Compute the nth Fibonacci Number (Practice Interview Question)

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Write a method Fib that takes an integer n and returns the nth Fibonacci number.

Let's say our Fibonacci series is 0-indexed and starts with 0. So:

Fib(0); // => 0 Fib(1); // => 1 Fib(2); // => 1 Fib(3); // => 2 Fib(4); // => 3 ...

Our solution runs in n time.

There's a clever, more mathy solution that runs in time, but we'll leave that one as a bonus.

If you wrote a recursive method, think carefully about what it does. It might do repeat work, like computing Fib(2) multiple times!

We can do this in space. If you wrote a recursive method, there might be a hidden space cost in the call stack!

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It's easy and quick. No "reset password" flow. No password to forget.
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Actually, we don't support password-based login. Never have. Just the OAuth methods above. Why?

It's easy and quick. No "reset password" flow. No password to forget.
It lets us avoid storing passwords that hackers could access and use to try to log into our users' email or bank accounts.
It makes it harder for one person to share a paid Interview Cake account with multiple people.

time and space.

If you're good with matrix multiplication you can bring the time cost down even further, to . Can you figure out how?

Actually, we don't support password-based login. Never have. Just the OAuth methods above. Why?

It's easy and quick. No "reset password" flow. No password to forget.
It lets us avoid storing passwords that hackers could access and use to try to log into our users' email or bank accounts.
It makes it harder for one person to share a paid Interview Cake account with multiple people.