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https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_e... If ever there was a way t

by hacknat 12y ago

https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_e... If ever there was a way to impress an interviewer it is to bust out this baby when asked to make a fibonacci function.

mytochar 12y ago
Personally, I think the matrix powers method is more impressive. You're using the matrix as a state engine to get to whatever state you intend to reach. That has more applications than just the closed form, which a lot of people know about, and you most likely just happened to memorize. Don't get me wrong, it'd still be impressive "Woah, he memorized this!" but seeing someone do the matrix trick would be even more impressive, to me.
- hacknat 12y ago
  fair enough.
- fdej 12y ago
  The closed form is just the diagonalized version of the matrix power, though.
  - mytochar 12y ago
    I honestly didn't know that until it was mentioned in another part of this thread. My point was that someone can memorize the formula. Chances are, they'll see the matrix form and actually know how to use that in other situations. Now, if you derived the formula on the board from the matrix, that'd be incredibly impressive. The idea here is how the person's brain thinks. When I see them write an equation on the board, I think "Oh, they memorized it" when I see them step through the process of creating a matrix and doing matrix multiplication, I think "Wow, they /really/ know their stuff". If they just threw up the matrix and couldn't explain it, I wouldn't be as impressed. Same as if they wrote the equation and couldn't explain it. At the end of the day, if they could explain either approach, I'd be impressed, I think the matrix form just lends itself to more likely be in a way that the person can explain it
dagw 12y ago
It would be impressive if you could derive or prove it, not if you'd just memorized it.
- hacknat 12y ago
  not even a little bit impressed?
Fede_V 12y ago
The closed form solution is not that difficult to derive at all if you put the problem as a reoccurrence equation with boundary conditions.
- mmaldacker 12y ago
  or just calculate the eigenvalues & eigenvectors of Q.

by hacknat 12y ago

mytochar 12y ago

Personally, I think the matrix powers method is more impressive. You're using the matrix as a state engine to get to whatever state you intend to reach. That has more applications than just the closed form, which a lot of people know about, and you most likely just happened to memorize. Don't get me wrong, it'd still be impressive "Woah, he memorized this!" but seeing someone do the matrix trick would be even more impressive, to me.

hacknat 12y ago
fair enough.
fdej 12y ago
The closed form is just the diagonalized version of the matrix power, though.
- mytochar 12y ago
  I honestly didn't know that until it was mentioned in another part of this thread. My point was that someone can memorize the formula. Chances are, they'll see the matrix form and actually know how to use that in other situations. Now, if you derived the formula on the board from the matrix, that'd be incredibly impressive. The idea here is how the person's brain thinks. When I see them write an equation on the board, I think "Oh, they memorized it" when I see them step through the process of creating a matrix and doing matrix multiplication, I think "Wow, they /really/ know their stuff". If they just threw up the matrix and couldn't explain it, I wouldn't be as impressed. Same as if they wrote the equation and couldn't explain it. At the end of the day, if they could explain either approach, I'd be impressed, I think the matrix form just lends itself to more likely be in a way that the person can explain it

dagw 12y ago

It would be impressive if you could derive or prove it, not if you'd just memorized it.

hacknat 12y ago
not even a little bit impressed?

Fede_V 12y ago

The closed form solution is not that difficult to derive at all if you put the problem as a reoccurrence equation with boundary conditions.

mmaldacker 12y ago
or just calculate the eigenvalues & eigenvectors of Q.