{"id":988424,"date":"2024-12-27T08:02:10","date_gmt":"2024-12-27T00:02:10","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/988424.html"},"modified":"2024-12-27T08:02:14","modified_gmt":"2024-12-27T00:02:14","slug":"python%e5%a6%82%e4%bd%95%e5%88%a4%e5%ae%9a%e6%98%af%e7%b4%a0%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/988424.html","title":{"rendered":"python\u5982\u4f55\u5224\u5b9a\u662f\u7d20\u6570"},"content":{"rendered":"

\"python\u5982\u4f55\u5224\u5b9a\u662f\u7d20\u6570\"<\/p>\n

Python\u5224\u5b9a\u7d20\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5305\u62ec\u8bd5\u9664\u6cd5\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u3001\u7c73\u52d2-\u62c9\u5bbe\u7d20\u6027\u6d4b\u8bd5\u3002\u8bd5\u9664\u6cd5\u9002\u7528\u4e8e\u5c0f\u8303\u56f4\u7d20\u6570\u5224\u5b9a\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u9002\u5408\u751f\u6210\u7d20\u6570\u5217\u8868\u3001\u7c73\u52d2-\u62c9\u5bbe\u7d20\u6027\u6d4b\u8bd5\u9002\u7528\u4e8e\u5927\u8303\u56f4\u7d20\u6570\u5224\u5b9a\u3002<\/strong>\u8bd5\u9664\u6cd5\u662f\u6700\u7b80\u5355\u7684\u5224\u5b9a\u65b9\u6cd5\uff0c\u901a\u8fc7\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u80fd\u88ab\u5c0f\u4e8e\u5176\u5e73\u65b9\u6839\u7684\u6570\u6574\u9664\u6765\u786e\u5b9a\u5176\u662f\u5426\u4e3a\u7d20\u6570\u3002\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u901a\u8fc7\u7b5b\u9664\u5408\u6570\u6765\u751f\u6210\u4e00\u7cfb\u5217\u7d20\u6570\u3002\u7c73\u52d2-\u62c9\u5bbe\u7d20\u6027\u6d4b\u8bd5\u662f\u4e00\u79cd\u6982\u7387\u7b97\u6cd5\uff0c\u9002\u7528\u4e8e\u8f83\u5927\u7684\u6570\u3002\u4e0b\u9762\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e9b\u65b9\u6cd5\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u8bd5\u9664\u6cd5<\/p>\n<\/p>\n

\u8bd5\u9664\u6cd5\u662f\u6700\u57fa\u672c\u7684\u7d20\u6570\u5224\u5b9a\u65b9\u6cd5\uff0c\u901a\u8fc7\u5c06\u4e00\u4e2a\u6570\u4e0e\u5c0f\u4e8e\u5176\u5e73\u65b9\u6839\u7684\u6570\u8fdb\u884c\u9664\u6cd5\u8fd0\u7b97\u6765\u5224\u65ad\u5176\u662f\u5426\u4e3a\u7d20\u6570\u3002<\/p>\n<\/p>\n

    \n
  1. \n

    \u57fa\u672c\u5b9e\u73b0<\/strong><\/p>\n<\/p>\n

    \u8bd5\u9664\u6cd5\u7684\u57fa\u672c\u601d\u8def\u662f\uff0c\u5982\u679c\u4e00\u4e2a\u6570n\u662f\u7d20\u6570\uff0c\u90a3\u4e48\u5b83\u53ea\u80fd\u88ab1\u548cn\u6574\u9664\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ea\u9700\u8981\u68c0\u67e5n\u80fd\u5426\u88ab2\u5230sqrt(n)\u4e4b\u95f4\u7684\u4efb\u4f55\u4e00\u4e2a\u6570\u6574\u9664\u3002\u5982\u679cn\u80fd\u88ab\u5176\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u6570\u6574\u9664\uff0c\u5219n\u4e0d\u662f\u7d20\u6570\uff0c\u5426\u5219\u5b83\u662f\u7d20\u6570\u3002<\/p>\n<\/p>\n

    import math<\/p>\n
    def is_prime(number):<\/p>\n
        if number <= 1:<\/p>\n
            return False<\/p>\n
        if number <= 3:<\/p>\n
            return True<\/p>\n
        if number % 2 == 0 or number % 3 == 0:<\/p>\n
            return False<\/p>\n
        i = 5<\/p>\n
        while i * i <= number:<\/p>\n
            if number % i == 0 or number % (i + 2) == 0:<\/p>\n
                return False<\/p>\n
            i += 6<\/p>\n
        return True<\/p>\n
    <\/code><\/pre>\n<\/p>\n<\/li>\n
  2. \n
    \u4f18\u5316\u63aa\u65bd<\/strong><\/p>\n<\/p>\n
    \u5728\u57fa\u672c\u8bd5\u9664\u6cd5\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u4f18\u5316\uff0c\u901a\u8fc7\u8df3\u8fc7\u5076\u6570\u548c\u5df2\u7ecf\u68c0\u6d4b\u8fc7\u7684\u56e0\u6570\u4ee5\u52a0\u5feb\u8ba1\u7b97\u901f\u5ea6\u3002\u7531\u4e8e\u5076\u6570\uff08\u9664\u4e862\uff09\u4e0d\u53ef\u80fd\u662f\u7d20\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece3\u5f00\u59cb\uff0c\u5e76\u53ea\u68c0\u67e5\u5947\u6570\u3002<\/p>\n<\/p>\n
    def is_prime_optimized(number):<\/p>\n
        if number <= 1:<\/p>\n
            return False<\/p>\n
        if number == 2:<\/p>\n
            return True<\/p>\n
        if number % 2 == 0:<\/p>\n
            return False<\/p>\n
        for i in range(3, int(math.sqrt(number)) + 1, 2):<\/p>\n
            if number % i == 0:<\/p>\n
                return False<\/p>\n
        return True<\/p>\n
    <\/code><\/pre>\n<\/p>\n<\/li>\n<\/ol>\n
    \u4e8c\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5<\/p>\n<\/p>\n
    \u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u662f\u4e00\u79cd\u751f\u6210\u7d20\u6570\u5217\u8868\u7684\u9ad8\u6548\u7b97\u6cd5\uff0c\u7279\u522b\u9002\u7528\u4e8e\u751f\u6210\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002<\/p>\n<\/p>\n
      \n
    1. \n
      \u7b97\u6cd5\u539f\u7406<\/strong><\/p>\n<\/p>\n
      \u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u7684\u57fa\u672c\u539f\u7406\u662f\u901a\u8fc7\u53cd\u590d\u6807\u8bb0\u5408\u6570\u6765\u7b5b\u9009\u51fa\u7d20\u6570\u3002\u9996\u5148\uff0c\u4ece2\u5f00\u59cb\uff0c\u5c06\u5176\u6240\u6709\u7684\u500d\u6570\u6807\u8bb0\u4e3a\u5408\u6570\u3002\u7136\u540e\uff0c\u627e\u5230\u4e0b\u4e00\u4e2a\u672a\u6807\u8bb0\u7684\u6570\uff0c\u5b83\u5c31\u662f\u4e0b\u4e00\u4e2a\u7d20\u6570\u3002\u91cd\u590d\u8fd9\u4e00\u8fc7\u7a0b\uff0c\u76f4\u5230\u5904\u7406\u5b8c\u6240\u6709\u6570\u3002<\/p>\n<\/p>\n
      def sieve_of_eratosthenes(limit):<\/p>\n
          primes = [True] * (limit + 1)<\/p>\n
          p = 2<\/p>\n
          while (p * p <= limit):<\/p>\n
              if primes[p] == True:<\/p>\n
                  for i in range(p * p, limit + 1, p):<\/p>\n
                      primes[i] = False<\/p>\n
              p += 1<\/p>\n
          prime_numbers = [p for p in range(2, limit + 1) if primes[p]]<\/p>\n
          return prime_numbers<\/p>\n
      <\/code><\/pre>\n<\/p>\n<\/li>\n
    2. \n
      \u5e94\u7528\u573a\u666f<\/strong><\/p>\n<\/p>\n
      \u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u9002\u5408\u751f\u6210\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u7d20\u6570\u5217\u8868\uff0c\u6bd4\u5982\u5728\u5904\u7406\u9700\u8981\u5927\u91cf\u7d20\u6570\u5224\u65ad\u7684\u95ee\u9898\u65f6\u3002\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n log log n)\uff0c\u6bd4\u9010\u4e2a\u5224\u65ad\u662f\u5426\u4e3a\u7d20\u6570\u7684\u65b9\u6cd5\u8981\u5feb\u5f97\u591a\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n
      \u4e09\u3001\u7c73\u52d2-\u62c9\u5bbe\u7d20\u6027\u6d4b\u8bd5<\/p>\n<\/p>\n
      \u7c73\u52d2-\u62c9\u5bbe\u7d20\u6027\u6d4b\u8bd5\u662f\u4e00\u79cd\u6982\u7387\u7b97\u6cd5\uff0c\u7528\u4e8e\u5224\u65ad\u5927\u6570\u662f\u5426\u4e3a\u7d20\u6570\u3002\u5b83\u9002\u7528\u4e8e\u5927\u8303\u56f4\u7d20\u6570\u5224\u5b9a\uff0c\u5c24\u5176\u662f\u6d89\u53ca\u5230\u52a0\u5bc6\u7b97\u6cd5\u7684\u573a\u5408\u3002<\/p>\n<\/p>\n
        \n
      1. \n
        \u7b97\u6cd5\u539f\u7406<\/strong><\/p>\n<\/p>\n
        \u7c73\u52d2-\u62c9\u5bbe\u6d4b\u8bd5\u662f\u4e00\u79cd\u57fa\u4e8e\u6570\u8bba\u7684\u6982\u7387\u7b97\u6cd5\u3002\u5b83\u901a\u8fc7\u968f\u673a\u9009\u62e9\u201c\u89c1\u8bc1\u8005\u201d\u6765\u6d4b\u8bd5\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u3002\u82e5\u7ecf\u8fc7\u591a\u6b21\u6d4b\u8bd5\u540e\uff0c\u6570\u4ecd\u672a\u88ab\u8bc1\u660e\u4e3a\u5408\u6570\uff0c\u5219\u53ef\u4ee5\u8ba4\u4e3a\u5b83\u662f\u7d20\u6570\u3002<\/p>\n<\/p>\n
        import random<\/p>\n
        def miller_rabin_test(d, n):<\/p>\n
            a = 2 + random.randint(1, n - 4)<\/p>\n
            x = pow(a, d, n)<\/p>\n
            if x == 1 or x == n - 1:<\/p>\n
                return True<\/p>\n
            while d != n - 1:<\/p>\n
                x = (x * x) % n<\/p>\n
                d *= 2<\/p>\n
                if x == 1:<\/p>\n
                    return False<\/p>\n
                if x == n - 1:<\/p>\n
                    return True<\/p>\n
            return False<\/p>\n
        def is_prime_miller_rabin(n, k=5):<\/p>\n
            if n <= 1 or n == 4:<\/p>\n
                return False<\/p>\n
            if n <= 3:<\/p>\n
                return True<\/p>\n
            d = n - 1<\/p>\n
            while d % 2 == 0:<\/p>\n
                d \/\/= 2<\/p>\n
            for _ in range(k):<\/p>\n
                if not miller_rabin_test(d, n):<\/p>\n
                    return False<\/p>\n
            return True<\/p>\n
        <\/code><\/pre>\n<\/p>\n<\/li>\n
      2. \n
        \u4f18\u7f3a\u70b9<\/strong><\/p>\n<\/p>\n
        \u7c73\u52d2-\u62c9\u5bbe\u6d4b\u8bd5\u7684\u4f18\u70b9\u5728\u4e8e\u5176\u901f\u5ea6\u5feb\uff0c\u5c24\u5176\u9002\u5408\u5927\u6570\u5224\u5b9a\u3002\u7f3a\u70b9\u662f\u5b83\u662f\u4e00\u4e2a\u6982\u7387\u7b97\u6cd5\uff0c\u7ed3\u679c\u6709\u53ef\u80fd\u51fa\u9519\u3002\u901a\u8fc7\u591a\u6b21\u6d4b\u8bd5\uff0c\u53ef\u4ee5\u4f7f\u9519\u8bef\u6982\u7387\u964d\u4f4e\u5230\u53ef\u4ee5\u63a5\u53d7\u7684\u8303\u56f4\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n
        \u56db\u3001\u603b\u7ed3<\/p>\n<\/p>\n
        \u5728Python\u4e2d\u5224\u5b9a\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u65b9\u6cd5\u3002\u5bf9\u4e8e\u5c0f\u6570\uff0c\u8bd5\u9664\u6cd5\u662f\u7b80\u5355\u800c\u6709\u6548\u7684\u9009\u62e9\uff1b\u5982\u679c\u9700\u8981\u751f\u6210\u5927\u91cf\u7d20\u6570\uff0c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u662f\u6700\u4f73\u9009\u62e9\uff1b\u5728\u5904\u7406\u5927\u6570\u65f6\uff0c\u7c73\u52d2-\u62c9\u5bbe\u7d20\u6027\u6d4b\u8bd5\u63d0\u4f9b\u4e86\u4e00\u79cd\u5feb\u901f\u4e14\u53ef\u8c03\u8282\u7cbe\u5ea6\u7684\u65b9\u6cd5\u3002\u6839\u636e\u5177\u4f53\u7684\u5e94\u7528\u573a\u666f\u9009\u62e9\u5408\u9002\u7684\u7b97\u6cd5\uff0c\u53ef\u4ee5\u63d0\u9ad8\u4ee3\u7801\u7684\u6548\u7387\u548c\u51c6\u786e\u6027\u3002\u4e0d\u540c\u7b97\u6cd5\u9002\u7528\u4e8e\u4e0d\u540c\u89c4\u6a21\u548c\u573a\u666f\u7684\u95ee\u9898\uff0c\u56e0\u6b64\u7406\u89e3\u8fd9\u4e9b\u65b9\u6cd5\u7684\u4f18\u7f3a\u70b9\u80fd\u591f\u5e2e\u52a9\u5f00\u53d1\u8005\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u505a\u51fa\u66f4\u660e\u667a\u7684\u9009\u62e9\u3002<\/p>\n<\/p>\n
        \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
         \u4ec0\u4e48\u662f\u7d20\u6570\uff0c\u5982\u4f55\u5728Python\u4e2d\u5b9a\u4e49\u5b83\uff1f<\/strong>
        \u7d20\u6570\u662f\u6307\u5927\u4e8e1\u7684\u81ea\u7136\u6570\uff0c\u4e14\u53ea\u80fd\u88ab1\u548c\u5b83\u672c\u8eab\u6574\u9664\u3002\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u901a\u8fc7\u7f16\u5199\u4e00\u4e2a\u51fd\u6570\u6765\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u3002\u5e38\u89c1\u7684\u505a\u6cd5\u662f\u68c0\u67e5\u4ece2\u5230\u8be5\u6570\u5e73\u65b9\u6839\u4e4b\u95f4\u7684\u6240\u6709\u6574\u6570\uff0c\u770b\u662f\u5426\u6709\u80fd\u591f\u6574\u9664\u8be5\u6570\u7684\u6574\u6570\u3002<\/p>\n
        \u5728Python\u4e2d\u5224\u65ad\u7d20\u6570\u7684\u9ad8\u6548\u65b9\u6cd5\u6709\u54ea\u4e9b\uff1f<\/strong>
        \u4e3a\u4e86\u63d0\u9ad8\u5224\u65ad\u7d20\u6570\u7684\u6548\u7387\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e9b\u4f18\u5316\u6280\u5de7\uff0c\u6bd4\u5982\u53ea\u68c0\u67e5\u5230\u6570\u7684\u5e73\u65b9\u6839\uff0c\u6216\u662f\u8df3\u8fc7\u5076\u6570\u7684\u68c0\u67e5\uff08\u5728\u68c0\u67e5\u5b8c2\u4e4b\u540e\uff09\u3002\u6b64\u5916\uff0c\u4f7f\u7528\u7b5b\u6cd5\uff08\u5982\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\uff09\u53ef\u4ee5\u5feb\u901f\u627e\u51fa\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002<\/p>\n
        \u5982\u679c\u6211\u60f3\u68c0\u67e5\u4e00\u4e2a\u5217\u8868\u4e2d\u7684\u6240\u6709\u6570\u5b57\u662f\u5426\u4e3a\u7d20\u6570\uff0c\u5e94\u8be5\u600e\u4e48\u505a\uff1f<\/strong>
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