LeetCode 263: Ugly Number

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本文介绍了一个简单的算法，用于判断一个给定的正整数是否为丑数。丑数定义为只包含质因数2、3和5的正整数。文章提供了一段C++代码实现，并解释了其背后的逻辑。

263. Ugly Number

Difficulty: Easy
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.

思路

丑数的质因子仅可能为2,3,5。也就是，丑数=(2^a)(3^b)(5^c)，a,b,c为非负整数。因此，整数可以一直除以2,3,5，直到不能被整除，最终结果为1就是丑数。

代码

[C++]

class Solution {
public:
    bool isUgly(int num) {
        if(num <= 0) return false;
        else if(num == 1) return true;

        while(num >= 2 && num % 2 == 0) num /= 2;
        while(num >= 3 && num % 3 == 0) num /= 3;
        while(num >= 5 && num % 5 == 0) num /= 5;

        return num == 1;
    }
};