# 264     Ugly Number II

## 264. [Ugly Number II](https://leetcode.com/problems/ugly-number-ii/description/)

## 1. Question

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**.

## 2. Implementation

**(1) DP**

思路: dp\[i]表示第i个ugly number, 由于ugly number只有2, 3, 5这三个factor，当我们要找下一个ugly number时，我们需要取当前ugly number分别乘以2， 3， 5后最小的数，所以我们分别用三个变量index2, index3, index5找到对应的ugly number

```java
class Solution {
    public int nthUglyNumber(int n) {
        int factor2 = 2, factor3 = 3, factor5 = 5;
        int index2 = 0, index3 = 0, index5 = 0;
        int min = Integer.MAX_VALUE;

        int[] dp = new int[n];
        dp[0] = 1;

        for (int i = 1; i < n; i++) {
            min = Math.min(factor2, Math.min(factor3, factor5));
            dp[i] = min;

            if (min == factor2) {
                factor2 = 2 * dp[++index2];
            }

            if (min == factor3) {
                factor3 = 3 * dp[++index3];
            }

            if (min == factor5) {
                factor5 = 5 * dp[++index5];
            }
        }
        return dp[n - 1];
    }
}
```

## 3. Time & Space Complexity

**Heap:** 时间复杂度O(n), 空间复杂度O(n)
