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

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

Options:

Correct Answer: 7

Solution:

The maximum number of comparisons needed is log2(16) = 4, but since we start counting from 0, it takes 5 comparisons.

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

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

Step 1: Understand that a binary search works by repeatedly dividing the array in half.
Step 2: Know that the size of the array is 16.
Step 3: Calculate log2(16). This means we want to find out how many times we can divide 16 by 2 until we get to 1.
Step 4: Since 16 is 2 raised to the power of 4 (because 2^4 = 16), we find that log2(16) = 4.
Step 5: Remember that in binary search, we start counting comparisons from 0. So, if it takes 4 divisions to reach 1, we actually make 5 comparisons (0, 1, 2, 3, and 4).
Step 6: Conclude that in the worst case, 5 comparisons are needed for a binary search on an array of size 16.

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.
Counting Comparisons – Understanding how to count the number of comparisons made during the search process, including the starting point of the count.