I need help to solving all the questions
Homework #2 #1 Suppose we know that an algorithm has n classes of complexity for a problem of size n. We have T1(n) = 2, T2(n) = 4, T3(n) = 6 , …, and Tn(n) = 2n. We also know that the probability of each class is the same. Find the average complexity of the algorithm. Homework #2 #2 Suppose we know that an algorithm has 5 classes of complexity for a problem of size n. The complexities T1(n) .. T5(n) are given below. Regarding probabilities, suppose that p1 is twice as likely as p2, p2 is twice as likely as p3, , p3 is twice as likely as p4 and p4 is twice as likely as p5. Ti for all instances: T1(n) = n, T2(n) = 2n, T3(n) =3n4, T4(n) = 4n and T5(n) = 5n (a) Find all five probabilities p1, p2, p3, p4 , p5. [Hint: the sum of all probabilities equal 1.0] (b) Find the A(n) for the algorithm. Homework #2 #3 Suppose we find complexities of two algorithms as follows. Let p be a probability function, i.e. 0.0 ≤ p ≤ 1.0 A1(n) = 4n2p + (n+1)(1-p) A2(n) = n2(1-p) + 8np (a) Determine the range of values for p when A1 executes fewer characteristic operations on average than A2? [Hint, set the inequality, isolate p, and analyze your result] (b) Determine the range of values for p when A1 executes fewer characteristic operations on average than A2 given that n = 100. (c) Determine the range of values for p when A1 executes fewer characteristic operations on average than A2 given that n is a very large number. Homework #2 #4 Find the closed form for the recurrence using the method of characteristic roots. an = 4an-1 – 3an-2 a0 = 2 a1 = 3
Collepals.com Plagiarism Free Papers
Are you looking for custom essay writing service or even dissertation writing services? Just request for our write my paper service, and we'll match you with the best essay writer in your subject! With an exceptional team of professional academic experts in a wide range of subjects, we can guarantee you an unrivaled quality of custom-written papers.
Get ZERO PLAGIARISM, HUMAN WRITTEN ESSAYS
Why Hire Collepals.com writers to do your paper?
Quality- We are experienced and have access to ample research materials.
We write plagiarism Free Content
Confidential- We never share or sell your personal information to third parties.
Support-Chat with us today! We are always waiting to answer all your questions.
