If a binary search is performed on an array of size 16, how many comparisons wil

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Question: If a binary search is performed on an array of size 16, how many comparisons will it take in the worst case?

Options:

Correct Answer: 5

Solution:

In the worst case, binary search will take log2(16) = 4 comparisons, but since we start counting from 0, it will take 5 comparisons.

If a binary search is performed on an array of size 16, how many comparisons will it take in the worst case?

If a binary search is performed on an array of size 16, how many comparisons will it take in the worst case?

Step 1: Understand that binary search works on a sorted array by repeatedly dividing the search interval in half.
Step 2: Know that the size of the array is 16.
Step 3: Calculate the logarithm base 2 of the size of the array: log2(16).
Step 4: Since 16 is 2 raised to the power of 4 (2^4 = 16), log2(16) equals 4.
Step 5: In binary search, we start counting comparisons from 0, so the total number of comparisons in the worst case is log2(16) + 1, which is 4 + 1 = 5.

Binary Search – A search algorithm that finds the position of a target value within a sorted array by repeatedly dividing the search interval in half.
Logarithmic Complexity – The time complexity of binary search is O(log n), which indicates that the number of comparisons grows logarithmically with the size of the array.
Zero-based Indexing – In programming, arrays often use zero-based indexing, which can affect how comparisons are counted.