Assessment Tool

Lecture 15: Linear and Binary Search

Content Tested: Motivation for Binary Search

Lecture Content:

Searching an array
Linear search
Binary search
Comparing algorithm performance

Goals:

Develop ability to apply principles and generalizations already learned to new problems and situations
Develop problem-solving skills
Develop appropriate study skills, strategies, and habits
Improve mathematical skills
Prepare for transfer or graduate study
Learn techniques and methods used to gain new knowledge in this subject

Assessment Technique: Game

Purpose:

Instructors can find out how students design strategies for the "Choose My Number" game. This activity should precede the viewing of this lecture in order to motivate the process of binary search.

Activity:

This is an entire class activity. The instructor leads the "Choose My Number" game.

Instructor says: I'm thinking of a number between 1 and 100, inclusive. It's your job to guess my number. Upon each guess, I'll say "that's my number", "my number is higher", or "my number is lower". You will then have more turns to guess my number. Your goal is to guess my number in 8 guesses.

At this point, the instructor should declare a process for guessing among the students. The students could take turns guessing, the students could agree as a group before guessing as a class, or there could be some other way of organizing the guessing.

Possible Solution

Most likely, the students will come up with binary search to guess the instructor's number. They'll find that if they apply the binary search technique properly, they will succeed in finding the number in 8 or fewer guesses.

The students might do random guessing. In this case they probably won't find the number. Ask them to think together as a class about a better strategy for guessing and play the game again.

Possible Uses of Activity:

Have the students formalize their strategy as an algorithm and write in on the board. Compare their algorithm to binary search (should be very close) during the discussion of binary search on the video.
Ask the students motivating questions such as the following:

If I give you 20 guesses to guess my number, how large can the range of numbers be from which you're guessing? (You need to guess the number correctly with those 20 guesses).

Answer: 2^20 which is 1048576 (See if they can come up with the relationship on their own by examining the number of guesses used for a range of 1 to 100).

Is it always better to use the "halving strategy" over simply guessing numbers in order from 1, 2, 3, up to 100?

Answer: No. If you know the number is at the beginning of the sequence, it's best to just start guessing there. For example, if the secret number is 1 then it only takes 1 guess using the guessing in order strategy.