【UVa 136】Ugly Numbers

 Ugly Numbers 

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>.

 

嗯，好，这是一道比较直接的题目啊。

大家可以直接百度一下。啦啦啦~~~~~~~

开玩笑。

现在有几个问题，找最小、判重。那这两个问题都是比较费时的。

我们可以用小根堆+HASH，当然C++党可以用优先队列+SET。

OK！现在问题都解决，直接上就行了。

#include<cstdio>
#include<cstring>
#include<iostream>
#include<vector>
#include<set>
#include<queue>
using namespace std;

typedef long long LL;
set<LL> h;
priority_queue<LL, vector<LL>, greater<LL> > heap;
int orig[3] = {2, 3, 5};

int main()
{
    heap.push(1);
    h.insert(1);
    for (int i = 1;; ++i)
    {
        LL x = heap.top();
        heap.pop();
        if (i == 1500)
        {
            cout << "The 1500'th ugly number is " << x << ".\n";
            break;
        }
        for (int j = 0; j < 3; ++j)
        {
            LL in = x * orig[j];
            if (!h.count(in))
            {
                h.insert(in);
                heap.push(in);
            }
        }
    }
    return 0;
}