数论 FZU 1759 Super A^B mod C

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00

#include <iostream>
#include <cmath>
#include <cstring>
typedef long long llt ;
using namespace std;

int euler_phi(int n)
{
int m = floor(sqrt(n+0.5));
int ans = n;
for(int i = 2; i <= m; i++) if(n%i == 0){
ans = ans / i * (i-1);
while(n%i == 0)
n /= i;
}
if(n > 1) ans = ans / n *(n-1);
return ans;
}

//利用二进制计算a*b%mod
llt multiMod(llt a,llt b,llt mod){
llt ret = 0LL;
a %= mod;
while( b ){
if ( b & 1LL ) ret = ( ret + a ) % mod, --b;
b >>= 1LL;
a = ( a + a ) % mod;
}
return ret;
}

//计算a^b%mod
llt powerMod(llt a,llt b,llt mod){
llt ret = 1LL;
a %= mod;
while( b ){
if ( b & 1LL ) ret = multiMod(ret,a,mod),--b;
b >>= 1LL;
a = multiMod(a,a,mod);
}
return ret;
}

char big[1000050];
llt  bigMod(int mod){
llt ret = 0;
int len = strlen(big);
for (int i = 0;i < len ;++i){
ret %= mod;
ret = ret * 10 + big[i]-'0';
}ret %= mod;
ret += mod;
return ret;
}

int main(){
llt a,b,c;
ios::sync_with_stdio(false);
while(cin>>a>>big>>c){
int er = euler_phi(c);
llt ans;
int len = strlen(big);
if ( len <= 10 ) {
b = 0;
for (int i = 0 ;i < len;++i)
b = b*10 + big[i]-'0';

ans = powerMod(a,b,c);
}
else {
b = bigMod(er);
ans = powerMod(a,b,c);
}
cout <<ans<<endl;
}

}