263. Ugly Number

问题描述

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.

题目链接：

---

思路分析

判断一个整数是不是ugly number。定义是因数只有2，3，5的数是ugly的。

首先判断0，1的情况。然后根据定义循环除这三个数，如果最后剩下的数为1说明只有这三个数为因数，返回true；否则就还有其他因数，返回false。

代码

class Solution {
public:
    bool isUgly(int num) {
        if (num == 1)
            return true;
        if (num == 0)
            return false;
        while (num % 2 == 0)
            num = num / 2;  //same to num >> 1,right shift 1 digit.
        while (num % 3 == 0)
            num = num / 3;
        while (num % 5 == 0)
            num = num / 5;
        return num == 1;
    }
};

时间复杂度：$O(logn)$
空间复杂度：$O(1)$

---

反思

又是一道数学题，感觉只要找到了定义或者接触过就会做的。