Question

2.5. Solve the following recurrence relations and give a Θ bound for each of them.

(e) T(n) 8T(n/2) n (f) T(n) = 49T(n/25) + n3/2 log n (g) T(n) = T(n-1) + 2 (h) T(n) T(n 1)ne, where c 21 is a constant (i) T(n) = T(n-1) + c", where c > 1 is some constant (j) T(n) = 2T(n-1) + 1 (k) T(n) T(vn) +1

Answer 1

SOLUTION:

THIS solution includes all the part of question as well as full explanation,and upper bounds for each recurrence relation .

Explanation:

since master method is very easiest way to solve some kind of recurrence which is of type given below:

T(n)=aT(n/b)+n^k log^p n   ......(1)

and just we have to compare by this

equation and accordingly value of a ,b,p,k we will apply particular formula .

that is given while solving the question in solution page below .

and other we have to use substitution method .

In which we replace n by by n-1 , and n-1 by n-2 , and so on ...

after that from equation (1) we get some pattern .

on the basis of that we move forward.

PART E:

Master method is used:

2. Hthi line recumene to Sorve, at the ne curr n cr ㅨ db the boom hener So, a 2. 8lrs

PART F:

master method is used in part B:

To Sopve it masts thearn as e on Gmpoing both ean 2. P- 251.. 125 So, a

PART G:

substitution method is used :

use ler セ Sole TD) a t be Lem n-k더 c,(n Har,

PART H:

substitution method is used:

Replace ne co ith② り-3 プク C. Er bna Ki ツーバ

pART I:

substitution method is used:

Now, ทุ-2- 2 n-k Fro basc can 2-Ki nt/

PART J:

substitution method is used:

From O, ayl or barr car う 2

PART K:

substitution method is used:

Fos base case 2.

your satisfaction is first priority for any expert .

THAT'S why full explanation is provided.apart from this if any problem in understanding the solution feel free to ask in comment section.