USACO 3.1 Humble Numbers

For a given set of K prime numbers S = {p1, p2, ..., pK}, consider the set of all numbers whose prime factors are a subset of S. This set contains, for example, p1, p1p2, p1p1, and p1p2p3 (among others). This is the set of `humble numbers' for the input set S. Note: The number 1 is explicitly declared not to be a humble number.

Your job is to find the Nth humble number for a given set S. Long integers (signed 32-bit) will be adequate for all solutions.

PROGRAM NAME: humble

INPUT FORMAT

Line 1:	Two space separated integers: K and N, 1 <= K <=100 and 1 <= N <= 100,000.
Line 2:	K space separated positive integers that comprise the set S.

SAMPLE INPUT (file humble.in)

4 19

2 3 5 7

OUTPUT FORMAT

The Nth humble number from set S printed alone on a line.

SAMPLE OUTPUT (file humble.out)

27

 

这道题目也是一道常见题目，是一种步步递进的方式获取最终的结果。

时间复杂度为O（k×n），但是由于系数很小，因此最后时间仍然非常快，最复杂的情况也仅仅有0.076ms。

USER: millky wang [ts_mill1]

TASK: humble

LANG: C++

 

Compiling...

Compile: OK

 

Executing...

   Test 1: TEST OK [0.000 secs, 3112 KB]

   Test 2: TEST OK [0.000 secs, 3112 KB]

   Test 3: TEST OK [0.022 secs, 3112 KB]

   Test 4: TEST OK [0.000 secs, 3108 KB]

   Test 5: TEST OK [0.011 secs, 3112 KB]

   Test 6: TEST OK [0.011 secs, 3112 KB]

   Test 7: TEST OK [0.022 secs, 3108 KB]

   Test 8: TEST OK [0.000 secs, 3112 KB]

   Test 9: TEST OK [0.011 secs, 3108 KB]

   Test 10: TEST OK [0.011 secs, 3112 KB]

   Test 11: TEST OK [0.000 secs, 3112 KB]

   Test 12: TEST OK [0.076 secs, 3112 KB]

1. /*
2. ID: millky
3. PROG: humble
4. LANG: C++
5. */
6. #include <iostream>
7. #include <fstream>
8. #include <string>
9. #include <cmath>
10. #include <cstdio>
11. #include <algorithm>
12. #include <vector>
13. #include<iomanip>
14. using namespace std;
15. struct factor 
16. {
17.     int prime,pt,val;
18. };
19. bool myComp(const factor& A,const factor& B)
20. {
21.     return A.prime<B.prime;
22. }
23. int k,n,humble[100000],ea[100],ean;
24. factor primes[100];
25. int main()
26. {
27.     freopen("humble.in","r",stdin);
28.     freopen("humble.out","w",stdout);
29.     int cur,curI;
30.     scanf("%d%d",&k,&n);
31.     for (int i=0;i<k;++i) {
32.         scanf("%d",&primes[i].prime);
33.         primes[i].pt=0;
34.         primes[i].val=primes[i].prime;
35.     }
36.     sort(primes,primes+k,myComp);
37.     for (int i=0;i<n;++i)
38.     {
39.         ean=0;
40.         cur=primes[0].val;
41.         for (int j=1;j<k;++j)
42.             if(primes[j].val<cur)
43.                 cur=primes[j].val;
44.         humble[i]=cur;
45.         for (int j=0;j<k;++j)
46.             if(primes[j].val==cur)
47.                 primes[j].val=primes[j].prime*humble[primes[j].pt++];       
48.     }
49.     printf("%d/n",humble[n-1]);
50.     return 0;
51. }