Project Euler #35 - Circular Primes（结果不正确 1）

Question

我正在尝试尝试 project euler (click here) 的第 35 个问题。问题是这样的：

The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.
There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
How many circular primes are there below one million?

所以我创建了一个带有前百万数的筛子，以得到所有小于一百万的素数，并用它来比较素数的旋转结果。

arr = []

for i in range(2, len(sieve)):
    if sieve[i]:
        sub_arr = retCircular(i)
        count = len(sub_arr)
        carry = 0
        for j in sub_arr:
            if sieve[j]:
                carry += 1
                sieve[j] = False
            else:
                break
        if carry == count:
            for j in sub_arr:
                arr.append(j)

print "Number of circular primes =", len(arr)

这个程序给出的100万以下的循环素数是54个，而实际答案是55个。谁能帮我看看我错在哪里？

注：

retCircular(n) 是一个用户定义的函数，它 returns 数组中数字的所有循环形式。
'sieve' 是一个布尔值数组，在所有主要位置索引处包含 True，在所有复合位置索引处包含 False。

P/S，如果谁有更好的解决方法，请告诉我！

Answer 1

我将在这里使用我的顾问的 ESP：您的 retCircular 方法没有正确处理重复模式，这使得它错过了 repunit（1 的字符串）质数。特别是 retCircular(11) returns [11, 11]，这会使您的算法错过该数字作为循环素数。这是我的方法的蛮力版本：

def retCircular(prime):
    prime_str = str(prime)
    family = [prime]
    for _ in range(len(prime_str)-1):
        prime_str = prime_str[1:] + prime_str[0]
        child = int(prime_str)
        if child == prime:
            break
        family.append(int(prime_str))
    return family

...我用你的主程序得到了 55 个素数:

Prime family: [2]
Prime family: [3]
Prime family: [5]
Prime family: [7]
Prime family: [11]
Prime family: [13, 31]
Prime family: [17, 71]
Prime family: [37, 73]
Prime family: [79, 97]
Prime family: [113, 131, 311]
Prime family: [197, 971, 719]
Prime family: [199, 991, 919]
Prime family: [337, 373, 733]
Prime family: [1193, 1931, 9311, 3119]
Prime family: [3779, 7793, 7937, 9377]
Prime family: [11939, 19391, 93911, 39119, 91193]
Prime family: [19937, 99371, 93719, 37199, 71993]
Prime family: [193939, 939391, 393919, 939193, 391939, 919393]
Prime family: [199933, 999331, 993319, 933199, 331999, 319993]
Number of circular primes = 55

Project Euler #35 - Circular Primes（结果不正确 1）

Project Euler #35 - Circular Primes (Incorrect Result by 1)

python

algorithm

primes

project