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A sorted list of numbers contains 500 elements. Which of the following is closest to the maximum number of list elements that will be examined when performing a binary search for a value in the list?

Question

A sorted list of numbers contains 500 elements. Which of the following is closest to the maximum number of list elements that will be examined when performing a binary search for a value in the list?

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Solution

When performing a binary search, the maximum number of elements that will be examined can be calculated by taking the base-2 logarithm of the number of elements in the list, and rounding up to the nearest whole number. This is because a binary search works by repeatedly dividing the list in half until the desired value is found.

Here are the steps to calculate this:

  1. Take the base-2 logarithm of the number of elements in the list. In this case, log2(500) ≈ 8.97.

  2. Round up to the nearest whole number. In this case, 8.97 rounds up to 9.

So, the maximum number of elements that will be examined when performing a binary search for a value in a sorted list of 500 elements is approximately 9.

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