Å—è –Ω–∞ –≤—Å–µ–≥–æ. –î–∞–≤–∞–π—Ç–µ –≤—ã–∑–æ–≤–µ–º –Ω–∞—à—É —Ñ—É–Ω–∫—Ü–∏—é, —á—Ç–æ–±—ã –Ω–∞–π—Ç–∏ —Ñ–∞–∫—Ç–æ—Ä–∏–∞–ª:

–ù–∞—à –∫–æ–¥ –≤–æ–∑–≤—Ä–∞—â–∞–µ—Ç: 24. –ß—Ç–æ–±—ã –ø—Ä–∏–π—Ç–∏ –∫ —ç—Ç–æ–º—É —Ä–µ—à–µ–Ω–∏—é, –Ω–∞—à –∫–æ–¥ –∑–∞–ø—É—Å–∫–∞–µ—Ç—Å—è:

1 * 1 = 1
2 * 2 = 4
4 * 3 = 8
8 * 4 = 24

–ö–∞–∫ –≤–∏–¥–∏—Ç–µ, –Ω–∞—à –∫–æ–¥ —É–º–Ω–æ–∂–∞–µ—Ç 4 –Ω–∞ –≤—Å–µ —á–∏—Å–ª–∞ –Ω–∏–∂–µ, —á–µ–º –æ–Ω, –∞ –∑–∞—Ç–µ–º –Ω–∞ —Å–µ–±—è.

–≠—Ç–æ—Ç –∫–æ–¥ —Ä–∞–±–æ—Ç–∞–µ—Ç. –ï–¥–∏–Ω—Å—Ç–≤–µ–Ω–Ω—ã–π –Ω–µ–¥–æ—Å—Ç–∞—Ç–æ–∫ - —ç—Ç–æ –Ω–µ —Ç–∞–∫ —ç–ª–µ–≥–∞–Ω—Ç–Ω–æ, –∫–∞–∫ –º–æ–≥–ª–æ –±—ã –±—ã—Ç—å. –í–æ—Ç –≥–¥–µ –ø—Ä–∏–≥–æ–¥—è—Ç—Å—è —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–µ —Ñ—É–Ω–∫—Ü–∏–∏.

–§–∞–∫—Ç–æ—Ä–∏–∞–ª—ã: –ø—Ä–∏–º–µ—Ä —Ä–µ–∫—É—Ä—Å–∏–∏

–î–∞–≤–∞–π—Ç–µ –Ω–∞–ø–∏—à–µ–º —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—É—é —Ñ—É–Ω–∫—Ü–∏—é, –∫–æ—Ç–æ—Ä–∞—è –≤—ã—á–∏—Å–ª—è–µ—Ç —Ñ–∞–∫—Ç–æ—Ä–∏–∞–ª. –û—Ç–∫—Ä–æ–π—Ç–µ –Ω–æ–≤—ã–π —Ñ–∞–π–ª Python –∏ –≤—Å—Ç–∞–≤—å—Ç–µ —Å–ª–µ–¥—É—é—â–∏–π –∫–æ–¥:

–í —ç—Ç–æ–º –∫–æ–¥–µ –∏—Å–ø–æ–ª—å–∑—É–µ—Ç—Å—è —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–π –ø–æ–¥—Ö–æ–¥. –ü—Ä–∏ –∑–∞–ø—É—Å–∫–µ —ç—Ç–æ–π —Ñ—É–Ω–∫—Ü–∏–∏ –ø–æ—è–≤–ª—è–µ—Ç—Å—è —Å–æ–æ–±—â–µ–Ω–∏–µ " if " –∏–Ω—Å—Ç—Ä—É–∫—Ü–∏—è –≤—ã–ø–æ–ª–Ω—è–µ—Ç—Å—è. –≠—Ç–æ—Ç –æ–ø–µ—Ä–∞—Ç–æ—Ä –ø—Ä–æ–≤–µ—Ä—è–µ—Ç, —Ä–∞–≤–Ω–æ –ª–∏ —á–∏—Å–ª–æ, –ø–µ—Ä–µ–¥–∞–Ω–Ω–æ–µ –≤ —Ñ—É–Ω–∫—Ü–∏—é, 1. –ï—Å–ª–∏ —ç—Ç–æ —Ç–∞–∫, –Ω–∞—à–∞ —Ñ—É–Ω–∫—Ü–∏—è –≤–æ–∑–≤—Ä–∞—â–∞–µ—Ç 1. –í –ø—Ä–æ—Ç–∏–≤–Ω–æ–º —Å–ª—É—á–∞–µ –≤—ã—á–∏—Å–ª—è–µ—Ç—Å—è —Ñ–∞–∫—Ç–æ—Ä–∏–∞–ª –Ω–∞—à–µ–≥–æ —á–∏—Å–ª–∞.

–≠—Ç–æ—Ç —Ä–∞—Å—á–µ—Ç —Ä–∞–±–æ—Ç–∞–µ—Ç –ø—É—Ç–µ–º —É–º–Ω–æ–∂–µ–Ω–∏—è —á–∏—Å–ª–æ, –ø–µ—Ä–µ–¥–∞–Ω–Ω–æ–µ –≤ —Ñ—É–Ω–∫—Ü–∏—é —Ñ–∞–∫—Ç–æ—Ä–∏–∞–ª–æ–º –ø—Ä–µ–¥—ã–¥—É—â–µ–≥–æ —á–∏—Å–ª–∞. –≠—Ç–∞ —Ñ—É–Ω–∫—Ü–∏—è –≤—ã–∑—ã–≤–∞–µ—Ç—Å—è —Å–Ω–æ–≤–∞ –∏ —Å–Ω–æ–≤–∞, –ø–æ–∫–∞ " number " —Ä–∞–≤–Ω–æ 1. –ö–∞–∂–¥—ã–π —Ä–∞–∑ –ø—Ä–∏ –≤—ã–∑–æ–≤–µ —Ñ—É–Ω–∫—Ü–∏–∏ –∑–Ω–∞—á–µ–Ω–∏–µ " number " —É–º–µ–Ω—å—à–∞–µ—Ç—Å—è –Ω–∞ 1.

–î–∞–≤–∞–π—Ç–µ –ø–æ–ø—Ä–æ–±—É–µ–º –Ω–∞—à –∫–æ–¥ —Å –Ω–æ–º–µ—Ä–æ–º 4:

–í–æ–∑–≤—Ä–∞—â–µ–Ω –æ—Ç–≤–µ—Ç 24. –ù–∞—à –æ—Ç–≤–µ—Ç –ø—Ä–∞–≤–∏–ª—å–Ω—ã–π; –æ–Ω —Ç–∞–∫–æ–π –∂–µ, –∫–∞–∫ –∏ –≤ –Ω–∞—à–µ–º –ø–æ—Å–ª–µ–¥–Ω–µ–º –ø—Ä–∏–º–µ—Ä–µ. –ú—ã –Ω–∞—à–ª–∏ —Ä–µ—à–µ–Ω–∏–µ —Ä–µ—à–∏—Ç—å —ç—Ç—É –ø—Ä–æ–±–ª–µ–º—É —Ä–µ–∫—É—Ä—Å–∏–≤–Ω–æ, –∞ –Ω–µ –∏—Ç–µ—Ä–∞—Ç–∏–≤–Ω–æ.

–í–∞–º –≤—Å–µ –µ—â–µ –Ω—É–∂–Ω–∞ –Ω–µ–±–æ–ª—å—à–∞—è –ø–æ–º–æ—â—å? –î–∞–≤–∞–π—Ç–µ —Ä–∞—Å—Å–º–æ—Ç—Ä–∏–º –µ—â–µ –æ–¥–∏–Ω –ø—Ä–∏–º–µ—Ä —Ä–µ–∫—É—Ä—Å–∏–∏.

–†–µ–∫—É—Ä—Å–∏—è —Å –ø–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç—å—é –§–∏–±–æ–Ω–∞—á—á–∏ < / h2>
–ü–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç—å –§–∏–±–æ–Ω–∞—á—á–∏ - —ç—Ç–æ –º–∞—Ç–µ–º–∞—Ç–∏—á–µ—Å–∫–∞—è –ø–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç—å, –≤ –∫–æ—Ç–æ—Ä–æ–π –∫–∞–∂–¥–æ–µ —á–∏—Å–ª–æ —è–≤–ª—è–µ—Ç—Å—è —Å—É–º–º–æ–π –¥–≤—É—Ö –ø—Ä–µ–¥—ã–¥—É—â–∏—Ö —á–∏—Å–µ–ª. –≠—Ç–∞ –ø–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç—å –Ω–∞—á–∏–Ω–∞–µ—Ç—Å—è —Å: 0, 1, 1, 2, 3, 5, 8, 13 –∏ —Ç. –¥.

–≠—Ç–∞ –ø–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç—å –¥–æ–±–∞–≤–ª—è–µ—Ç –¥–≤–∞ —á–∏—Å–ª–∞, —á—Ç–æ–±—ã –Ω–∞–π—Ç–∏ —Å–ª–µ–¥—É—é—â–µ–µ —á–∏—Å–ª–æ. –≠—Ç–æ –¥–µ–ª–∞–µ—Ç –µ–µ –∏–¥–µ–∞–ª—å–Ω–æ–π –¥–ª—è —Ä–µ–∫—É—Ä—Å–∏–∏.

–û—Ç–∫—Ä–æ–π—Ç–µ —Ñ–∞–π–ª Python –∏ –≤—Å—Ç–∞–≤—å—Ç–µ —ç—Ç–æ—Ç –∫–æ–¥: < br>

–≠—Ç–æ—Ç –∫–æ–¥ –±—É–¥–µ—Ç –≤—ã—á–∏—Å–ª—è—Ç—å —Å—É–º–º—É –¥–≤—É—Ö –ø—Ä–µ–¥—ã–¥—É—â–∏—Ö —á–∏—Å–µ–ª –≤ —Å–ø–∏—Å–∫–µ, –µ—Å–ª–∏ " number " –±–æ–ª—å—à–µ 1. –í –ø—Ä–æ—Ç–∏–≤–Ω–æ–º —Å–ª—É—á–∞–µ –≤–æ–∑–≤—Ä–∞—â–∞–µ—Ç—Å—è " —á–∏—Å–ª–æ & rdquo ;. –ê —Ç–µ–ø–µ—Ä—å –ø–æ–∑–≤–æ–ª—å—Ç–µ –Ω–∞–º –≤—ã–∑–≤–∞—Ç—å –Ω–∞—à—É —Ñ—É–Ω–∫—Ü–∏—é:

"–ö–∞—Ä—å–µ—Ä–Ω–∞—è –∫–∞—Ä–º–∞ –≤–æ—à–ª–∞ –≤ –º–æ—é –∂–∏–∑–Ω—å, –∫–æ–≥–¥–∞ —è –±–æ–ª—å—à–µ –≤—Å–µ–≥–æ –≤ –Ω–µ–π –Ω—É–∂–¥–∞–ª–∞—Å—å, –∏ –±—ã—Å—Ç—Ä–æ –ø–æ–º–æ–≥–ª–∞ –º–Ω–µ –ø—Ä–æ–π—Ç–∏ –∫—É—Ä—Å –æ–±—É—á–µ–Ω–∏—è. –ß–µ—Ä–µ–∑ –¥–≤–∞ –º–µ—Å—è—Ü–∞ –ø–æ—Å–ª–µ –æ–∫–æ–Ω—á–∞–Ω–∏—è —É—á–µ–±—ã —è –Ω–∞—à–µ–ª —Ä–∞–±–æ—Ç—É —Å–≤–æ–µ–π –º–µ—á—Ç—ã, –∫–æ—Ç–æ—Ä–∞—è —Å–æ–≥–ª–∞—Å–æ–≤–∞–Ω—ã —Å –º–æ–∏–º–∏ —Ü–µ–Ω–Ω–æ—Å—Ç—è–º–∏ –∏ —Ü–µ–ª—è–º–∏ –≤ –∂–∏–∑–Ω–∏! "

–í–µ–Ω–µ—Ä–∞, –∏–Ω–∂–µ–Ω–µ—Ä-–ø—Ä–æ–≥—Ä–∞–º–º–∏—Å—Ç Rockbot

–ü–µ—Ä–µ–º–µ–Ω–Ω–∞—è –≤—ã–ø–æ–ª–Ω–µ–Ω–∏—è –æ—Ç—Å–ª–µ–∂–∏–≤–∞–µ—Ç, —Å–∫–æ–ª—å–∫–æ —á–∏—Å–µ–ª –≤ –ø–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç—å –§–∏–±–æ–Ω–∞—á—á–∏, –∫–æ—Ç–æ—Ä—É—é –º—ã —Ö–æ—Ç–∏–º –≤—ã—á–∏—Å–ª–∏—Ç—å. –ú—ã –∏—Å–ø–æ–ª—å–∑—É–µ–º —ç—Ç–æ –¥–ª—è —Å–æ–∑–¥–∞–Ω–∏—è —Ü–∏–∫–ª–∞ for, –∫–æ—Ç–æ—Ä—ã–π –≤—ã–∑—ã–≤–∞–µ—Ç –Ω–∞—à—É —Ñ—É–Ω–∫—Ü–∏—é `fibonacci ()` –¥–ª—è –∫–∞–∂–¥–æ–≥–æ —á–∏—Å–ª–∞ –≤ –¥–∏–∞–ø–∞–∑–æ–Ω–µ 1 –∏ –∑–Ω–∞—á–µ–Ω–∏—è " –≤—ã–ø–æ–ª–Ω–µ–Ω–∏–π "

–ü–µ—Ä–µ–¥ –∑–∞–ø—É—Å–∫–æ–º —Ü–∏–∫–ª–∞ for –º—ã –ø–µ—á–∞—Ç–∞–µ–º " –ü–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç—å –§–∏–±–æ–Ω–∞—á—á–∏: " –∫ –∫–æ–Ω—Å–æ–ª–∏. –í —ç—Ç–æ–º –ø—Ä–∏–º–µ—Ä–µ –Ω–∞—à " for " –≤—ã–ø–æ–ª–Ω—è–µ—Ç—Å—è —Ü–∏–∫–ª:

–î–∞–≤–∞–π—Ç–µ –≤–º–µ—Å—Ç–µ –∑–∞–ø—É—Å—Ç–∏–º –Ω–∞—à –∫–æ–¥ –∏ –ø–æ—Å–º–æ—Ç—Ä–∏–º, —á—Ç–æ –ø—Ä–æ–∏–∑–æ–π–¥–µ—Ç:

–ù–∞—à –∫–æ–¥ –≤—ã—á–∏—Å–ª—è–µ—Ç –ø–µ—Ä–≤—ã–µ –ø—è—Ç—å —á–∏—Å–µ–ª –≤ –ø–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç–∏ –§–∏–±–æ–Ω–∞—á—á–∏. –ú—ã –º–æ–≥–ª–∏ –±—ã –≤—ã—á–∏—Å–ª–∏—Ç—å –±–æ–ª—å—à–µ —á–∏—Å–µ–ª, —É–≤–µ–ª–∏—á–∏–≤ –∑–Ω–∞—á–µ–Ω–∏–µ " Executions & rdquo ;.

–ì–ª—É–±–∏–Ω–∞ —Ä–µ–∫—É—Ä—Å–∏–∏ –∏ –±–∞–∑–æ–≤—ã–µ —É—Å–ª–æ–≤–∏—è

–†–µ–∫—É—Ä—Å–∏–≤–Ω–∞—è —Ñ—É–Ω–∫—Ü–∏—è –¥–æ–ª–∂–Ω–∞ –∏–º–µ—Ç—å –±–∞–∑–æ–≤–æ–µ —É—Å–ª–æ–≤–∏–µ. –≠—Ç–æ —É—Å–ª–æ–≤–∏–µ, –∫–æ—Ç–æ—Ä–æ–µ –æ—Å—Ç–∞–Ω–∞–≤–ª–∏–≤–∞–µ—Ç —Ä–µ–∫—É—Ä—Å–∏—é –ø—Ä–∏ –≤—ã–ø–æ–ª–Ω–µ–Ω–∏–∏ –æ–ø—Ä–µ–¥–µ–ª–µ–Ω–Ω–æ–≥–æ –±–∞–∑–æ–≤–æ–≥–æ —Å–ª—É—á–∞—è. –ë–µ–∑ –±–∞–∑–æ–≤–æ–π —Ñ—É–Ω–∫—Ü–∏–∏ –±—É–¥–µ—Ç —Å–æ–∑–¥–∞–Ω –±–µ—Å–∫–æ–Ω–µ—á–Ω—ã–π —Ü–∏–∫–ª.

–ü–æ —É–º–æ–ª—á–∞–Ω–∏—é —Ä–µ–∫—É—Ä—Å–∏–≤–Ω–∞—è —Ñ—É–Ω–∫—Ü–∏—è –º–æ–∂–µ—Ç –≤—ã–ø–æ–ª–Ω—è—Ç—å—Å—è –Ω–µ –±–æ–ª–µ–µ 1000 —Ä–∞–∑. –ü—Ä–∏ –¥–æ—Å—Ç–∏–∂–µ–Ω–∏–∏ —ç—Ç–æ–≥–æ –ø—Ä–µ–¥–µ–ª–∞ –ø–æ—è–≤–ª—è–µ—Ç—Å—è —Ç–∞–∫–∞—è –æ—à–∏–±–∫–∞:

–í–æ—Ç –±–∞–∑–æ–≤–æ–µ —É—Å–ª–æ–≤–∏–µ –¥–ª—è –Ω–∞—à–µ–π –ø—Ä–æ–≥—Ä–∞–º–º—ã –§–∏–±–æ–Ω–∞—á—á–∏:

–≠—Ç–æ —É—Å–ª–æ–≤–∏–µ –ø—Ä–æ–≤–µ—Ä—è–µ—Ç, —Ä–∞–≤–Ω–æ –ª–∏ –∑–Ω–∞—á–µ–Ω–∏–µ " number " –≤–Ω—É—Ç—Ä–∏ –Ω–∞—à–µ–π –ø—Ä–æ–≥—Ä–∞–º–º—ã –§–∏–±–æ–Ω–∞—á—á–∏ 1. –ï—Å–ª–∏ –¥–∞, —Ç–æ –≤–æ–∑–≤—Ä–∞—â–∞–µ—Ç—Å—è –∑–Ω–∞—á–µ–Ω–∏–µ " number " –≤ –ø—Ä–æ—Ç–∏–≤–Ω–æ–º —Å–ª—É—á–∞–µ –∑–∞–ø—É—Å–∫–∞–µ—Ç—Å—è —Ä–µ–∫—É—Ä—Å–∏–≤–Ω–∞—è —Ñ—É–Ω–∫—Ü–∏—è.

–ü–æ—á–µ–º—É –°—Ç–æ–∏—Ç –ª–∏ –∏—Å–ø–æ–ª—å–∑–æ–≤–∞—Ç—å —Ä–µ–∫—É—Ä—Å–∏—é?

–í —á–µ–º –ø—Ä–µ–∏–º—É—â–µ—Å—Ç–≤–æ –∏—Å–ø–æ–ª—å–∑–æ–≤–∞–Ω–∏—è —Ä–µ–∫—É—Ä—Å–∏–∏ –ø–µ—Ä–µ–¥ –∏—Ç–µ—Ä–∞—Ç–∏–≤–Ω—ã–º–∏ —Ñ—É–Ω–∫—Ü–∏—è–º–∏? –¢–µ—Ö–Ω–∏—á–µ—Å–∫–∏ –æ–±–∞ –º–µ—Ç–æ–¥–∞ –º–æ–≥—É—Ç –¥–∞—Ç—å –æ–¥–∏–Ω –∏ —Ç–æ—Ç –∂–µ —Ä–µ–∑—É–ª—å—Ç–∞—Ç. –†–µ–∫—É—Ä—Å–∏—è –∑–∞–∫–ª—é—á–∞–µ—Ç—Å—è –≤ —Ç–æ–º, —á—Ç–æ –µ–µ –ª–µ–≥—á–µ —á–∏—Ç–∞—Ç—å.

–ö–æ–≥–¥–∞ –≤—ã –≤–∏–¥–∏—Ç–µ —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—É—é —Ñ—É–Ω–∫—Ü–∏—é, —Å—Ç–∞–Ω–æ–≤–∏—Ç—Å—è —è—Å–Ω–æ, —á—Ç–æ –æ—Ç–≤–µ—Ç –Ω–∞ –ø—Ä–æ–±–ª–µ–º—É –∑–∞–∫–ª—é—á–∞–µ—Ç—Å—è –≤ –µ–µ —Ä–∞–∑–±–∏–µ–Ω–∏–∏ –Ω–∞ –±–æ–ª–µ–µ –º–µ–ª–∫–∏–µ —á–∞—Å—Ç–∏. –•–æ—Ç—è –∏—Ç–µ—Ä–∞—Ü–∏–æ–Ω–Ω—ã–µ —Ü–∏–∫–ª—ã –∏–Ω–æ–≥–¥–∞ –º–æ–≥—É—Ç –±—ã—Ç—å –±—ã—Å—Ç—Ä–µ–µ, —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–µ —Ñ—É–Ω–∫—Ü–∏–∏ –æ–±—ã—á–Ω–æ –ø—Ä–µ–¥–ø–æ—á—Ç–∏—Ç–µ–ª—å–Ω–µ–µ –∏–∑-–∑–∞ –∏—Ö —É–¥–æ–±–æ—á–∏—Ç–∞–µ–º–æ—Å—Ç–∏.

–ü–æ—Å–∫–æ–ª—å–∫—É —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–µ —Ñ—É–Ω–∫—Ü–∏–∏ –ª–µ–≥—á–µ —á–∏—Ç–∞—Ç—å, –∏—Ö —Ç–∞–∫–∂–µ –ª–µ–≥—á–µ –ø–æ–¥–¥–µ—Ä–∂–∏–≤–∞—Ç—å –∏ –æ—Ç–ª–∞–∂–∏–≤–∞—Ç—å. –≠—Ç–æ –æ—Å–æ–±–µ–Ω–Ω–æ –ø–æ–ª–µ–∑–Ω–æ, –∫–æ–≥–¥–∞ –≤—ã –ø–∏—à–µ—Ç–µ —Å–ª–æ–∂–Ω—ã–µ –∞–ª–≥–æ—Ä–∏—Ç–º—ã, –∫–æ—Ç–æ—Ä—ã–µ –º–æ–≥—É—Ç –±—ã—Ç—å —Ç—Ä—É–¥–Ω—ã–º–∏ –¥–ª—è –ø–æ–Ω–∏–º–∞–Ω–∏—è.

–ó–∞–∫–ª—é—á–µ–Ω–∏–µ

–†–µ–∫—É—Ä—Å–∏–≤–Ω–∞—è —Ñ—É–Ω–∫—Ü–∏—è - —ç—Ç–æ —Ñ—É–Ω–∫—Ü–∏—è, –∫–æ—Ç–æ—Ä–∞—è –≤—ã–∑—ã–≤–∞–µ—Ç —Å–µ–±—è, —á—Ç–æ–±—ã –Ω–∞–π—Ç–∏ —Ä–µ—à–µ–Ω–∏–µ –ø—Ä–æ–±–ª–µ–º—ã. & Nbsp ;

–†–µ–∫—É—Ä—Å–∏–≤–Ω—ã–µ —Ñ—É–Ω–∫—Ü–∏–∏ —Ä–∞–∑–±–∏–≤–∞—é—Ç –ø—Ä–æ–±–ª–µ–º—É –Ω–∞ –Ω–µ—Å–∫–æ–ª—å–∫–æ —á–∞—Å—Ç–µ–π –∏ —Ä–µ—à–∞—é—Ç –æ–¥–Ω—É —á–∞—Å—Ç—å –ø—Ä–æ–±–ª–µ–º—ã –∑–∞ –∏—Ç–µ—Ä–∞—Ü–∏—é. –†–µ–∫—É—Ä—Å–∏–≤–Ω—ã–µ —Ñ—É–Ω–∫—Ü–∏–∏ –æ–±—ã—á–Ω–æ –∏—Å–ø–æ–ª—å–∑—É—é—Ç—Å—è –¥–ª—è –≤—ã—á–∏—Å–ª–µ–Ω–∏—è —Ñ–∞–∫—Ç–æ—Ä–∏–∞–ª–æ–≤ –∏ —á–∏—Å–µ–ª –≤ –ø–æ—Å–ª–µ–¥–æ–≤–∞—Ç–µ–ª—å–Ω–æ—Å—Ç–∏ –§–∏–±–æ–Ω–∞—á—á–∏. –û–Ω–∏ —Ç–∞–∫–∂–µ –∏—Å–ø–æ–ª—å–∑—É—é—Ç—Å—è –≤ —Ä—è–¥–µ –∞–ª–≥–æ—Ä–∏—Ç–º–æ–≤.

–¢–µ–ø–µ—Ä—å –≤—ã –≥–æ—Ç–æ–≤—ã –Ω–∞—á–∞—Ç—å —Ä–∞–±–æ—Ç—É —Å —Ä–µ–∫—É—Ä—Å–∏–≤–Ω—ã–º–∏ —Ñ—É–Ω–∫—Ü–∏—è–º–∏ –≤ Python.