Ugly Numbers

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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>.

这道题应用到优先队列——priority_queue，优先队列出队列的不是最先进入队列的而是优先级最高的。相关操作与队列一样，只不过取队首元素变成了取优先级最高的元素：s.top()。优先队列包含在头文件<queue>中，priority_queue（int，vector<int>，cmp），cmp是比较函数，类似qsort，可以认为当返回值为true时交换两个数的位置，排在前面的优先级大（实际并未交换），因此取队首元素就变成取优先级高的元素了。代码如下：

#include<queue>#include<cstdio>#include<set>using namespace std;typedef long long LL; //是long long const int b[3]={2,3,5};int main(){set<LL> num;priority_queue<LL,vector<LL>,greater<LL> > pq;pq.push(1);num.insert(1);int i=0;while(1){LL t=pq.top();pq.pop();i++;if(i==1500){printf("The 1500'th ugly number is %lld.\n",t);//注意输出格式，不要漏掉“.”break;}for(int j=0;j<3;j++){LL t1=t*b[j];               //LL t1=t*b[j];

if(!num.count(t1))            if(num.insert(t1).second) pq.push(t1);{                                                    num.insert(t1);pq.push(t1);}}}return 0;}