Big O Problem

Show that if: T(1) = a T(n) = T(n-1) + n^k, for n > 1 then T(n) is O(n^(k+1)). You may assume k>=0. Also, show that this is the tightest simple big-oh upper bound, that is, that T(n) is not O(n^m) if m < k+1. Hint: Expand T(n) in terms of T(n-i), for i = 1,2,..., to get the upper bound. For the lower bound, show that T(n) is at least cn^(k+1) for some particular c >0.

Big O Problem

Consider the recurrence T(1)=a T(n)=cT(n/d)+bn^k, for n a power of d Iteratively expand T(n) in terms of T(n/d^i) for i=1,2,.... Show that a) if c > d^k, then T(n) is O(n^logd c) b) if c = d^k, then T(n) is O(n^k log n) c) if c < d^k, then T(n) is O(n^k)

convert structure to matlab m-file

Convert the following structure plan into a function m-file with two inputs (M and N): Get M and N values if M does not equal round(M) Give error message that inputs must be integers end if if N does not equal round(N) Give error message that inputs must be integers end if while remainder of M divided by N is not zero Set R to the remainder of M divided by N Set M to be N Set N to be R end while Return final value of N as output

Objects and classes

Design an inventory Class that can hold information and calculate data for items in a hardware store's inventory. The Class should have the following private member attributes: (See attachment for full question)

Pleaes provide the following information

Describe a situation or program that would use a decision structure and a loop.