as the title said,How to speed up some integer operations?

For example: fast integer multiplication, fast integer division (round down), and fast modulus.

These things can sometimes be related to whether a question is passed or not.

So I asked you how you can speed up integer arithmetic.

as the title said,I had a problem solving some questions about hashing:

If you write a hash with high accuracy, you will exceed the time limit, but if you write a hash with low accuracy, you do not know whether it will be hacked by the data.

What should I do then?

As you can see, most of my games have a "natural" problem with data structures that I can't even think about, and instead I keep thinking about how to further reduce the amount of information stored, which causes me to fail most of the problems that I would otherwise solve.

How to solve this problem? I hope you can give us some answers. If your answer is helpful to me, then I really appreciate it. This question has troubled me for a long time.