【STL + 模拟】Ugly Numbers UVA - 136

【STL + 模拟】Ugly Numbers UVA - 136

Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, …
shows the first 11 ugly numbers. By convention, 1 is included.
Write a program to find and print the 1500’th ugly number.
Input
There is no input to this program.
Output
Output should consist of a single line as shown below, with replaced by the number
computed.
Sample Output
The 1500’th ugly number is

题意：
质因数为2，3或 5的数为丑数，1也包含其中。要求输出第1500个丑数。

思路：
如果一个数a是丑数，那么 2*a，3*a， 5*a一定也是丑数。
因此只需要每次从队列中找到最小的（每一次都找一个新的，之前没用过的），然后*2，*3， *5，判断哪些数之前没有出现过【用set记录】，然后将他们放入队列中，直到队列数量达到1500。

AC代码：

#include 
#include 
#include 
#include 
#include 

using namespace std;

priority_queue<long long, vector<long long>, greater<long long> > p;
set<long long> q;

int main()
{
    long long cur;
    p.push(1);
    q.insert(1);
    for(int i = 1; i < 1500; i++)
    {
        long long a, b, c;
        cur = p.top();
        p.pop();
        a = 2 * cur;
        b = 3 * cur;
        c = 5 * cur;
        if(q.find(a) == q.end())
        {
            p.push(a);
            q.insert(a);
        }
        if(q.find(b) == q.end())
        {
            p.push(b);
            q.insert(b);
        }
        if(q.find(c) == q.end())
        {
            p.push(c);
            q.insert(c);
        }
    }
    cur = p.top();
    printf("The 1500'th ugly number is %lld.\n", cur);
    return 0;
}