What is the maximum number of comparisons necessary when performing a binary search of100,000 items?a) 13b) 14c) 15d) 16# e) 17
Question
What is the maximum number of comparisons necessary when performing a binary search of 100,000 items?
a) 13
b) 14
c) 15
d) 16
e) 17
Solution
The maximum number of comparisons necessary when performing a binary search can be calculated using the formula log2(n), where n is the number of items.
Step 1: Calculate log2(100,000) Step 2: If the result is not a whole number, round it up to the nearest whole number. This is because you can't make a fraction of a comparison - you always have to make a whole number of comparisons.
Using a calculator, log2(100,000) is approximately 16.61.
Step 3: Round up 16.61 to the nearest whole number, which is 17.
So, the maximum number of comparisons necessary when performing a binary search of 100,000 items is 17. Therefore, the answer is e) 17.
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