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

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. For example, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is the sequence of the first 10 ugly numbers.

Note that 1 is typically treated as an ugly number.

Hint:

1. The naive approach is to call isUgly for every number until you reach the nth one. Most numbers are not ugly. Try to focus your effort on generating only the ugly ones.
2. An ugly number must be multiplied by either 2, 3, or 5 from a smaller ugly number.
3. The key is how to maintain the order of the ugly numbers. Try a similar approach of merging from three sorted lists: $L_1$, $L_2$, and $L_3$.
4. Assume you have $U_k$, the $k^{th}$ ugly number. Then $U_{k+1}$ must be Min($L_1$ * 2, $L_2$ * 3, $L_3$ * 5).

解题思路

见题目中的提示，主要就是维持一个丑数序列，一个丑数一定是序列中比它小的丑数乘以2,3或5的结果。

实现代码

Java：

// Runtime: 9 ms
public class Solution {
    public int nthUglyNumber(int n) {
        int[] num = new int[n];
        num[0] = 1;
        int n2 = 0;
        int n3 = 0;
        int n5 = 0;
        int i = 1;
        while (i < n) {
            int ugly = Math.min(Math.min(num[n2] * 2, num[n3] * 3), num[n5] * 5);
            num[i++] = ugly;
            if (ugly == num[n2] * 2) {
                n2++;
            }
            if (ugly == num[n3] * 3) {
                n3++;
            }
            if (ugly == num[n5] * 5) {
                n5++;
            }
        }

        return num[n - 1];
    }
}