Quoteit is somewhat hard to understand the equation because it looks like you are typing in latex but with syntax error. but thank you v much. Good point. I'll try the real latex editor next time.

<t>Assuming phi(u) is deterministic (otherwise the process is not gaussian), if you write the integral as the limit of \sum_i phi(u_{t_i}) * (W_{t_i} - W_{{t_i-1}})over finer partitions of the form 0=t0<t1<...<tn=T, then you see the process is a gaussian (because of independent increments), its expe...

<t>lega85, both cycles approaches use the same number of swaps; every element always get swapped to the right position, so the number of swaps is less or equal than n*m-2. When no extra memory is used you certainly need to follow the cycles (without any swaps) so it would at most be of the order O(n...

Good eye! I ran several timing tests, but pasted only a few in here. Below are some more results with different gcd(n,m) values.

<t>lega85, that's an interesting idea, but it'll be less efficient than the other method where we do a dry-run to determine if the element was already swapped or not. The problem here is that on each iteration you need to reorder a lot of data in the array. Notably, your method works quite well if t...

<t>I thought about doing such a dry-run on the cycle to determine whether position i was already swapped or not, but at the the time it seemed quite inefficient.On the other hand, maybe the interviewer wanted exactly that kind of answer. I assumed the question was on optimizing the memory usage with...

<t>I recently got asked this question during a phone interview:Suppose you have a n x m matrix stored in an one dimensional array in column-major order, that is, element (i,j) in the matrix is at position i+j*n in the one dimensional array. Write an algorithm that transposes the matrix in-place.Acco...

I'm also interested in this subject. Any relevant literature?

<t>Hi,What is the real probability of getting a real quant job after spending a few years in one of those quantitative analyst positions that consist of lots of SQL, Matlab and Excel?My situation is the following:I am currently considering a couple offers of comparable salary. One of the positions i...

<t>For the expected number of rolls:The probability of not winning up to roll N is C(n-1, N) / n^N where C(a,b) denotes "a choose b". The reason for this value is that X(1), ..., X(N) must form an increasing sequence and none of them can be 1, otherwise the game would end. Letting L(N) = Probability...

<t>The integral is zero when the limits are (2k+1)*(pi/2) to infinity, where k is an integer:Rewrite f(x),f(x) = (sin x + cos x) / (e^x + cos x) = (sin x - e^x + e^x + cos x) / (e^x + cos x) = 1 - (e^x - sin x)/(e^x + cos x)Then it's straightforward that the derivative of e^x + cos x is e^x - sin x,...

14/3 = 4.66666....

<t>In order to get the 9% discount you must spend $150 in the previous month (month 0). Since you only use $100 monthly, no matter how you refill during the previous month, you will have at least $50 worth of gas left in the tank. Thus, during the current month (month 1), when you have a 9% discount...

The expression you wrote in the case when n = 2k+1 is a degree 2k+3 polynomial. I guess you probably meant to writewhich is the characteristic polynomial corresponding to the solutions on the other thread.