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>.

丑数是指不能被2，3，5以外的其他素数整除的数。把丑数从小到大排列起来，结果如下：
           1,2,3,4,5,6,8,9,10,12,15,…
求第1500个丑数。

#include <cstdio>
#include <queue>
using namespace std;

const int maxNum = 1505;

int main() {
    long long a, b, c;
    // 优先队列
    priority_queue<long long, vector<long long>, greater<long long> > pq;
    // 初始化队列有1这个元素
    pq.push(1);
    // 计数
    long long num = 0;
    for(int i = 1; i < maxNum; i++) {
        long long ans = pq.top();
        // test
        // printf("%d \t", ans);
        pq.pop();
        num++;
        if(num == 1500) {
            printf("The 1500'th ugly number is %d.\n", ans);
        }
        // 如果ans是ugly number，则2ans,3ans,5ans都是丑数
        a = ans * 2;
        b = ans * 3;
        c = ans * 5;
        // a 如果与 b或c是同一数的因数关系，那么该数一定在b或c中出现过
        // 因为b或c比a大
        if((a % 5) && (a % 3)) {
            pq.push(a);
        }
        // 同理
        if((b % 5)) {
            pq.push(b);
        }
        pq.push(c);
    }
    return 0;
}