Algorithms Lesson 5: Binary Search

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Questions and Answers

What is the maximum number of comparisons required to find an item in 1000 items using binary search?

8 comparisons

14 comparisons

12 comparisons

10 comparisons (correct)

Which of the following is NOT a characteristic of binary search?

Can handle unordered lists (correct)

Requires data to be sorted

Is an efficient search algorithm

Eliminates data by halves with each comparison

Why are items in phone books and dictionaries sorted?

To follow alphabetical rules strictly

To reduce the number of total items

To help with memorization of entries

To allow for quicker access to information (correct)

Which statement is true regarding linear search compared to binary search?

Linear search examines every item sequentially Signup and view all the answers

What task must be performed before conducting a binary search on a set of cards?

Sort the cards from lowest to highest Signup and view all the answers

What is the first step in the binary search algorithm?

Set the range to be the entire list. Signup and view all the answers

If the midpoint item is less than the search item, what should you do next?

Change the range to focus on the items after the midpoint. Signup and view all the answers

What happens if the midpoint item equals the search item?

Stop searching. Signup and view all the answers

During a binary search, when should you stop checking items?

When the range is empty. Signup and view all the answers

What is the purpose of finding the midpoint in a binary search?

To eliminate half of the remaining items from consideration. Signup and view all the answers

Which of the following statements describes the change in range when the midpoint item is greater than the search item?

The range eliminates all items after the midpoint. Signup and view all the answers

How is the initial range for the binary search determined?

It is the entire ordered list of items. Signup and view all the answers

Which of the following best describes the term 'midpoint' in the context of binary search?

The number located exactly in the middle of the current range. Signup and view all the answers

What is the first step in the binary search process when looking for the number 68?

Set the initial range to the entire list Signup and view all the answers

When a midpoint item is found to be less than the search item, what action should be taken?

Change the range to focus on the items after the midpoint Signup and view all the answers

If a search item is located at the midpoint, what does that indicate?

The search has concluded successfully Signup and view all the answers

In a binary search, how is the midpoint determined if there is an even number of items?

Select the middle-left item Signup and view all the answers

What should be done after comparing the midpoint item with the search item?

Decide whether to narrow the range of search Signup and view all the answers

What is essential about the arrangement of items for binary search to be effective?

Items must be arranged in ascending order Signup and view all the answers

If you are searching for the number 68, which cup would be checked first?

Cup 5 Signup and view all the answers

What is the main reason for changing the search range during a binary search?

To more efficiently locate the target number Signup and view all the answers

What is the primary advantage of using binary search over linear search?

It requires fewer comparisons to find an item. Signup and view all the answers

Which of the following statements is true about binary search?

It requires the data to be ordered prior to searching. Signup and view all the answers

If you are using binary search to find the number 68 in the list [5, 23, 28, 47, 52, 68, 73, 77, 90], which number would you guess first?

52 Signup and view all the answers

When first guessing a number between 1-15, what would be the result after guessing 8 and receiving a 'lower' response?

You can eliminate all numbers greater than 8. Signup and view all the answers

In which situation would binary search be applicable?

Finding a name in a list sorted by last names. Signup and view all the answers

What happens if the middle number guessed in binary search is correct?

You ignore all the remaining numbers. Signup and view all the answers

What is indicated if the middle number guessed in binary search is higher than the target?

The target is below the middle number. Signup and view all the answers

Study Notes

Binary Search Overview

A binary search is an efficient algorithm for finding the position of an item in an ordered list.
It operates by repeatedly dividing the search interval in half, checking the middle item each time.

Steps of Binary Search

Start with a range covering the entire list, specified by the first and last item indices.
Calculate the midpoint of the current range.
Compare the midpoint item with the target item:
- If equal, the search is complete.
- If the midpoint is lower than the target, adjust the range to focus on the upper half.
- If the midpoint is higher, adjust the range to focus on the lower half.
Repeat the process until the item is found or the range is empty.

Efficiency

Binary search significantly reduces search time compared to linear search, especially with large datasets.
For a list of 1000 items, at most 10 comparisons are needed, and for 2000 items, at most 11 comparisons.

Requirements for Binary Search

Data must be ordered (sorted) for binary search to work effectively.
If the data is unordered, either sort it first or use a linear search.

Comparison with Linear Search

A linear search checks items sequentially and does not require a sorted list.
Binary search is faster due to halving the search space with each comparison.

Practical Application

The algorithm can be visualized through activities such as searching a number hidden under cups or performing searches on cards arranged in order.
It's essential to maintain the index range while searching and adjust it based on comparisons.

Next Steps in Learning

Future lessons will include investigating sorting algorithms, focusing on bubble sort.

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Description

In this lesson, you will explore the concept of binary search through an interactive guessing game. The activity will enhance your understanding of algorithms and how they work to efficiently locate a target number within a specific range.