Computer Science : Comparing Run Times

Study concepts, example questions & explanations for Computer Science

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Example Questions

Example Question #1 : Comparing Run Times

for( int i = 0; i < n; ++i){

    for( int j = 1; j < n; j *= 2){

        someFunction();

    }

}

 

For the code above, what is the run time in Big O notation?

Possible Answers:

None of the above

O(n log(n) )

O( n )

O( log(n) )

O(  )

Correct answer:

O(n log(n) )

Explanation:

At first glance we might be tempted to pick O(  ) because there are 2 for loops. But, upon closer inspection we can see that the first loop will yield a O( n ) running time but the second loop does not. The second loop has only an O( log(n) ) running time because "j" doubles each iteration and does not increase linearly. That will yield O( log(n) ) since O( log(n) ) is a much faster running time. So the final result is O( n log(n) ).

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