Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

GATE | GATE CS 2013 | Question 31

  • Difficulty Level : Medium
  • Last Updated : 31 May, 2021

Consider the following function:

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.




int unknown(int n) {
    int i, j, k = 0;
    for (i  = n/2; i <= n; i++)
        for (j = 2; j <= n; j = j * 2)
            k = k + n/2;
    return k;
 }
(A)

\Theta(n^2)

(B)

\Theta(n^2Logn)



(C)

\Theta(n^3)

(D)

\Theta(n^3Logn)

(A) A
(B) B
(C) C
(D) D


Answer: (B)

Explanation: Here we have to tell the value of k returned not the time complexity. 
 

for (i  = n/2; i <= n; i++)
        for (j = 2; j <= n; j = j * 2)
            k = k + n/2;
    return k;

The outer loop runs n/2 times 
The inner loop runs logn times.(2^k = n => k = logn). 
Now looking at the value of k in inner loop, n is added to k, logn times as the inner loop is running logn times. 
Therefore total time complexity is inner multiplied with outer loop complexity which (n for outer and nlogn for inner) n*logn. 

Therefore the value of k after running the inner loop one time is  n^2logn.
See http://geeksquiz.com/algorithms-analysis-of-algorithms-question-5/
This solution is contributed by Parul Sharma.


Quiz of this Question

My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!