PAT 1015 Reversible Primes python解法

1015 Reversible Primes （20 分）
A reversible prime in any number system is a prime whose “reverse” in that number system is also a prime. For example in the decimal system 73 is a reversible prime because its reverse 37 is also a prime.

Now given any two positive integers N (<10⁵) and D (1<D≤10), you are supposed to tell if N is a reversible prime with radix D.

Input Specification:
The input file consists of several test cases. Each case occupies a line which contains two integers N and D. The input is finished by a negative N.

Output Specification:
For each test case, print in one line Yes if N is a reversible prime with radix D, or No if not.

Sample Input:
73 10
23 2
23 10
-2
Sample Output:
Yes
Yes
No

题意：给出来两个数n和b，如果n是一个素数，并且在b进制下反转之后还是一个素数，那这个数n就是一个可逆素数，输出Yes，否则输出No。

解题思路：
1.构造2个函数，isprime(n)用来判断n是否为素数，reverse(n, b)用来将n在b进制下反转并转回十进制。
2.判断素数的方法参考PAT 1152 Google Recruitment python解法。
3.reverse(n, b)中就是正常的除和取余获得n的b进制数，反转之后再乘起来变成十进制。
4.最后注意此题的循环结束条件是输入负数时结束循环，没有在最开始给出输入几行数据。

import math
def isprime(n):
    if n <= 3:
        return n > 1
    if n%6 != 1 and n%6 != 5:
        return False
    for i in range(5,int(math.sqrt(n)),6):
        if n%i==0 or n%(i+2)==0:
            return False
    return True

def reverse(n, b):
    l = []
    while n >= b:
        a = n%b
        n = n//b
        l.append(a)
    l.append(n)
    l = l[::-1]
    s = 0
    for i in range(len(l)):
        s += l[i]*(b**i)
    return s
     
while 1:
    l = list(map(int,input().split()))
    if l[0]<0:
        break
    if isprime(l[0]) and isprime(reverse(l[0],l[1])):
        print('Yes')
    else:
        print('No')

PAT 1015 Reversible Primes python解法

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