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id	title	challengeType	videoUrl	dashedName
5900f38f1000cf542c50fea2	问题35：循环素数	5		problem-35-circular-primes

--description--

这个数字197被称为循环素数，因为数字的所有旋转：197,971和719本身都是素数。在100：2,3,5,7,11,13,17,31,37,71,73,79和97之下有十三个这样的素数。在n下面有多少个圆形素数，而100 <= n < = 1000000？

--hints--

circularPrimes(100)应该返回13。

assert(circularPrimes(100) == 13);

circularPrimes(100000)应该返回43。

assert(circularPrimes(100000) == 43);

circularPrimes(250000)应该返回45。

assert(circularPrimes(250000) == 45);

circularPrimes(500000)应该返回49。

assert(circularPrimes(500000) == 49);

circularPrimes(750000)应该返回49。

assert(circularPrimes(750000) == 49);

circularPrimes(1000000)应该返回55。

assert(circularPrimes(1000000) == 55);

--seed--

--seed-contents--

function circularPrimes(n) {

  return n;
}

circularPrimes(1000000);

--solutions--

function rotate(n) {
  if (n.length == 1) return n;
  return n.slice(1) + n[0];
}

function circularPrimes(n) {
  // Nearest n < 10^k
  const bound = 10 ** Math.ceil(Math.log10(n));
  const primes = [0, 0, 2];
  let count = 0;

  // Making primes array
  for (let i = 4; i <= bound; i += 2) {
    primes.push(i - 1);
    primes.push(0);
  }

  // Getting upperbound
  const upperBound = Math.ceil(Math.sqrt(bound));

  // Setting other non-prime numbers to 0
  for (let i = 3; i < upperBound; i += 2) {
    if (primes[i]) {
      for (let j = i * i; j < bound; j += i) {
        primes[j] = 0;
      }
    }
  }

  // Iterating through the array
  for (let i = 2; i < n; i++) {
    if (primes[i]) {
      let curr = String(primes[i]);
      let tmp = 1; // tmp variable to hold the no of rotations
      for (let x = rotate(curr); x != curr; x = rotate(x)) {
        if (x > n && primes[x]) {
          continue;
        }
        else if (!primes[x]) {
          // If the rotated value is 0 then it isn't a circular prime, break the loop
          tmp = 0;
          break;
        }
        tmp++;
        primes[x] = 0;
      }
      count += tmp;
    }
  }
  return count;
}

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