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878. Nth Magical Number 👍

  • Time: $O(\log(\min(A, B) \cdot n))$
  • Space: $O(1)$
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class Solution {
 public:
  int nthMagicalNumber(long n, long a, long b) {
    constexpr int kMod = 1'000'000'007;
    const long lcm = a * b / __gcd(a, b);
    long l = min(a, b);
    long r = min(a, b) * n;

    while (l < r) {
      const long m = (l + r) / 2;
      if (m / a + m / b - m / lcm >= n)
        r = m;
      else
        l = m + 1;
    }

    return l % kMod;
  }
};

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class Solution {
  public int nthMagicalNumber(long n, long a, long b) {
    final int kMod = 1_000_000_007;
    final long lcm = a * b / gcd(a, b);
    long l = Math.min(a, b);
    long r = Math.min(a, b) * n;

    while (l < r) {
      final long m = (l + r) / 2;
      if (m / a + m / b - m / lcm >= n)
        r = m;
      else
        l = m + 1;
    }

    return (int) (l % kMod);
  }

  private long gcd(long a, long b) {
    return b == 0 ? a : gcd(b, a % b);
  }
}

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class Solution:
  def nthMagicalNumber(self, n: int, a: int, b: int) -> int:
    lcm = a * b // math.gcd(a, b)
    l = bisect.bisect_left(range(min(a, b), min(a, b) * n), n,
                           key=lambda m: m // a + m // b - m // lcm) + min(a, b)
    return l % (10**9 + 7)