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3233. Find the Count of Numbers Which Are Not Special 👍

  • Time: $O(n\log(\log \sqrt{r}))$
  • Space: $O(\sqrt{r})$
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class Solution {
 public:
  int nonSpecialCount(int l, int r) {
    const int maxRoot = sqrt(r);
    const vector<bool> isPrime = sieveEratosthenes(maxRoot + 1);
    int specialCount = 0;

    for (int num = 2; num <= sqrt(r); ++num)
      if (isPrime[num] && l <= num * num && num * num <= r)
        ++specialCount;

    return r - l + 1 - specialCount;
  }

 private:
  vector<bool> sieveEratosthenes(int n) {
    vector<bool> isPrime(n, true);
    isPrime[0] = false;
    isPrime[1] = false;
    for (int i = 2; i * i < n; ++i)
      if (isPrime[i])
        for (int j = i * i; j < n; j += i)
          isPrime[j] = false;
    return isPrime;
  }
};

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class Solution {
  public int nonSpecialCount(int l, int r) {
    final int maxRoot = (int) Math.sqrt(r);
    final boolean[] isPrime = sieveEratosthenes(maxRoot + 1);
    int specialCount = 0;

    for (int num = 2; num <= Math.sqrt(r); ++num)
      if (isPrime[num] && l <= num * num && num * num <= r)
        ++specialCount;

    return r - l + 1 - specialCount;
  }

  private boolean[] sieveEratosthenes(int n) {
    boolean[] isPrime = new boolean[n];
    Arrays.fill(isPrime, true);
    isPrime[0] = false;
    isPrime[1] = false;
    for (int i = 2; i * i < n; ++i)
      if (isPrime[i])
        for (int j = i * i; j < n; j += i)
          isPrime[j] = false;
    return isPrime;
  }
}

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class Solution:
  def nonSpecialCount(self, l: int, r: int) -> int:
    maxRoot = math.isqrt(r)
    isPrime = self._sieveEratosthenes(maxRoot + 1)
    specialCount = 0

    for num in range(2, math.isqrt(r) + 1):
      if isPrime[num] and l <= num**2 <= r:
        specialCount += 1

    return r - l + 1 - specialCount

  def _sieveEratosthenes(self, n: int) -> list[bool]:
    isPrime = [True] * n
    isPrime[0] = False
    isPrime[1] = False
    for i in range(2, int(n**0.5) + 1):
      if isPrime[i]:
        for j in range(i * i, n, i):
          isPrime[j] = False
    return isPrime