LS 38 Geometric sum（数论+二分快速幂）

Geometric sum

Compute  (a+a2+…an)modm .

Input

Three integers  a,n,m .

( 1≤a,n,m≤1018 )

Output

The only integer denotes the result.

Sample input

2 2 1000000000

Sample output

6 

思路；看代码吧

#include<iostream>
#include<cstring>
using namespace std;
long long c,x,n;
long long mul(long long a,long long b)///(a*b)%c
{ long long ret=0;
  a%=c;b%=c;
  while(a)
  {
    if(a&1)
    ret=(ret+b)%c;
    a>>=1;b<<=1;b%=c;
  }
  return ret;
}
long long sqr(long long x,long long n)///(x^n)%c
{ long long ret=1;
  if(n==1)return x%c;
  while(n)
  {if(n&1)ret=mul(x,ret);
   x=mul(x,x);n>>=1;
  }
  return ret;
}
long long pow(long long x,long long n)///(x+x^2...)%c
{ long long ret=0;
  if(n==1)return x%c;
  if(n&1)
  {
    ret=mul(pow(x,n/2),sqr(x,n/2+1L)+x);
    ret=(ret+x)%c;
  }
  else
  {
    ret=mul(pow(x,n/2),sqr(x,n/2)+1L);
  }
  return ret;
}
int main()
{
  while(cin>>x>>n>>c)
  { 
    cout<<pow(x,n)<<"\n";
  }
}