GATE | GATE-CS-2007 | Question 85

Consider the following segment of C-code:

  int j, n;
  j = 1;
  while (j <= n)
        j = j*2; 

The number of comparisons made in the execution of the loop for any n > 0 is:

Base of Log is 2 in all options.
(A) CEIL(logn) + 2
(B) n
(C) CEIL(logn)
(D) FLOOR(logn) + 2


Answer: (D)

Explanation:



We can see it by taking few examples like n = 1, n = 3, etc.

For example, for n=5 we have the following (4) comparisons:
------------------------
1 <= 5 (T)
2 <= 5 (T)
4 <= 5 (T)
8 <= 5 (F)

------------------------
FLOOR(log_2 n)+2 = FLOOR(log_2 5) + 2 = FLOOR(2.3) + 2 = 2 + 2 = 4


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