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Yes, the complexity of a binary search is O(log2 (N)).
As an example, if you have 127 elements you want to search
through, you can guarantee a decision one way or another in
7 or less steps...

what is this int(expr) function?
did you mean to type (int) expr ?

Define "fastest."

If you mean shortest execution time, I think you'll find that for
most programs you write, if you compile it to machine code it's
going to run comparably under most languages. ...

I'm not quite sure what you're asking by your example.
First off, are you using interrupts? That's a good way to do it when they're
bursty. You read the Rx register as long as there are bytes to...

Well, not knowing the device you're using in particular, I'll just
point out one fact about most UARTS: the TxD line is tied to a
shift register that's loaded when the next byte is to be...

a) A struct sockaddr contains more than just an IP address.
It contains information about the destination address (which might
not even be an IP address!), the port, and some other things.

Note...