878. Nth Magical Number

Problem

A positive integer is magical if it is divisible by either a or b.

Given the three integers n, a, and b, return the nth magical number. Since the answer may be very large, **return it modulo **10^9 + 7.

  Example 1:

Input: n = 1, a = 2, b = 3
Output: 2

Example 2:

Input: n = 4, a = 2, b = 3
Output: 6

  Constraints:

• 1 <= n <= 10^9

• 2 <= a, b <= 4 * 10^4

Solution

class Solution {
    private static final int MOD = 1_000_000_007;

    public int nthMagicalNumber(int n, int a, int b) {
        long c = lcm(a, b);
        long l = 2;
        long r = n * c;
        long ans = r;
        while (l <= r) {
            long mid = l + (r - l) / 2;
            long cnt = mid / a + mid / b - mid / c;
            if (cnt < n) {
                l = mid + 1;
            } else {
                ans = mid;
                r = mid - 1;
            }
        }
        return (int) (ans % MOD);
    }

    private long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    private long gcd(long a, long b) {
        long t;
        while (b != 0) {
            t = b;
            b = a % b;
            a = t;
        }
        return a;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).