264. Ugly Number II

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, and n does not exceed 1690.

题目含义：这道题是 26. Ugly Number的扩展，要求我们找到第n个丑数

思路：

1. 申请一个长度为n的数组uglyNumbers，用于从小到大顺序存储n个丑数，数组中的首项为1，即第一个丑数为1

2. 设置三个变量idx2、idx3、idx5存储下标，初始值都为1

3. 找出数组uglyNumbers[idx2]*2、uglyNumbers[idx3]*3、uglyNumbers[idx5]*5的最小值，最小值即为下一个丑数，同时更新最小值对应的下标，如果多个数字同时为最小值，则它们的下标都要更新

4. 找到第n个丑数时，循环结束

    public int GetUglyNumber_Solution(int index) {
        if(index<=6) return index;
        int[] dp = new int[index];
        dp[0] = 1;
        int position2 = 0, position3 = 0, position5 = 0;
        for (int i = 1; i < index; i++) {
            dp[i] = Math.min(dp[position2] * 2, Math.min(dp[position3] * 3, dp[position5] * 5));
            if (dp[i] == dp[position2] * 2) position2++;
            if (dp[i] == dp[position3] * 3) position3++;
            if (dp[i] == dp[position5] * 5) position5++;
        }
        return dp[index - 1];        
    }