UVA-136：Ugly Numbers

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UVA-136：Ugly Numbers

来源：UVA

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参考资料：《算法竞赛入门经典》P120

相似题目：

题目

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.

输入

There is no input to this program.

输出

Output should consist of a single line as shown below, with ‘<number>’ replaced by the number computed.

输出样例

The 1500’th ugly number is <number>.

解题思路

若x是丑数，则2x，3x，5x都是丑数。

参考代码

#include<stdio.h>
#include<vector>
#include<queue>
#include<set>
using namespace std;
typedef long long LL;
const int coeff[3]={2,3,5};

int main(){
	priority_queue<LL,vector<LL>,greater<LL> > pq;
	set<LL> s;
	pq.push(1);
	s.insert(1);
	for(int i=1;;i++){
		LL x=pq.top();
		pq.pop();
		if(i==1500){
			printf("The 1500'th ugly number is %d.\n",x);
			break;
		}
		for(int j=0;j<3;j++){
			LL x2=x*coeff[j];
			if(!s.count(x2)){
				s.insert(x2);
				pq.push(x2);
			}
		}
	}
	return 0;
}