Calculate (a^b)%c where 0<=a,b,c<=10^18

Question

How can I calculate (a ^ b) % c, where 0 <= a, b, c <= 10^18. Here, (a ^ b) means a to the power b, not

Answer 1

You have a problem with temp*temp (long long overflow). You can omit this problem using algorithm of fast mod power to multiply them mod m. Here You have working code:

unsigned long long bigMultiply(unsigned long long b,unsigned long long p, unsigned long long m)
{
  if(p == 0 )return b;
  if(p%2 == 0)
  {  
     unsigned long long temp = bigMultiply(b,p/2ll,m);
     return ((temp)+(temp))%m;
  }
  else
    return (b  +  bigMultiply(b,p-1,m))%m;
}    
unsigned long long bigMod(unsigned long long b,unsigned long long p, unsigned long long m)
{

  if(b == 1)
    return b;
  if(p == 0 )return 1;
  if( p == 1)return b;
  if(p%2 == 0)
  {  
     unsigned ll temp = bigMod(b,p/2ll,m);
     return bigMultiply(temp,temp,m);
  }
  else
    return (b  *  bigMod(b,p-1,m))%m;
}