Question

Please show the work. I already know the answers, but don't understand how to get there.

5. Q5. Algorithm Efficiency I. Algorithm A performs (n) binary searches in an array of size n/2. Algorithm B performs e(n) sequential searches in an array of size 4n. Answer the following questions. (a) 1) What is the worst case running time of Algorithm A, in terms of e? (b) [1] What is the worst case running time of Algorithm B, in terms of e? (c) [1] Which algorithm runs faster in the worst case) when n becomes very large?

Answer 1

a) worst case time of algo A =

e(n) binary searches

single binary search operation on a list of n/2 elements take =

elogn) time

Total time taken by algo A =

elogn) * (n) = (nlogn)

b) worst case time of algo B =

(Vn – sequenntial searches

single sequential search operation on a list of 4n elements take =

on) time

Total time taken by algo B =

) Ꮎ = ( u )Ꮎ * ( u* }Ꮎ

c) Asymptotically ​​​​​​​

O(n1.5) > (nlogn)

Hence, algorithm A is more efficient