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约数

1.试除法求约数

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <stack>
 7 #include <queue>
 8 #include <vector>
 9 #include <map>
10 #include <set>
11 #include <unordered_set>
12 #include <unordered_map>
13 #define ll long long
14 #define fi first
15 #define se second
16 #define pb push_back
17 #define me memset
18 const int N = 1e6 + 10;
19 const int M = 1e9 + 7;
20 using namespace std;
21 typedef pair<int,int> PII;
22 typedef pair<long,long> PLL;
23 
24 int n;
25 int x;
26 vector<int> res;
27 
28 void divide(int n){
29     res.clear();
30     for(int i=1;i<=n/i;++i){
31         if(n%i==0) {
32             res.pb(i);
33             if (i!=n/i) res.pb(n/i);
34         }
35     }
36     sort(res.begin(),res.end());
37     vector<int>::iterator iter;
38      for(iter=res.begin();iter!=res.end();++iter) printf("%d ",*iter);
39      printf("\n");
40 }
41 
42 int main() {
43     ios::sync_with_stdio(false);
44     cin>>n;
45      while(n--){
46          cin>>x;
47           divide(x);
48      }
49 
50     return 0;
51 }

 

2.求约数个数/求约数之和

分析:我们将n作质因数分解,利用约数个数定理和约数和定理即可

 

求约数个数:

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <stack>
 7 #include <queue>
 8 #include <vector>
 9 #include <map>
10 #include <set>
11 #include <unordered_set>
12 #include <unordered_map>
13 #define ll long long
14 #define fi first
15 #define se second
16 #define pb push_back
17 #define me memset
18 const int N = 1e6 + 10;
19 const int mod = 1e9 + 7;
20 using namespace std;
21 typedef pair<int,int> PII;
22 typedef pair<long,long> PLL;
23 
24 ll n,x;
25 ll ans=1;
26 unordered_map<int,int> Hash;
27 void divide(ll x){
28     for(ll i=2;i<=x/i;++i){
29         if(x%i==0) {
30             while (x % i == 0) {
31                 x/=i;
32                 Hash[i]++;
33             }
34         }
35     }
36     if(x>1) Hash[x]++;
37 }
38 
39 void sum(){
40     unordered_map<int,int>::iterator iter;
41      for(iter=Hash.begin();iter!=Hash.end();++iter){
42          ans=ans*(iter->se+1)%mod;
43      }
44      printf("%lld\n",ans);
45 }
46 
47 
48 
49 int main() {
50     ios::sync_with_stdio(false);
51     cin>>n;
52      while(n--){
53          cin>>x;
54           divide(x);
55      }
56      sum();
57 
58     return 0;
59 }

 

求约数和:

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <stack>
 7 #include <queue>
 8 #include <vector>
 9 #include <map>
10 #include <set>
11 #include <unordered_set>
12 #include <unordered_map>
13 #define ll long long
14 #define fi first
15 #define se second
16 #define pb push_back
17 #define me memset
18 const int N = 1e6 + 10;
19 const int mod = 1e9 + 7;
20 using namespace std;
21 typedef pair<int,int> PII;
22 typedef pair<long,long> PLL;
23 
24 int n,x;
25 unordered_map<int,int> Hash;
26 ll ans=1;
27 
28 void divide(int x){
29     for(int i=2;i<=x/i;++i){
30         while(x%i==0){
31             x/=i;
32             Hash[i]++;
33         }
34     }
35     if(x>1) Hash[x]++;
36 }
37 
38 void sum(){
39     unordered_map<int,int>::iterator iter;
40      for(iter=Hash.begin();iter!=Hash.end();++iter){
41          ll tmp=1;
42          while(iter->se--){
43              tmp=(tmp*iter->fi+1)%mod;
44          }
45          ans=ans*tmp%mod;
46      }
47      printf("%lld\n",ans);
48 }
49 
50 int main() {
51     ios::sync_with_stdio(false);
52     cin>>n;
53      while(n--){
54          cin>>x;
55           divide(x);
56      }
57     sum();
58 
59     return 0;
60 }

 

posted @ 2020-04-06 10:12  Rayotaku  阅读(355)  评论(0)  编辑  收藏  举报