USACO 3.1 Humble Numbers

Posted 2020-08-21 sigongzi

Humble Numbers

For a given set of K prime numbers S = {p₁, p₂, ..., p_K}, 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

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所以就是一道set的简单应用

然而我的内存在最后一个测试点炸了

事实上操作内存不需要n*k然后第n次的begin，只要不断维护这个序列是n长最后把--end抛出去

然后就没有内存问题了，还会比较快

 1 /*
 2 ID: ivorysi
 3 PROG: humble
 4 LANG: C++
 5 */
 6 #include <iostream>
 7 #include <cstdio>
 8 #include <cstring>
 9 #include <algorithm>
10 #include <queue>
11 #include <set>
12 #define siji(i,x,y) for(int i=(x);i<=(y);++i)
13 #define gongzi(j,x,y) for(int j=(x);j>=(y);--j)
14 #define xiaosiji(i,x,y) for(int i=(x);i<(y);++i)
15 #define sigongzi(j,x,y) for(int j=(x);j>(y);--j)
16 #define inf 0x7fffffff
17 #define MAXN 100005
18 #define ivorysi
19 using namespace std;
20 typedef long long ll;
21 set<int> s;
22 int n,k,pri[105];
23 void solve() {
24     scanf("%d%d",&k,&n);
25     siji(i,1,k) {scanf("%d",&pri[i]);s.insert(pri[i]);}
26     siji(i,1,k){
27         set<int>::iterator k=s.begin();
28         while(1) {
29             int tm=(*k)*pri[i];
30             if(tm<0) break;
31             if(s.size()>n) {
32                 s.erase(--s.end());
33                 if(tm>(*--s.end())) 
34                     break;
35             }
36             s.insert(tm);
37             ++k;
38         }
39     }
40     printf("%d\n",*(--s.end()));
41 }
42 int main(int argc, char const *argv[])
43 {
44 #ifdef ivorysi
45     freopen("humble.in","r",stdin);
46     freopen("humble.out","w",stdout);
47 #else
48     freopen("f1.in","r",stdin);
49 #endif
50     solve();
51 }