{"id":1188467,"date":"2025-01-15T20:17:37","date_gmt":"2025-01-15T12:17:37","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1188467.html"},"modified":"2025-01-15T20:17:40","modified_gmt":"2025-01-15T12:17:40","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e7%94%9f%e6%88%90%e8%b4%a8%e6%95%b0%e8%a1%a8","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1188467.html","title":{"rendered":"\u5982\u4f55\u7528Python\u751f\u6210\u8d28\u6570\u8868"},"content":{"rendered":"

\"\u5982\u4f55\u7528Python\u751f\u6210\u8d28\u6570\u8868\"<\/p>\n

\u7528Python\u751f\u6210\u8d28\u6570\u8868\u53ef\u4ee5\u901a\u8fc7\u7b5b\u9009\u6cd5\u3001\u8bd5\u9664\u6cd5\u3001\u4f18\u5316\u7684\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u6765\u5b9e\u73b0\u3002<\/strong> \u5176\u4e2d\uff0c\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u662f\u4e00\u79cd\u7ecf\u5178\u4e14\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u53ef\u4ee5\u5feb\u901f\u751f\u6210\u8d28\u6570\u8868\u3002\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u901a\u8fc7\u6807\u8bb0\u975e\u8d28\u6570\u7684\u65b9\u5f0f\u6765\u7b5b\u9009\u8d28\u6570<\/strong>\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u7684\u5b9e\u73b0\u3002<\/p>\n<\/p>\n

\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u7684\u57fa\u672c\u601d\u60f3\u662f\uff0c\u4ece2\u5f00\u59cb\uff0c\u5c06\u5176\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\uff0c\u7136\u540e\u627e\u5230\u4e0b\u4e00\u4e2a\u672a\u6807\u8bb0\u7684\u6570\u5b57\uff0c\u628a\u5b83\u7684\u500d\u6570\u4e5f\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\uff0c\u4f9d\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230\u6240\u9700\u8303\u56f4\u7684\u6240\u6709\u6570\u5b57\u90fd\u88ab\u5904\u7406\u5b8c\u6bd5\u3002\u6700\u7ec8\uff0c\u672a\u88ab\u6807\u8bb0\u7684\u6570\u5b57\u5c31\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u5b9e\u73b0<\/h3>\n<\/p>\n

\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u7684\u5b9e\u73b0\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<\/p>\n

    \n
  1. \u521b\u5efa\u4e00\u4e2a\u5e03\u5c14\u6570\u7ec4\uff0c\u6807\u8bb0\u6240\u6709\u6570\u5b57\u662f\u5426\u4e3a\u8d28\u6570\u3002<\/li>\n
  2. \u4ece\u7b2c\u4e00\u4e2a\u8d28\u65702\u5f00\u59cb\uff0c\u5c06\u5176\u6240\u6709\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\u3002<\/li>\n
  3. \u627e\u5230\u4e0b\u4e00\u4e2a\u672a\u6807\u8bb0\u7684\u6570\u5b57\uff0c\u5e76\u5c06\u5176\u6240\u6709\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\u3002<\/li>\n
  4. \u91cd\u590d\u6b65\u9aa43\uff0c\u76f4\u5230\u5904\u7406\u5b8c\u6240\u6709\u6570\u5b57\u3002<\/li>\n<\/ol>\n

    \u4ee5\u4e0b\u662f\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u7684Python\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n

    def sieve_of_eratosthenes(n):<\/p>\n
        # \u521b\u5efa\u4e00\u4e2a\u5e03\u5c14\u6570\u7ec4\u6765\u6807\u8bb0\u6570\u5b57\u662f\u5426\u4e3a\u8d28\u6570<\/p>\n
        is_prime = [True] * (n + 1)<\/p>\n
        p = 2<\/p>\n
        while (p * p <= n):<\/p>\n
            # \u5982\u679cis_prime[p]\u6ca1\u6709\u88ab\u6807\u8bb0\u4e3a\u975e\u8d28\u6570<\/p>\n
            if is_prime[p]:<\/p>\n
                # \u5c06p\u7684\u6240\u6709\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u8d28\u6570<\/p>\n
                for i in range(p * p, n + 1, p):<\/p>\n
                    is_prime[i] = False<\/p>\n
            p += 1<\/p>\n
        # \u6536\u96c6\u6240\u6709\u8d28\u6570<\/p>\n
        prime_numbers = [p for p in range(2, n + 1) if is_prime[p]]<\/p>\n
        return prime_numbers<\/p>\n
    \u6d4b\u8bd5\u51fd\u6570<\/strong><\/h2>\n
    n = 100<\/p>\n
    print(f"\u5c0f\u4e8e\u7b49\u4e8e{n}\u7684\u8d28\u6570\u6709\uff1a")<\/p>\n
    print(sieve_of_eratosthenes(n))<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u4e8c\u3001\u8bd5\u9664\u6cd5\u751f\u6210\u8d28\u6570\u8868<\/h3>\n<\/p>\n
    \u8bd5\u9664\u6cd5\u662f\u4e00\u79cd\u7b80\u5355\u4f46\u6548\u7387\u8f83\u4f4e\u7684\u751f\u6210\u8d28\u6570\u8868\u7684\u65b9\u6cd5\u3002\u5176\u57fa\u672c\u601d\u60f3\u662f\uff1a\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5019\u9009\u6570n\uff0c\u5224\u65ad\u5176\u662f\u5426\u80fd\u88ab\u5c0f\u4e8e\u6216\u7b49\u4e8esqrt(n)\u7684\u8d28\u6570\u6574\u9664\uff0c\u5982\u679c\u4e0d\u80fd\uff0c\u5219\u5b83\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n
    \u8bd5\u9664\u6cd5\u7684\u5b9e\u73b0\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
      \n
    1. \u521b\u5efa\u4e00\u4e2a\u7a7a\u5217\u8868\u5b58\u50a8\u8d28\u6570\u3002<\/li>\n
    2. \u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5019\u9009\u6570\uff0c\u5224\u65ad\u5176\u662f\u5426\u80fd\u88ab\u5df2\u77e5\u7684\u8d28\u6570\u6574\u9664\uff0c\u5982\u679c\u4e0d\u80fd\uff0c\u5219\u5c06\u5176\u52a0\u5165\u8d28\u6570\u5217\u8868\u3002<\/li>\n
    3. \u91cd\u590d\u6b65\u9aa42\uff0c\u76f4\u5230\u6240\u9700\u8303\u56f4\u7684\u6240\u6709\u6570\u5b57\u90fd\u88ab\u5904\u7406\u5b8c\u6bd5\u3002<\/li>\n<\/ol>\n
      \u4ee5\u4e0b\u662f\u8bd5\u9664\u6cd5\u7684Python\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
      def trial_division(n):<\/p>\n
          if n < 2:<\/p>\n
              return []<\/p>\n
          primes = []<\/p>\n
          for num in range(2, n + 1):<\/p>\n
              is_prime = True<\/p>\n
              for prime in primes:<\/p>\n
                  if prime * prime > num:<\/p>\n
                      break<\/p>\n
                  if num % prime == 0:<\/p>\n
                      is_prime = False<\/p>\n
                      break<\/p>\n
              if is_prime:<\/p>\n
                  primes.append(num)<\/p>\n
          return primes<\/p>\n
      \u6d4b\u8bd5\u51fd\u6570<\/strong><\/h2>\n
      n = 100<\/p>\n
      print(f"\u5c0f\u4e8e\u7b49\u4e8e{n}\u7684\u8d28\u6570\u6709\uff1a")<\/p>\n
      print(trial_division(n))<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u4e09\u3001\u4f18\u5316\u7684\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5<\/h3>\n<\/p>\n
      \u4e3a\u4e86\u8fdb\u4e00\u6b65\u4f18\u5316\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\uff0c\u53ef\u4ee5\u4ece2\u7684\u500d\u6570\u5f00\u59cb\uff0c\u5c06\u6bcf\u6b21\u6807\u8bb0\u975e\u8d28\u6570\u7684\u8d77\u59cb\u4f4d\u7f6e\u8c03\u6574\u4e3a\u5f53\u524d\u8d28\u6570\u7684\u5e73\u65b9\u4f4d\u7f6e\u3002\u8fd9\u662f\u56e0\u4e3a\u8f83\u5c0f\u7684\u500d\u6570\u5728\u4e4b\u524d\u7684\u6b65\u9aa4\u4e2d\u5df2\u7ecf\u88ab\u6807\u8bb0\u8fc7\u4e86\u3002<\/p>\n<\/p>\n
      \u4ee5\u4e0b\u662f\u4f18\u5316\u540e\u7684\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u7684Python\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
      def optimized_sieve_of_eratosthenes(n):<\/p>\n
          # \u521b\u5efa\u4e00\u4e2a\u5e03\u5c14\u6570\u7ec4\u6765\u6807\u8bb0\u6570\u5b57\u662f\u5426\u4e3a\u8d28\u6570<\/p>\n
          is_prime = [True] * (n + 1)<\/p>\n
          p = 2<\/p>\n
          while (p * p <= n):<\/p>\n
              # \u5982\u679cis_prime[p]\u6ca1\u6709\u88ab\u6807\u8bb0\u4e3a\u975e\u8d28\u6570<\/p>\n
              if is_prime[p]:<\/p>\n
                  # \u5c06p\u7684\u6240\u6709\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\uff0c\u4ecep*p\u5f00\u59cb<\/p>\n
                  for i in range(p * p, n + 1, p):<\/p>\n
                      is_prime[i] = False<\/p>\n
              p += 1<\/p>\n
          # \u6536\u96c6\u6240\u6709\u8d28\u6570<\/p>\n
          prime_numbers = [p for p in range(2, n + 1) if is_prime[p]]<\/p>\n
          return prime_numbers<\/p>\n
      \u6d4b\u8bd5\u51fd\u6570<\/strong><\/h2>\n
      n = 100<\/p>\n
      print(f"\u5c0f\u4e8e\u7b49\u4e8e{n}\u7684\u8d28\u6570\u6709\uff1a")<\/p>\n
      print(optimized_sieve_of_eratosthenes(n))<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u56db\u3001\u751f\u6210\u6307\u5b9a\u6570\u91cf\u7684\u8d28\u6570<\/h3>\n<\/p>\n
      \u6709\u65f6\u6211\u4eec\u4e0d\u4ec5\u9700\u8981\u751f\u6210\u5c0f\u4e8e\u67d0\u4e2a\u6570\u7684\u8d28\u6570\u8868\uff0c\u8fd8\u9700\u8981\u751f\u6210\u6307\u5b9a\u6570\u91cf\u7684\u8d28\u6570\u3002\u4e3a\u6b64\uff0c\u53ef\u4ee5\u7ed3\u5408\u8bd5\u9664\u6cd5\u548c\u52a8\u6001\u6570\u7ec4\u6765\u5b9e\u73b0\u3002<\/p>\n<\/p>\n
      \u4ee5\u4e0b\u662f\u751f\u6210\u6307\u5b9a\u6570\u91cf\u8d28\u6570\u7684Python\u5b9e\u73b0\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
      def generate_primes(count):<\/p>\n
          if count < 1:<\/p>\n
              return []<\/p>\n
          primes = []<\/p>\n
          candidate = 2<\/p>\n
          while len(primes) < count:<\/p>\n
              is_prime = True<\/p>\n
              for prime in primes:<\/p>\n
                  if prime * prime > candidate:<\/p>\n
                      break<\/p>\n
                  if candidate % prime == 0:<\/p>\n
                      is_prime = False<\/p>\n
                      break<\/p>\n
              if is_prime:<\/p>\n
                  primes.append(candidate)<\/p>\n
              candidate += 1<\/p>\n
          return primes<\/p>\n
      \u6d4b\u8bd5\u51fd\u6570<\/strong><\/h2>\n
      count = 25<\/p>\n
      print(f"\u524d{count}\u4e2a\u8d28\u6570\u662f\uff1a")<\/p>\n
      print(generate_primes(count))<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u4e94\u3001\u6bd4\u8f83\u4e0d\u540c\u65b9\u6cd5\u7684\u6027\u80fd<\/h3>\n<\/p>\n
      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9009\u62e9\u5408\u9002\u7684\u8d28\u6570\u751f\u6210\u65b9\u6cd5\u975e\u5e38\u91cd\u8981\u3002\u4e0d\u540c\u7684\u65b9\u6cd5\u5728\u4e0d\u540c\u7684\u8f93\u5165\u89c4\u6a21\u4e0b\u6027\u80fd\u8868\u73b0\u5dee\u5f02\u5f88\u5927\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u5728\u5904\u7406\u8f83\u5927\u7684\u8f93\u5165\u65f6\u8868\u73b0\u66f4\u597d\uff0c\u800c\u8bd5\u9664\u6cd5\u5728\u5904\u7406\u8f83\u5c0f\u7684\u8f93\u5165\u65f6\u4e5f\u80fd\u63d0\u4f9b\u8db3\u591f\u7684\u6027\u80fd\u3002<\/p>\n<\/p>\n
      \u4e3a\u4e86\u6bd4\u8f83\u4e0d\u540c\u65b9\u6cd5\u7684\u6027\u80fd\uff0c\u53ef\u4ee5\u4f7f\u7528Python\u7684time<\/code>\u6a21\u5757\u6765\u6d4b\u91cf\u6bcf\u79cd\u65b9\u6cd5\u7684\u6267\u884c\u65f6\u95f4\u3002\u4ee5\u4e0b\u662f\u6027\u80fd\u6bd4\u8f83\u7684\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
      import time<\/p>\n
      def measure_time(func, *args):<\/p>\n
          start_time = time.time()<\/p>\n
          result = func(*args)<\/p>\n
          end_time = time.time()<\/p>\n
          return end_time - start_time<\/p>\n
      n = 100000<\/p>\n
      print(f"\u751f\u6210\u5c0f\u4e8e\u7b49\u4e8e{n}\u7684\u8d28\u6570\u6240\u9700\u65f6\u95f4\uff08\u79d2\uff09\uff1a")<\/p>\n
      time_sieve = measure_time(sieve_of_eratosthenes, n)<\/p>\n
      print(f"\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5: {time_sieve:.6f}\u79d2")<\/p>\n
      time_optimized_sieve = measure_time(optimized_sieve_of_eratosthenes, n)<\/p>\n
      print(f"\u4f18\u5316\u7684\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5: {time_optimized_sieve:.6f}\u79d2")<\/p>\n
      \u5bf9\u4e8e\u8bd5\u9664\u6cd5\uff0cn\u8bbe\u7f6e\u8f83\u5c0f\u7684\u503c\u4ee5\u907f\u514d\u957f\u65f6\u95f4\u7b49\u5f85<\/strong><\/h2>\n
      n_small = 10000<\/p>\n
      time_trial = measure_time(trial_division, n_small)<\/p>\n
      print(f"\u8bd5\u9664\u6cd5: {time_trial:.6f}\u79d2\uff08n={n_small}\uff09")<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u901a\u8fc7\u8fd0\u884c\u4e0a\u8ff0\u4ee3\u7801\uff0c\u53ef\u4ee5\u89c2\u5bdf\u5230\u5728\u5904\u7406\u8f83\u5927\u7684\u8f93\u5165\u65f6\uff0c\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u548c\u4f18\u5316\u7684\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u5177\u6709\u660e\u663e\u7684\u6027\u80fd\u4f18\u52bf<\/strong>\u3002<\/p>\n<\/p>\n
      \u516d\u3001\u5e76\u884c\u5316\u5904\u7406<\/h3>\n<\/p>\n
      \u5728\u73b0\u4ee3\u8ba1\u7b97\u673a\u4e2d\uff0c\u901a\u8fc7\u5e76\u884c\u5904\u7406\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u7b97\u6cd5\u7684\u6027\u80fd\u3002\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u53ef\u4ee5\u8fdb\u884c\u5e76\u884c\u5316\u5904\u7406\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u53ef\u4ee5\u5c06\u7b5b\u9009\u8fc7\u7a0b\u5206\u6210\u591a\u4e2a\u7ebf\u7a0b\u6216\u8fdb\u7a0b\uff0c\u6bcf\u4e2a\u7ebf\u7a0b\u6216\u8fdb\u7a0b\u8d1f\u8d23\u6807\u8bb0\u4e00\u90e8\u5206\u6570\u5b57\u7684\u500d\u6570\u3002<\/p>\n<\/p>\n
      \u4ee5\u4e0b\u662f\u4f7f\u7528concurrent.futures<\/code>\u6a21\u5757\u5b9e\u73b0\u7684\u5e76\u884c\u5316\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u7684\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
      import concurrent.futures<\/p>\n
      def parallel_sieve_of_eratosthenes(n):<\/p>\n
          is_prime = [True] * (n + 1)<\/p>\n
          def mark_non_primes(start, step):<\/p>\n
              for i in range(start, n + 1, step):<\/p>\n
                  is_prime[i] = False<\/p>\n
          p = 2<\/p>\n
          with concurrent.futures.ThreadPoolExecutor() as executor:<\/p>\n
              while (p * p <= n):<\/p>\n
                  if is_prime[p]:<\/p>\n
                      executor.submit(mark_non_primes, p * p, p)<\/p>\n
                  p += 1<\/p>\n
          prime_numbers = [p for p in range(2, n + 1) if is_prime[p]]<\/p>\n
          return prime_numbers<\/p>\n
      \u6d4b\u8bd5\u51fd\u6570<\/strong><\/h2>\n
      n = 100000<\/p>\n
      print(f"\u5c0f\u4e8e\u7b49\u4e8e{n}\u7684\u8d28\u6570\u6709\uff1a")<\/p>\n
      print(parallel_sieve_of_eratosthenes(n))<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u901a\u8fc7\u5e76\u884c\u5316\u5904\u7406\uff0c\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u8d28\u6570\u751f\u6210\u7684\u6548\u7387\uff0c\u7279\u522b\u662f\u5728\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u65f6\u3002<\/p>\n<\/p>\n
      \u4e03\u3001\u603b\u7ed3<\/h3>\n<\/p>\n
      \u751f\u6210\u8d28\u6570\u8868\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u6570\u5b66\u9886\u57df\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u672c\u6587\u4ecb\u7ecd\u4e86\u51e0\u79cd\u5e38\u7528\u7684\u751f\u6210\u8d28\u6570\u8868\u7684\u65b9\u6cd5\uff0c\u5305\u62ec\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u3001\u8bd5\u9664\u6cd5\u4ee5\u53ca\u5b83\u4eec\u7684\u4f18\u5316\u7248\u672c\u3002\u901a\u8fc7\u6bd4\u8f83\u4e0d\u540c\u65b9\u6cd5\u7684\u6027\u80fd\uff0c\u53ef\u4ee5\u9009\u62e9\u9002\u5408\u7279\u5b9a\u5e94\u7528\u573a\u666f\u7684\u7b97\u6cd5\u3002\u6b64\u5916\uff0c\u901a\u8fc7\u5e76\u884c\u5316\u5904\u7406\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u7b97\u6cd5\u7684\u6027\u80fd\u3002<\/p>\n<\/p>\n
      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9009\u62e9\u5408\u9002\u7684\u8d28\u6570\u751f\u6210\u65b9\u6cd5\u548c\u4f18\u5316\u7b56\u7565\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002\u5e0c\u671b\u672c\u6587\u5bf9\u60a8\u7406\u89e3\u548c\u5b9e\u73b0\u751f\u6210\u8d28\u6570\u8868\u7684\u65b9\u6cd5\u6709\u6240\u5e2e\u52a9\u3002<\/p>\n<\/p>\n
      \u516b\u3001\u53c2\u8003\u6587\u732e<\/h3>\n<\/p>\n
        \n
      1. Knuth, D. E. (1997). The Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd Edition). Addison-Wesley Professional.<\/li>\n
      2. Sedgewick, R., & Wayne, K. (2011). Algorithms (4th Edition). Addison-Wesley Professional.<\/li>\n
      3. Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to Algorithms (3rd Edition). The MIT Press.<\/li>\n<\/ol>\n
        \u8fd9\u4e9b\u53c2\u8003\u6587\u732e\u63d0\u4f9b\u4e86\u66f4\u591a\u5173\u4e8e\u7b97\u6cd5\u548c\u6570\u636e\u7ed3\u6784\u7684\u8be6\u7ec6\u4fe1\u606f\uff0c\u9002\u5408\u6df1\u5165\u5b66\u4e60\u548c\u7814\u7a76\u3002<\/p>\n<\/p>\n
        \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
         \u5982\u4f55\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u662f\u8d28\u6570\uff1f<\/strong>
        \u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u662f\u8d28\u6570\uff0c\u53ef\u4ee5\u901a\u8fc7\u68c0\u67e5\u8be5\u6570\u662f\u5426\u4ec5\u80fd\u88ab1\u548c\u81ea\u8eab\u6574\u9664\u6765\u5b9e\u73b0\u3002\u901a\u5e38\uff0c\u4f7f\u7528\u5faa\u73af\u4ece2\u5230\u8be5\u6570\u7684\u5e73\u65b9\u6839\u8fdb\u884c\u68c0\u67e5\uff0c\u5982\u679c\u5728\u8fd9\u4e2a\u8303\u56f4\u5185\u627e\u5230\u4efb\u4f55\u56e0\u6570\uff0c\u5219\u8be5\u6570\u4e0d\u662f\u8d28\u6570\u3002Python\u4e2d\u53ef\u4ee5\u4f7f\u7528\u51fd\u6570\u6765\u5c01\u88c5\u8fd9\u4e2a\u903b\u8f91\uff0c\u4f7f\u5f97\u5224\u65ad\u8d28\u6570\u53d8\u5f97\u7b80\u5355\u4e14\u9ad8\u6548\u3002<\/p>\n
        \u4f7f\u7528Python\u751f\u6210\u8d28\u6570\u8868\u65f6\uff0c\u6027\u80fd\u5982\u4f55\u4f18\u5316\uff1f<\/strong>
        \u5728\u751f\u6210\u8d28\u6570\u8868\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e9b\u7b97\u6cd5\u4f18\u5316\uff0c\u6bd4\u5982\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\uff08Sieve of Eratosthenes\uff09\u3002\u8be5\u7b97\u6cd5\u901a\u8fc7\u521b\u5efa\u4e00\u4e2a\u5e03\u5c14\u6570\u7ec4\u6765\u6807\u8bb0\u5408\u6570\uff0c\u4ece\u800c\u9ad8\u6548\u5730\u751f\u6210\u6240\u6709\u8d28\u6570\u3002\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u751f\u6210\u5927\u8303\u56f4\u8d28\u6570\u7684\u901f\u5ea6\u3002<\/p>\n
        \u6709\u54ea\u4e9b\u5e93\u53ef\u4ee5\u8f85\u52a9\u751f\u6210\u8d28\u6570\u8868\uff1f<\/strong>
        Python\u6709\u591a\u4e2a\u5e93\u53ef\u4ee5\u7528\u4e8e\u751f\u6210\u8d28\u6570\u8868\uff0c\u4f8b\u5982sympy<\/code>\u5e93\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u6570\u5b66\u529f\u80fd\uff0c\u5176\u4e2d\u5305\u62ec\u8d28\u6570\u751f\u6210\u7684\u51fd\u6570\u3002\u6b64\u5916\uff0cnumpy<\/code>\u5e93\u4e5f\u53ef\u4ee5\u901a\u8fc7\u6570\u7ec4\u64cd\u4f5c\u6765\u5b9e\u73b0\u8d28\u6570\u7684\u751f\u6210\u3002\u4f7f\u7528\u8fd9\u4e9b\u5e93\u53ef\u4ee5\u7b80\u5316\u4ee3\u7801\u5e76\u63d0\u9ad8\u53ef\u8bfb\u6027\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u7528Python\u751f\u6210\u8d28\u6570\u8868\u53ef\u4ee5\u901a\u8fc7\u7b5b\u9009\u6cd5\u3001\u8bd5\u9664\u6cd5\u3001\u4f18\u5316\u7684\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u6765\u5b9e\u73b0\u3002 \u5176\u4e2d\uff0c\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u9009\u6cd5\u662f\u4e00\u79cd\u7ecf […]","protected":false},"author":3,"featured_media":1188473,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1188467"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1188467"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1188467\/revisions"}],"predecessor-version":[{"id":1188475,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1188467\/revisions\/1188475"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1188473"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1188467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1188467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1188467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}