GATE 2007
October 14, 2023Database-Management-System
October 14, 2023GATE 2007
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Question 15
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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.
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⌈log2n⌉ + 1
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n
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⌈log2n⌉
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⌊log2n⌋ + 1
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Question 15 Explanation:
Let us consider n=6, then
1<=6 (✔️)
2<=6 (✔️)
4<=6 (✔️)
8<=6 (❌)
4 comparisons required
Option A:
[log n]+1
[log 6]+1
3+1 = 4 (✔)
Option B:
n=6 (❌)
Option C:
[log n]
[log 6]=3 (❌)
Option D:
[log2n]+1
[log26]+1 = 2+1 = 3 (❌)
1<=6 (✔️)
2<=6 (✔️)
4<=6 (✔️)
8<=6 (❌)
4 comparisons required
Option A:
[log n]+1
[log 6]+1
3+1 = 4 (✔)
Option B:
n=6 (❌)
Option C:
[log n]
[log 6]=3 (❌)
Option D:
[log2n]+1
[log26]+1 = 2+1 = 3 (❌)
Correct Answer: A
Question 15 Explanation:
Let us consider n=6, then
1<=6 (✔️)
2<=6 (✔️)
4<=6 (✔️)
8<=6 (❌)
4 comparisons required
Option A:
[log n]+1
[log 6]+1
3+1 = 4 (✔)
Option B:
n=6 (❌)
Option C:
[log n]
[log 6]=3 (❌)
Option D:
[log2n]+1
[log26]+1 = 2+1 = 3 (❌)
1<=6 (✔️)
2<=6 (✔️)
4<=6 (✔️)
8<=6 (❌)
4 comparisons required
Option A:
[log n]+1
[log 6]+1
3+1 = 4 (✔)
Option B:
n=6 (❌)
Option C:
[log n]
[log 6]=3 (❌)
Option D:
[log2n]+1
[log26]+1 = 2+1 = 3 (❌)
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