Fast power of power OR multiplication by exponentiation

About the fast power this algorithm, already did not want to say, very early also will this algorithm, but originally always rely on the template foggy, recently re-study, found that overlooked an important problem, that is, if the number of modulus is greater than the int type, even if for __int64 when should do, so you have to use the multiplication of fast Power + Power quickly.

The fast power is generally to solve the problem of exponentiation, obviously the idea is two points, the following paste on the fast power template:

1 __int64 Mulpow (__int64 a,__int64 p,__int64 m)2 {3__int64 ans =1;4      while(P)5     {6         if(p&1)7Ans = ans * a%m;8P >>=1;9A = a * a%m;Ten     } One     returnans; A}

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However, the above code has a problem, it is not suitable for m over int, the following is a solution to the case of M over int

1__int64 multi (__int64 a,__int64 b,__int64 N)//Multiplication Fast Power2 {3__int64 temp=0;4      while(b)5     {6         if(b&1)7         {8temp+=A;9             if(temp>=n) temp-=N;Ten         } Onea<<=1; A         if(a>=n) a-=N; -b>>=1; -     } the     returntemp; - } -  -__int64 Mulpow (__int64 a,__int64 m,__int64 N)//Power Fast + { -__int64 temp=1; +a%=N; A      while(m) at     { -         if(m&1) temp=multi (temp,a,n); -A=multi (a,a,n); -m>>=1; -     } -     returntemp; in}

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But the disadvantage is that the speed is slow, logn*logn

Fast power of power OR multiplication by exponentiation