大数的因子个数

  1 #include <iostream>
  2 #include <algorithm>
  3 #include <cstring>
  4 #include <cstdio>
  5 #include <vector>
  6 #include <queue>
  7 #include <stack>
  8 #include <cstdlib>
  9 #include <iomanip>
 10 #include <cmath>
 11 #include <cassert>
 12 #include <ctime>
 13 #include <map>
 14 #include <set>
 15 using namespace std;
 16 #pragma comment(linker, "/stck:1024000000,1024000000")
 17 #define lowbit(x) (x&(-x))
 18 #define max(x,y) (x>=y?x:y)
 19 #define min(x,y) (x<=y?x:y)
 20 #define MAX 100000000000000000
 21 #define MOD 1000000007
 22 #define pi acos(-1.0)
 23 #define ei exp(1)
 24 #define PI 3.1415926535897932384626433832
 25 #define ios() ios::sync_with_stdio(true)
 26 #define INF 0x3f3f3f3f
 27 #define mem(a) (memset(a,0,sizeof(a)))
 28 typedef long long ll;
 29 const int s=8;
 30 char ch[26];
 31 ll mult_mod(ll a,ll b,ll c)
 32 {
 33     a%=c;
 34     b%=c;
 35     ll ret=0;
 36     ll tmp=a;
 37     while(b)
 38     {
 39         if(b&1){
 40             ret+=tmp;
 41             if(ret>c) ret-=c;
 42         }
 43         tmp<<=1;
 44         if(tmp>c) tmp-=c;
 45         b>>=1;
 46     }
 47     return ret;
 48 }
 49 ll pow_mod(ll a,ll n,ll mod)
 50 {
 51     ll ans=1;
 52     ll tmp=a%mod;
 53     while(n)
 54     {
 55         if(n&1) ans=mult_mod(ans,tmp,mod);
 56         tmp=mult_mod(tmp,tmp,mod);
 57         n>>=1;
 58     }
 59     return ans;
 60 }
 61 bool check(ll a,ll n,ll x,ll t)
 62 {
 63     ll ret=pow_mod(a,x,n);
 64     ll last=ret;
 65     for(int i=1;i<=t;i++)
 66     {
 67         ret=mult_mod(ret,ret,n);
 68         if(ret==1 && last!=1 && last!=n-1) return true;
 69         last=ret;
 70     }
 71     if(ret!=1) return true;
 72     else return false;
 73 }
 74 bool miller_pabin(ll n)
 75 {
 76     if(n<2) return false;
 77     if(n==2) return true;
 78     if((n&1)==0) return false;
 79     ll x=n-1;
 80     ll t=0;
 81     while((x&1)==0) {x>>=1;t++;}
 82     srand(time(NULL));
 83     for(int i=0;i<s;i++){
 84         ll a=rand()%(n-1)+1;
 85         if(check(a,n,x,t)) return false;
 86     }
 87     return true;
 88 }
 89 ll factor[110];
 90 int tol=0;
 91 ll gcd(ll a,ll b)
 92 {
 93     ll t;
 94     while(b)
 95     {
 96         t=a;
 97         a=b;
 98         b=t%b;
 99     }
100     if(a>=0) return a;
101     else return -a;
102 }
103 ll pollard_rho(ll x,ll c)
104 {
105     ll i=1,k=2;
106     srand(time(NULL));
107     ll x0=rand()%(x-1)+1;
108     ll y=x0;
109     while(1)
110     {
111         i++;
112         x0=(mult_mod(x0,x0,x)+c)%x;
113         ll d=gcd(y-x0,x);
114         if(d!=1 && d!=x) return d;
115         if(y==x0) return x;
116         if(i==k){y=x0;k+=k;}
117     }
118 }
119 void findfac(ll n,ll k)
120 {
121     if(n==1) return ;
122     if(miller_pabin(n))
123     {
124         factor[tol++]=n;
125         return ;
126     }
127     ll p=n;
128     ll c=k;
129     while(p>=n) p=pollard_rho(p,c--);
130     findfac(p,k);
131     findfac(n/p,k);
132 }
133 int main()
134 {
135     ll n;
136     scanf("%lld",&n);
137     if(miller_pabin(n)) printf("2\n");
138     else
139     {
140         findfac(n,107);
141         ll ans=1;
142         for(int i=0;i<tol;i++)
143         {
144            
145             ll pos=0;
146             while(n>0 && (n%factor[i]==0))
147             {
148                 pos++;
149                 n/=factor[i];
150             }
151             if(pos) ans*=(pos+1);
152         }
153         printf("%lld\n",ans);
154     }
155     return 0;
156 }