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PAT乙级:1094 谷歌的招聘

2020-04-26 13:23:03
阅读：2690   •   评论：40
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2004 年 7 月，谷歌在硅谷的 101 号公路边竖立了一块巨大的广告牌（如下图）用于招聘。内容超级简单，就是一个以 .com 结尾的网址，而前面的网址是一个 10 位素数，这个素数是自然常数 e 中最早出现的 10 位连续数字。能找出这个素数的人，就可以通过访问谷歌的这个网站进入招聘流程的下一步。

谷歌招聘广告

自然常数 e 是一个著名的超越数，前面若干位写出来是这样的：e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921... 其中粗体标出的 10 位数就是答案。

本题要求你编程解决一个更通用的问题：从任一给定的长度为 L 的数字中，找出最早出现的 K 位连续数字所组成的素数。

输入格式：

输入在第一行给出 2 个正整数，分别是 L（不超过 1000 的正整数，为数字长度）和 K（小于 10 的正整数）。接下来一行给出一个长度为 L 的正整数 N。

输出格式：

在一行中输出 N 中最早出现的 K 位连续数字所组成的素数。如果这样的素数不存在，则输出 404。注意，原始数字中的前导零也计算在位数之内。例如在 200236 中找 4 位素数，0023 算是解；但第一位 2 不能被当成 0002 输出，因为在原始数字中不存在这个 2 的前导零。

输入样例 1：

20 5
23654987725541023819

输出样例 1：

49877

输入样例 2：

10 3
2468024680

输出样例 2：

404

编程语言：Python

解题思想：

例如L=11，K=3，A=23654826235，可以采用如下算法

1.对A的每一位进行遍历

2.生成A[:3]，A[:3]=236，对236进行素数判断，如果是则输出，不是则重复第1步

依次生成A[:3]=236，A[1:4]=365，A[2:5]=654····

时间复杂度：O(NlogN)

  1. import math
  2.  
  3. Length, PrimeLength = map(int, input().split())  # 输入数字长度、要寻找的素数串的长度
  4. Number = int(input())  # 输入该数字
  5. Judge = False  # 标记Number中是否存在素数，默认为否
  6.  
  7. for i in range(Length - PrimeLength + 1):
  8.     PrimeString = str(Number)[i:i + PrimeLength]  # 生成假定的素数串
  9.     PrimeNumber = int(PrimeString)  # 转为数字
  10.     PrimeJudge = True  # 标记PrimeNumber是否为素数，默认为是
  11.     for j in range(2, int(math.sqrt(PrimeNumber)) + 1):  # 素数判断
  12.         if PrimeNumber % j == 0:
  13.             PrimeJudge = False
  14.             break
  15.     if PrimeJudge:
  16.         print(PrimeString)
  17.         Judge = True
  18.         break
  19. if not Judge:
  20.     print("404")

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