*Ugly number

 

 

题目：

Write a program to check whether a given number is an ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. For example, 6, 8 are ugly while 14 is not ugly since it includes another prime factor 7.

Note that 1 is typically treated as an ugly number.

题目大意：

编写程序判断一个给定的数字是否为“丑陋数” ugly number

丑陋数是指只包含质因子2, 3, 5的正整数。例如，6, 8是丑陋数而14不是，因为它包含额外的质因子7

注意，数字1也被视为丑陋数

解题思路：

将输入数重复除2, 3, 5，判断得数是否为1即可

时间复杂度：

记num = 2^a * 3^b * 5^c * t，程序执行次数为 a + b + c，换言之，最坏情况为O(log num)

 

public class Solution {
    public boolean isUgly(int num) 
    {
        if(num <= 0) return false;
        int [] prime = {2,3,5};
        for (int x:prime)
        {
            while(num%x==0)
            num/=x;
        }
        
        return num==1;
        
    }
}

reference: http://bookshadow.com/weblog/2015/08/19/leetcode-ugly-number/