Super A^B mod C 快速冪+歐拉函數降冪

標籤：

uper A^B mod C  Time Limit:1000MS      Memory Limit:32768KB      64bit IO Format:%I64d & %I64uSubmit Status

Description

Given A,B,C, You should quickly calculate the result of A^B mod C. (1<=A,C<=1000000000,1<=B<=10^1000000).

Input

There are multiply testcases. Each testcase, there is one line contains three integers A, B and C, separated by a single space.

 

Output

For each testcase, output an integer, denotes the result of A^B mod C.

 

Sample Input

3 2 42 10 1000

Sample Output

124 首先要降冪，由降冪公式： （然而不知道公式是怎麼來的。。。求指教）降冪後用快速冪計算

 1 #include<iostream> 2 #include<cstdio> 3 #include<algorithm> 4 #include<cstring> 5 #include<cmath> 6 #define ll __int64 7 #define N 1000100 8 using namespace std; 9 char b[N];10 ll p[N];11 ll a, c;12 ll quick(ll a, ll b){ //快速冪13     ll k = 1;14     while(b){15         if(b%2==1){16             k = k*a;17             k %=c;18         }19         a = a*a%c;20         b /=2;21     }22     return k;23 }24 void priem(){25     memset(p, 0, sizeof(p));26     ll i, j;27     p[1] = 1;28     for(i=2; i<=sqrt(N); i++){29         for(j=2; j<=N/i; j++)30             p[i*j] = 1;31     }32 }33 ll ola(ll n){ //歐拉函數34     ll i, j, r, aa;35     r = n;36     aa = n;37     for(i=2; i<=sqrt(n); i++){38         if(!p[i]){39             if(aa%i==0){40                 r = r/i*(i-1);41                 while(aa%i==0)42                     aa /= i;43             }44         }45     }46     if(aa>1)47         r = r/aa*(aa-1);48     return r;49 }50 int main(){51     ll d, i, j;52     priem();53     while(~scanf("%I64d%s%I64d",&a,b,&c)){54         ll l = strlen(b);55         ll B=0;56         ll oc = ola(c);57       //  cout<<"oc = "<<oc<<endl;58         for(i=0; i<l; i++){59             B = B*10+b[i]-‘0‘;60             if(B>oc)61                 break;62         }63         //cout<<i<<endl;64         if(i==l)65             d = quick(a,B);66         else{67             B=0;68             for(i=0; i<l; i++){ //降冪69                 B = (B*10+b[i]-‘0‘)%oc;70             }71             d = quick(a,B+oc);72         }73       //  printf("B= %I64d\n",B);74         printf("%I64d\n",d);75     }76     return 0;77 }

 

Super A^B mod C 快速冪+歐拉函數降冪