Write a program to find the n-th ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5.

Example:

Input: n = 10
Output: 12
Explanation: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is the sequence of the first 10 ugly numbers.
Note:

1 is typically treated as an ugly number.
n does not exceed 1690.
思路：醜數序列是 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, …
因為醜數序列是通過乘以 2, 3, 5構建，所以可以構建三個序列，每次取其中最小的，序列的構建是因子乘以醜數序列中的數。

(1) 1×2, 2×2, 3×2, 4×2, 5×2, …
(2) 1×3, 2×3, 3×3, 4×3, 5×3, …
(3) 1×5, 2×5, 3×5, 4×5, 5×5, …

public int nthUglyNumber(int n) {
        int[] ugly = new int[n];
        ugly[0] = 1;
        int f2 = 2, f3 = 3, f5 = 5;
        int index2 = 0, index3 = 0, index5 = 0;
        for(int i = 1; i < n; i++){
            int min = Math.min(Math.min(f2,f3),f5);
            ugly[i] = min;
            if(f2 == min){
                f2 = ugly[++index2] * 2;
            }
            if(f3 == min){
                f3 = ugly[++index3] * 3;
            }
            if(f5 == min){
                f5 = ugly[++index5] * 5;
            }
        }
        return ugly[n-1];
    }