PAT(甲级)2020年春季考试 7-1 Prime Day

乔梓鑫

7-1 Prime Day (20分)

wbfg.JPG

The above picture is from Sina Weibo, showing May 23rd, 2019 as a very cool "Prime Day". That is, not only that the corresponding number of the date 20190523 is a prime, but all its sub-strings ended at the last digit 3 are prime numbers.

Now your job is to tell if a given date is a Prime Day.

Input Specification:

Each input file contains one test case. For each case, a date between January 1st, 0001 and December 31st, 9999 is given, in the format yyyymmdd.

Output Specification:

For each given date, output in the decreasing order of the length of the substrings, each occupies a line. In each line, print the string first, followed by a space, then Yes if it is a prime number, or No if not. If this date is a Prime Day, print in the last line All Prime!.

Sample Input 1:

20190523

Sample Output 1:

20190523 Yes
0190523 Yes
190523 Yes
90523 Yes
0523 Yes
523 Yes
23 Yes
3 Yes
All Prime!

Sample Input 2:

20191231

Sample Output 2:

20191231 Yes
0191231 Yes
191231 Yes
91231 No
1231 Yes
231 No
31 Yes
1 No

题目限制:

image.png

题目大意:

给定数字串,其子串定义为起点从0到最后位置,终点为最后位置的数字串,判断每一个子串是否为素数,如果是输出该数和Yes,否则输出该数和No,如果所有的子串都是素数,最后输出All Prime!

算法思路:

使用字符串s接受输入的数字,只要s长度大于0,就不断进行一下操作:

  • 1、将s转化为数字N,使用isPrime函数判断该数字是否为素数,如果是输出该数字和Yes,否则输出该数字和No,并使用allPrime记录不是所有子串都是素数。
  • 2、令s为下一个子串s = s.substr(1),转1

    最后判断allPrime是否为true,如果是输出All Prime!

提交结果:

image.png

AC代码:

#include<cstdio>
#include<vector>
#include<cstring>
#include<cmath>
#include<string>
#include<iostream>

using namespace std;

bool isPrime(int N){
    if(N<=1) return false;
    int sqrtn = (int)sqrt(1.0*N);
    for (int i = 2; i <= sqrtn; ++i) {
        if(N%i==0) return false;
    }
    return true;
}

int main(){
    string s;
    cin>>s;
    bool allPrime = true;
    while (s.size()>0){
        int N = stoi(s);
        if(isPrime(N)){
            printf("%s Yes\n",s.c_str());
        } else {
            allPrime = false;
            printf("%s No\n",s.c_str());
        }
        s = s.substr(1);
    }
    if(allPrime) printf("All Prime!");
    return 0;
}
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