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 }