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204. Count Primes 👍

  • Time: $O(n\log(\log n))$
  • Space: $O(n)$
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class Solution {
 public:
  int countPrimes(int n) {
    if (n <= 2)
      return 0;
    const vector<bool> isPrime = sieveEratosthenes(n);
    return ranges::count(isPrime, true);
  }

 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 countPrimes(int n) {
    if (n <= 2)
      return 0;
    final boolean[] isPrime = sieveEratosthenes(n);
    int ans = 0;
    return (int) IntStream.range(0, isPrime.length)
        .mapToObj(i -> isPrime[i])
        .filter(p -> p)
        .count();
  }

  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 countPrimes(self, n: int) -> int:
    if n <= 2:
      return 0
    return sum(self._sieveEratosthenes(n))

  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