UVA - 136 Ugly Numbers

Ugly Numbers

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Submit Status

Description




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>.

丑数是指不能被2,3,5以外的其他素数整除的数。求第1500个丑数。

最小的丑数是1，对任意丑数x，2x，3x，5x也是丑数。用优先 队列保存已经生成的丑数，再依次取出最小的丑数生成三个新的丑数就好了，注意生成丑数的来源多种，需要判断新生成的丑数是否已存在。

#include<iostream>
#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>pq;
	set<LL>s;
	pq.push(-1);
	s.insert(1);
	for (int i = 1;; i++)
	{
		LL x = -pq.top(); pq.pop();
		if (i == 1500)
		{
			cout << "The 1500'th ugly number is " << x << "." << endl;
			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;
}