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1808. Maximize Number of Nice Divisors

  • Time: $O(\log n)$
  • Space: $O(1)$
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class Solution {
 public:
  int maxNiceDivisors(int primeFactors) {
    if (primeFactors <= 3)
      return primeFactors;
    if (primeFactors % 3 == 0)
      return modPow(3, primeFactors / 3) % kMod;
    if (primeFactors % 3 == 1)
      return 4L * modPow(3, (primeFactors - 4) / 3) % kMod;
    return 2L * modPow(3, (primeFactors - 2) / 3) % kMod;
  }

 private:
  static constexpr int kMod = 1'000'000'007;

  long modPow(long x, long n) {
    if (n == 0)
      return 1;
    if (n % 2 == 1)
      return x * modPow(x % kMod, (n - 1)) % kMod;
    return modPow(x * x % kMod, (n / 2)) % kMod;
  }
};

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class Solution {
  public int maxNiceDivisors(int primeFactors) {
    if (primeFactors <= 3)
      return primeFactors;
    if (primeFactors % 3 == 0)
      return (int) (modPow(3, primeFactors / 3) % kMod);
    if (primeFactors % 3 == 1)
      return (int) (4 * modPow(3, (primeFactors - 4) / 3) % kMod);
    return (int) (2 * modPow(3, (primeFactors - 2) / 3) % kMod);
  }

  private static final int kMod = 1_000_000_007;

  private long modPow(long x, long n) {
    if (n == 0)
      return 1;
    if (n % 2 == 1)
      return x * modPow(x, n - 1) % kMod;
    return modPow(x * x % kMod, n / 2);
  }
}