Question

Subject: Algorithm

1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use the master theorem to solve the recurrence T(n)-3T(n/4) + n2. Show your work. 4. Use the substitution method to prove that the recurrence T(n) = T(n/2)+ n has solution T(n) = 0(n). Show all work. 5. Suppose I devised a searching algorithm on an array that I claim runs in e(log log n) time. I think that this algorithm is amazing and if I publish it, I'll gain acclaim in the computer science community. Should. I publish it? Why or why not?

solve only part 4 and 5 please.
need urgent.

Answer 1

Using repetitive substitution, we formed an equation. That equation contains a Geometric progression. We used sum of Geometric Progression to solve that. and formed a big O expression for T(n)

k-1 2k-2 2 k 2 2 k-2

2-1 2 k-i Since フ Substitte in Logn 1 2 e cenitant ) '.

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