Computer Science Homework Solutions
#26182
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.
What is this?
By OTA - Overall OTA Rating
Yongjun Luo, PhD (IP) - 4.8/5
Purchase Cost Now
$2.19 CAD (was ~$11.97)
Included in Download
- Plain text response
- Attached file(s):
- Proof.doc
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- 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 = ...
- Big O Problem - Proof - Show that F(n) + g(n) is O(max(f(n),g(n))). Any detail is appreciated.
- Obtain asymptotically tight bounds on lg(n!) without using Stirling's approximation. - Obtain asymptotically tight bounds (Big-Oh and Big-Omega) on lg(n!) without using Stirling's approximation. Instead, evaluate these using the expansion of lg(n!) as a summation.
- Big O Problem - The following is a big-oh relationship: n^10 is O(3^n) Please give witnesses n0 and c that can be used to prove the relationship. Choose your witnesses to be minimal, in the sense that n0-1 and ...
- Prove that the big-O relationship is transitive - Prove that the big-O relationship is transitive (give a direct proof). That is, if f(n), g(n) and h(n) are positive-valued functions: if f(n) is Ο(g(n)) and g(n) is Ο(h(n)) then f (n) is ...
