Question

Compute the time complexity for each of the following two program fragments with respect to N. Show your steps in reaching your answer.

1)             for(i=1; i < N; i = i*2) {

      for(j=0;j

            // Operations with constant time…

      } }

2)              for(i = 0; i < sqrt(N); i++){

      for(j=1; j < i+8; j++){

           for(k=0;k

                  // Operations with constant time…

           } } }

Answer 1

1)

it will be nlogn.

for the first loop it is multiplication by i and second loop in j is dependent on i and will run for n times as well so it will be nlogn.

2)

it should be roughly n² as the second first and second loop are dependent and will run together for roughly n times and the k for will run for n more times so n²