Integer power quick modulo

The calculation method must be simplified because the exponential result of an integer is large and may be far beyond the scope of computer processing.

Modulo properties: (A * B) mod m = (a mod m) * (B mod m) mod m,

 

The principle of quick search for integer power is as follows:

For example, to evaluate m ^ N, just expand N in binary format: for example, n = A0 * 2 ^ 0 + A1 * 2 ^ 1 + ..... + AK * 2 ^ K;

 

The quick power method is as follows:

 

Long long fastpow (int m, int N) <br/>{< br/> long res = 1; <br/> for (; n> 1) <br/> {<br/> If (N & 1) <br/> res * = m; <br/> M * = m; <br/>}</P> <p> return res; </P> <p>}

 

The method for quickly modulo integer power is similar to the above:

CodeAs follows:

 

 

Long long powermod (long a, int B, int K) <br/> {// (a ^ B) % K <br/> long TMP =, ret = 1; <br/> for (; B; B> 1) <br/>{< br/> If (B & 1) <br/> ret = (Ret * TMP) % K; // perform the modulo operation in each step. <br/> TMP = (TMP * TMP) % K; <br/>}< br/> return ret; <br/>}< br/>