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 include2, 3, 5. For example,6, 8are ugly while14is not ugly since it includes another prime factor7.

Note that1is typically treated as an ugly number.

• Notes:

  • It's important to not the property of associative of numbers when dividing. E.g. if we divide the number by 2 as much as we can, and then divide any number of times by 3, then within any of those instances, we wouldn't be able to divide by 2. We can for example, generate primes using the same, but iterative approach to this problem.

bool isUgly(int num) 
{
    if (num < 0 || num == 1) return true;

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

    return (num == 1);
}

vector<int> get_primes(long long n)
{
    vector<int> primes;
    for (int i = 2; i <= n; i++) {
        while (n % i == 0) {
            n /= i;
            primes.push_back(i);
        }
    }
    if (n != 1) primes.push_back(n);
    return primes;
}

int main()
{
    vector<int> all_primes = get_primes(480);
    print(all_primes);

    all_primes = get_primes(58);
    print(all_primes);

    all_primes = get_primes(79);
    print(all_primes);
}