What is the maximum number of comparisons needed to find an element in an array

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Question: What is the maximum number of comparisons needed to find an element in an array of size 16 using binary search?

Options:

Correct Answer: 5

Solution:

The maximum number of comparisons is log2(16) = 4, but since we count the initial comparison, it is 5.

What is the maximum number of comparisons needed to find an element in an array of size 16 using binary search?

What is the maximum number of comparisons needed to find an element in an array of size 16 using binary search?

Step 1: Understand that binary search works on a sorted array.
Step 2: Know that the size of the array is 16.
Step 3: Calculate log2(16). This means you find how many times you can divide 16 by 2 until you reach 1.
Step 4: Since 16 = 2^4, log2(16) = 4. This means it takes 4 divisions to find the element if it is present.
Step 5: Remember to count the initial comparison you make before starting the divisions. So, you add 1 to the 4 comparisons.
Step 6: Therefore, the total maximum number of comparisons needed is 4 + 1 = 5.

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