Question

Let T(n) represent the total execution time of a loop for which the loop test is true n times (i.e., the loop body will execute n times). For each possible value of T(n) listed below, give a tight upper bound for the time cost (in terms of O(…)) of one execution of the loop body (denote this by L(n)) that makes the statement true. Answer each part separately. Each answer should be of the form L(n) = O(…)

a. T(n) = O(n2 )

b. T(n) = O(n)

c. T(n) = O (n lg n)

Answer 1

Since the loop will be true n times

So, the net complexity will become n times too

So,

A)

L(n)=O(n^3)

B)

L(n)=O(n^2)

C)

L(n)=O(n^2*log(n))