How to Efficiently Calculate (a^b)%MOD in C When b Is Extremely Large?

How to Calculate (a^b)%MOD in C When b Is Extremely Large

In C , when tasked with calculating (a^b)%MOD and the value of b is excessively large, the standard long long data type may prove insufficient. This poses a challenge as the conventional log(b) time complexity method relies on the precise determination of b.

However, an alternative approach utilizes Euler's totient function and Euler's theorem. This method hinges on the principle that a^b can be reduced to a^(b % phi(MOD)). By leveraging integer factorization techniques, the computation becomes far more manageable.

Notably, the Carmichael function plays a crucial role in this calculation. It allows for the accurate determination of results for any combination of a, b, and MOD.

The above is the detailed content of How to Efficiently Calculate (a^b)%MOD in C When b Is Extremely Large?. For more information, please follow other related articles on the PHP Chinese website!