Log out Go to App
Go to App

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Complete the following table calculating the average and maximum number of comparisons the linear search will perform, and the maximum number of comparisons the binary search will perform. $$\begin{array}{l|lllll} \hline & 50 & 500 & 10,000 & 100,000 & 10,000,000 \\ \text { Array Size } \rightarrow & \text { Elements } & \text { Elements } & \text { Elements } & \text { Elements } & \text { Elements } \\ \hline \begin{array}{l} \text { Linear Search } \\ \text { (Average } \\ \text { Comparisons) } \end{array} & & & & \\ \hline \begin{array}{l} \text { Linear Search } \\ \text { (Maximum } \\ \text { Comparisons) } \end{array} & & & & & \\ \hline \begin{array}{l} \text { Binary Search } \\ \text { (Maximum } \\ \text { Comparisons) } \end{array} & & & & & \\ \hline \end{array}$$

Why is the linear search also called “sequential search”?

T F The average number of comparisons performed by the linear search on an array of N elements is N/2 (assuming the search values are consistently found).

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 selection sort more efficient than the bubble sort on large arrays?
See all solutions

Recommended explanations on Computer Science Textbooks

Computer Organisation and Architecture

Read Explanation

Issues in Computer Science

Read Explanation

Data Representation in Computer Science

Read Explanation

Databases

Read Explanation

Algorithms in Computer Science

Read Explanation

Problem Solving Techniques

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free