【Jason's_ACM_解题报告】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>.

此题有多种解决方案，本题使用优先级队列实现。priority_queue< int,vector<int>,cmp >或者将cmp改为greater<int>，cmp函数是优先级队列的比较函数，优先级高的先出队，也就是说，假如传给cmp两个参数x、y，当cmp返回值为true时x的优先级低于y的优先级。比如，若函数为return x>y;则代表，数大的优先级小；此处greater是一个模板函数，运行时，自动传给greater两个参数x、y，若x>y返回true，否则返回false。

附代码如下：

#include<set>
#include<vector>
#include<queue>
#include<cstdio>

using namespace std;

#define LL long long int

const int num[3]={2,3,5};

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

}
return 0;
}