java - time complexity for most programming language? -

java - time complexity for most programming language? -

i read time complexity modular arithmetic in many books . there thing don't understood . read in books following

for mod n, has multiplicative inverse modulo n if , if relatively prime n. when inverse exists, can found in time o(n^3) (where usual n denotes number of bits of n) running extended euclid algorithm. question revolves around *extended euclid algorithm* *is has o(n^3)*

when write in java integrated netbeans or c# or c++ programme line

a = b.modinverse(n) //here java syntax

in general. can line has time complexity o(n^3).

or necessary write same steps extended euclid algorithm.

unless documentation of modinverse method makes explicit guarantee time complexity, can't create assumptions running time. implementation different depending on runtime/library or version of runtime.

if have access source code, can verify algorithm used. can run own benchmarks different input sizes , you'll pretty image asymptotic behavior of concrete implementation.

that said, it's highly probable popular libraries arbitrary-precision arithmetic utilize best known algorithms basic operations modinverse.

java performance complexity-theory