Uva 136-丑数 ugly number

题目描述：

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 and Output

There is no input to this program. Output should consist of a single line as shown below, with <number> replaced by the number computed.

Sample output

The 1500'th ugly number is <number>.

分析：

本题难点不多，直接使用队列完成。

优先队列priority_queque的详细用法，请戳（http://www.cnblogs.com/void/archive/2012/02/01/2335224.html）

代码：

#include<iostream>
#include<set>
#include<queue>
#include<vector>
using namespace std;
typedef long long ll;
const int basic[3]={2,3,5};
int main()
{
    priority_queue<ll,vector<ll>,greater<ll> >pq;
    set<ll>q;
    q.insert(1);
    pq.push(1);
    for(int i=1;;i++)
    {
        ll x=pq.top();
        pq.pop();
        if(i==1500)
        {
            cout<<"The 1500'th ugly number is "<<x<<".
";
            break;
        }
        for(int j=0;j<3;j++)
        {
            ll x2=basic[j]*x;
            if(!q.count(x2))
            {
                q.insert(x2);
                pq.push(x2);
            }
        }    
    }
    return 0;
 }