问题

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.

例子

175
false

分析

不断用2 3 7除n，如果n在等于1之前除不尽，说明n不是丑数；否则是丑数。

要点

弄清丑数的概念。

时间复杂度

O(logn)

空间复杂度

O(1)

代码

class Solution {
public:
    bool isUgly(int num) {
        if (num < 1) return false;
        while (num > 1) {
            if (!(num & 1))
                num /= 2;
            else if (num % 3 == 0)
                num /= 3;
            else if (num % 5 == 0)
                num /= 5;
            else
                return false;
        }
        return true;
    }
};