GATE | GATE CS 2013 | Question 31

Consider the following function:

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 the value of k after running the inner loop one time is n*logn.
Therefore total time complexity is inner multiplied with outer loop complexity which (n for outer and nlogn for inner) n^2logn.

See http://geeksquiz.com/algorithms-analysis-of-algorithms-question-5/

This solution is contributed by Parul Sharma.

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