some interview question

Martingale · Post by **Martingale** » Tue Sep 28, 2004 8:02 pm

Consider the following C program for producing Fibonacci numbers

Int Fibonacci(int n)

{ if (n <=011 n==1) return 1;

else return Fibonacci(n-1)+Fibonacci(n-2);}

If for some large n, it takes 100 seconds to compute Fibonacci(n), how long will it take to compute Fibonacci(n+1), to the nearest second?

Energetic · Post by **Energetic** » Tue Sep 28, 2004 9:08 pm

162 seconds.

Martingale · Post by **Martingale** » Tue Sep 28, 2004 9:51 pm

Kinda of (1+sqrt(5))/2 * 100 , right?

Martingale · Post by **Martingale** » Tue Sep 28, 2004 10:06 pm

what about this one? Suppose that 2 cylinders each with radius 1 intersect at right angles and their centers also intersect. What is the volume of the intersection ?

Energetic · Post by **Energetic** » Tue Sep 28, 2004 10:22 pm

a. You got it.

b. I certainly was able to solve this stuff in high school but now I'm afraid to get a headache in the process. Run a MC simulation Smiley

drews · Post by **drews** » Tue Sep 28, 2004 10:47 pm

Intersecting cyllinders problem can be solved by a very simple integration, google for 'Steinmetz solid'. Crossections of that object by 3 perpendicular planes are: 2 circles and a square

Martingale · Post by **Martingale** » Wed Sep 29, 2004 6:11 pm

Here is another one, consider X_t = m*t+ B_t where B is a standard Brownian motion, what's the probability of X_t hit 3 before it hit -5? I know a very nice way of this for m=0, but for m<>0, is there a elegant answer?

chiral3 · Post by **chiral3** » Wed Sep 29, 2004 6:21 pm

Martingale, that one was all you, considering your background. Is the elegant way doob?

Martingale · Post by **Martingale** » Wed Sep 29, 2004 6:27 pm

Yes, Doob' way, for m=0 you have a neat answer, but what about for m<>0?

Energetic · Post by **Energetic** » Wed Sep 29, 2004 7:28 pm

Now, for the rest of us, doob it out, pls.