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1175. Prime Arrangements 👎

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class Solution {
 public:
  int numPrimeArrangements(int n) {
    constexpr int kMod = 1'000'000'007;
    const int count = countPrimes(n);
    return (factorial(count, kMod) * factorial(n - count, kMod)) % kMod;
  }

 private:
  int countPrimes(int n) {
    vector<bool> prime(n + 1, true);
    prime[0] = false;
    prime[1] = false;

    for (int i = 0; i <= sqrt(n); ++i)
      if (prime[i])
        for (int j = i * i; j <= n; j += i)
          prime[j] = false;

    return count(begin(prime), end(prime), true);
  }

  long factorial(int n, const int kMod) {
    long fact = 1;
    for (int i = 1; i <= n; ++i)
      fact = fact * i % kMod;
    return fact;
  }
};

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class Solution {
  public int numPrimeArrangements(int n) {
    final int kMod = 1_000_000_007;
    final int count = countPrimes(n);
    return (int) ((factorial(count, kMod) * factorial(n - count, kMod)) % kMod);
  }

  private int countPrimes(int n) {
    boolean[] prime = new boolean[n + 1];
    Arrays.fill(prime, 2, n + 1, true);

    for (int i = 0; i * i <= n; ++i)
      if (prime[i])
        for (int j = i * i; j <= n; j += i)
          prime[j] = false;

    int count = 0;

    for (boolean p : prime)
      if (p)
        ++count;

    return count;
  }

  long factorial(int n, final long kMod) {
    long fact = 1;
    for (int i = 1; i <= n; ++i)
      fact = fact * i % kMod;
    return fact;
  }
}

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class Solution:
  def numPrimeArrangements(self, n: int) -> int:
    kMod = 1_000_000_007

    def countPrimes(n: int) -> int:
      isPrime = [False] * 2 + [True] * (n - 1)

      for i in range(2, int(n**0.5) + 1):
        if isPrime[i]:
          for j in range(i * i, n + 1, i):
            isPrime[j] = False

      return sum(isPrime)

    def factorial(n: int) -> int:
      fact = 1

      for i in range(1, n + 1):
        fact = fact * i % kMod

      return fact

    count = countPrimes(n)
    return factorial(count) * factorial(n - count) % kMod