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 1024 using binary search?

Options:

Correct Answer: 11

Solution:

The maximum number of comparisons is log2(1024) = 10, but since we start counting from 0, it takes 11 comparisons in the worst case.

What is the maximum number of comparisons needed to find an element in an array of size 1024 using binary search?

What is the maximum number of comparisons needed to find an element in an array of size 1024 using binary search?

Step 1: Understand that binary search is a method to find an element in a sorted array by repeatedly dividing the search interval in half.
Step 2: Know that the size of the array is 1024.
Step 3: Calculate log2(1024) to find out how many times we can divide the array in half until we reach one element.
Step 4: Since 1024 is 2 raised to the power of 10 (2^10 = 1024), log2(1024) equals 10.
Step 5: Remember that we start counting comparisons from 0, so the maximum number of comparisons needed is 10 plus 1 for the final check, which equals 11.
Step 6: Conclude that in the worst case, it takes 11 comparisons to find an element in an array of size 1024 using binary search.

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