SPOJ Distinct Primes 打表

Posted 2020-10-03 EricJeffrey

题目链接：http://www.spoj.com/problems/AMR11E/

题目大意：Lucky Number指的是有至少三个不同素数相乘得到数。问1000以内的素因子。

解题思路：可以发现1000以内的满足条件的数字非常多，因此直接筛选打表，查看每个数的不同素因子个数，如果超过三个就满足条件。

代码：

 1 const int maxn = 1e4 + 5;
 2 int vis[maxn];
 3 vector<int> primes, lu;
 4 
 5 void dowork(){
 6     memset(vis, 0, sizeof(vis));
 7     for(int i = 2; i < maxn; i++) if(!vis[i])
 8         for(int j = i * i; j < maxn; j += i)
 9             if(j > 0) vis[j] = 1;
10     for(int i = 2; i < maxn; i++)
11         if(!vis[i]) primes.push_back(i);
12 } 
13 void solve(){
14     dowork();
15     memset(vis, 0, sizeof(vis));
16     int cnt = 0;
17     for(int i = 0; i < primes.size(); i++){
18         for(int j = 2; j < maxn; j++){
19             if(vis[j] >= 3) continue;
20             int tmp = 0, x = j;
21             while(x % primes[i] == 0 && x) {
22                 tmp = 1; x /= primes[i];
23             }
24             if(tmp) vis[j]++;
25         }
26     }
27     for(int i = 2; i < maxn; i++) 
28         if(vis[i] >= 3) lu.push_back(i);
29 }
30 int main(){
31     ios::sync_with_stdio(false);
32     int t;
33     solve();
34     cin >> t;
35     while(t--){
36         int n;
37         cin >> n;
38         cout << lu[n - 1] << endl;
39     }
40 }

题目：

Distinct Primes

#math #number-theory

 

Arithmancy is Draco Malfoy‘s favorite subject, but what spoils it for him is that Hermione Granger is in his class, and she is better than him at it. Prime numbers are of mystical importance in Arithmancy, and Lucky Numbers even more so. Lucky Numbers are those positive integers that have at least three distinct prime factors; 30 and 42 are the first two. Malfoy‘s teacher has given them a positive integer n, and has asked them to find the n-th lucky number. Malfoy would like to beat Hermione at this exercise, so although he is an evil git, please help him, just this once. After all, the know-it-all Hermione does need a lesson.

Input

The first line contains the number of test cases T. Each of the next T lines contains one integer n.

Output

Output T lines, containing the corresponding lucky number for that test case.

Constraints

1 <= T <= 20
1 <= n <= 1000

Example

Sample Input:
2
1
2

Sample Output:
30
42