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Chapter 8: Problem 5

What is the maximum number of comparisons that a binary search function will make when searching for a value in a 1,000-element array?

Short Answer

Expert verified
Answer: The maximum number of comparisons is 10.

Step by step solution

01

Understand binary search algorithm

A binary search algorithm is an efficient method for searching for a specific value in a sorted list (array) by repeatedly halving the search interval. It starts by comparing the middle element of the sorted array with the target value. If it finds the target value, the search is successful. If the target value is smaller than the middle element, the search continues in the lower half of the array. Similarly, if the target value is greater than the middle element, the search proceeds in the upper half of the array. The process keeps repeating until the target value is found, or until the interval has been reduced to zero, meaning the target value is not in the array.
02

Calculate the number of binary search iterations

The number of iterations (or comparisons) required by a binary search algorithm to find a specific value is determined by the number of times the array needs to be halved until 1 element remains. More formally, if the array has N elements, the maximum number of comparisons required for the binary search is ceil(log_2(N)).
03

Apply the formula to the given array size

In this exercise, we are given an array of 1,000 elements. To find the maximum number of comparisons, we apply the formula mentioned above: ceil(log_2(1000)).
04

Calculate the maximum number of comparisons

To calculate the ceiling of log_2(1000), we can use a calculator or a software tool that supports logarithm calculations. Upon calculation, we find that ceil(log_2(1000)) = 10. Therefore, the maximum number of comparisons that a binary search function will make when searching for a value in a 1,000-element array is 10.

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Most popular questions from this chapter

The _________ search algorithm repeatedly divides the portion of an array being searched in half.

The _________ search algorithm requires that the array’s contents be sorted.

In an average case involving an array of N elements, how many times will a linear search function have to read the array to locate a specific value?

Why is the bubble sort inefficient for large arrays?

Why is the selection sort more efficient than the bubble sort on large arrays?
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