263. Ugly Number

263. Ugly Number

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.
Link:
https://leetcode.com/problems/ugly-number/
Analysis:
方法一：找出这个数所有的质因数，这样在数大的时候计算量还是挺大的，会超时。
方法二：直接将其2、3、5的公约数全部约分，看最后是否等于1 。若等于1，则质因数只有2、3、5啦。
Source Code（C++）:

#include <iostream>#include <vector>using namespace std;/***************************找出所有的质因数，这种方法超时*******************************************//*class Solution {public:    bool isUgly(int num) {        if (num<1){            return false;        }        else if(num == 1) {            return true;        }        else {            int k=2;            vector<int> prime_number;            while(num!=1) {                if (num%k==0) {                    prime_number.push_back(k);                    num /= k;                }                else {                    k++;                }            }            for(int i=0; i<prime_number.size(); i++)            {                if (prime_number.at(i)!=2 &&prime_number.at(i)!=3 && prime_number.at(i)!=5 ) {                    return false;                }            }            return true;        }    }};*/class Solution {public:    bool isUgly(int num) {        if (num<1){            return false;        }        else if(num == 1) {            return true;        }        else {            while (num%2 == 0) {                num /= 2;            }            while (num%3 == 0) {                num /= 3;            }            while (num%5 == 0) {                num /= 5;            }            if (num == 1) {                return true;            }             else {                return false;            }        }    }};int main() {    Solution sol;    cout << sol.isUgly(90);    return 0;}