Ok, this is more of a follow-up question: http://stackoverflow.com/questions/874982/how-to-compute-optimal-paths-for-traveling-salesman-bitonic-tour First of all, for the bitonic tour of the traveling salesman problem I have the following recurrence relation: (a) When i = 1 and j = 2, l(i; j) = dist(pi; pj ) (b) When i < j - 1; l(i; j)...
Consider this example : T(n) = T(7n/8) + 2n I assumed T(1) = 0 and tried to solve it in the following way T(n) = T(7n/8) + 2n = T(49n/64) + 2.(7n/8) + 2n = T(343n/512) + 2.(7n/8).(7n/8)+ 2.(7n/8) + 2n = T(1) + 2n ( (7n/8)^i + ..... + 1) but I could not come to any conclusion about this. I am confu...
I need to derive the Big-O complexity of this expression: c^n + n*(log(n))^2 + (10*n)^c where c is a constant and n is a variable. I'm pretty sure I understand how to derive the Big-O complexity of each term individually, I just don't know how the Big-O complexity changes when the terms are combined like this. Ideas? Any help wo...
I am currently enrolled in a programming class and we are covering recurrence relations. I was just wondering if, ever these actually get used on the job. If so, I'd love to hear some examples of when it is useful. ...
I have a sequence. a1 = 1 - cos(x); ai = a1 + (-1)^(i-1) * x^(2*i-2) / (2*i-2)! I need to write this with and without recursion. But it has a different results. Here is my code: http://codepaste.net/q213q6 ...
Hello, I'm solving some recurrence relation problems for Big O and so far up till this point have only encountered recurrence relations that involved this form: T(n) = a*T(n/b) + f(n) For the above, it's quite easy for me to find the Big O notation. But I was recently thrown a curve ball with the following equation: T(n) = T(n-1) + ...
Hello, I'm trying to find Big O of this recurrence relation: T(n) = T(n-1) + n^c // where c is >=1 So I decided to solve this by using a recursion tree, which I have broken down as follows: n^c -> (n-1)^c -> (n-2)^c -> ... -> (n-i)^c I then formed the following sum: from 0 to n-1: (n-i)^c Reducing this sum gives: (n-(n-1))^c...
How to solve the recurrence relation: T(n) = T(n - 1) + T(n / 2)+ n by recursion tree to get an asymptotic upper bound? The height is n, but how to generalize the sum at each levels? ...
T(n) = 2T(n/2) + 0(1) T(n) = T(sqrt(n)) + 0(1) first one I use substitution method for n, logn, etc, all gave me wrong answers. Recurrence trees: I dont know if I can apply as the root will be a constant Can some one help? T ...