第 N 个神奇数字

/*
 * 思路：
 * 虽然Java Streams不适合处理这样的问题，但我们可以借助一些额外的工具类来使用流的方式进行计算。
 * 我们可以模拟流操作，但二分查找仍然是核心。
 */

import java.util.stream.LongStream;

public class MagicalNumberStream {
    private static final int MOD = 1000000007;

    public int nthMagicalNumber(int n, int a, int b) {
        long low = Math.min(a, b);
        long high = (long) n * Math.min(a, b);
        long lcm = lcm(a, b);

        while (low < high) {
            long mid = low + (high - low) / 2;
            if (LongStream.of(mid / a, mid / b).sum() - mid / lcm < n) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }

        return (int) (low % MOD);
    }

    private long gcd(long x, long y) {
        if (y == 0) return x;
        return gcd(y, x % y);
    }

    private long lcm(long x, long y) {
        return x * (y / gcd(x, y));
    }

    public static void main(String[] args) {
        MagicalNumberStream mn = new MagicalNumberStream();
        System.out.println(mn.nthMagicalNumber(1, 2, 3)); // 输出 2
        System.out.println(mn.nthMagicalNumber(4, 2, 3)); // 输出 6
    }
}