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; } |
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(A)
(B)
(C)
(D)
(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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