1 / 17

Puzzles

TO. Puzzles. ALGORITHMS. Brian Thompson bthom@cs.rutgers.edu. Why Puzzles?. Learning algorithms may be intimidating for students who are new to computer science Puzzles are more familiar and are frequently seen as challenging and fun

yamka
Download Presentation

Puzzles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. TO Puzzles ALGORITHMS Brian Thompson bthom@cs.rutgers.edu CS4HS Teacher Workshop @ Rutgers University

  2. Why Puzzles? • Learning algorithms may be intimidating for students who are new to computer science • Puzzles are more familiar and are frequently seen as challenging and fun • Strategy: use puzzles to introduce computer science concepts, algorithms, and data structures CS4HS Teacher Workshop @ Rutgers University

  3. Fair Cake-Splitting CS4HS Teacher Workshop @ Rutgers University

  4. Fair Cake-Splitting • Materials: worksheet, mini-cakes (be aware of allergies), knives, plates/napkins, Java applet: http://pidancer.com/Projects/CakeCutting/ • Puzzle: Split a cake amongst several people, so each is guaranteed to get his/her fair share • Goal: Introduce the idea of an algorithm, demonstrate that algorithms can be used to solve everyday problems CS4HS Teacher Workshop @ Rutgers University

  5. Fair Cake-Splitting • Hand out the worksheet, introduce the problem out loud. • Have students form groups of 3, discuss the 2-person cake-splitting scenario in groups, raise hand if they have questions. • After 5 minutes, choose a group to present their solution (and why it is fair for both participants). • While groups discuss 3-person cake-splitting, hand out a mini-cake with knife and plate/napkin per group to try out their solution. • After 5 minutes, ask for volunteers to present their solution. As a class, analyze whether the solution is fair. Encourage discussion. • Present the “SAY WHEN” n-person fair cake-splitting algorithm. Discuss/prove why it is fair. • Test out the “SAY WHEN” algorithm with the whole class using the Java applet here: http://pidancer.com/Projects/CakeCutting/. CS4HS Teacher Workshop @ Rutgers University

  6. Tower of Hanoi CS4HS Teacher Workshop @ Rutgers University

  7. Tower of Hanoi • Materials: Tower of Hanoi game, or make one yourself by bringing 4 stackable items of increasing size • Puzzle: Transfer a stack of disks (or objects) from one pile to another, following two rules:(1) can only move one disk at a time(2) can’t place any disk on top of a smaller disk • Goal: Introduce the (related) concepts of recursion and induction; problem-solving strategy of approaching a complex problem by first solving a simpler problem and then generalizing CS4HS Teacher Workshop @ Rutgers University

  8. Mazes CS4HS Teacher Workshop @ Rutgers University

  9. Mazes • Materials: Worksheet with a maze, should be challenging enough that students will not see the solution immediately • Puzzle: Design a general procedure to solve mazes that will work no matter how big or tricky the maze is • Goal: Can be used to teach back-tracking, binary trees, depth-first search CS4HS Teacher Workshop @ Rutgers University

  10. The Calendar Game CS4HS Teacher Workshop @ Rutgers University

  11. The Calendar Game • Materials: Calendar (handout or projector), pen or pencil, and scratch paper • Puzzle: The Calendar Game, a 2-person turn-based game played on a standard calendar • Goal: Learn how computers play games by thinking about how clever people play games; introduce the concepts of “winning positions” and “losing positions”; show how a different representation can make a problem easier CS4HS Teacher Workshop @ Rutgers University

  12. The Calendar Game • Start at January 1 • Alternate turns doing one of the following: • Jump to a later month, same day(e.g. January 1  August 1) • Jump to a later day, same month(e.g. January 1  January 12) • Can only jump forward in time • Must stay in the same year • Whoever ends up on December 31 wins CS4HS Teacher Workshop @ Rutgers University

  13. The Calendar Game Start Winner! CS4HS Teacher Workshop @ Rutgers University

  14. The Calendar Game • Explain the rules of the game • Play an example game with a student to demonstrate and make sure the rules are clear • Students pair up and play against each other; go around and clarify rules if necessary • After a few minutes, ask for volunteers to present their strategy; encourage discussion • Present the analysis on the following slides CS4HS Teacher Workshop @ Rutgers University

  15. The Calendar Game • Let’s represent the calendar a different way • Work backwards: What happens if your opponent moves to Nov. 30? Start Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Winner! CS4HS Teacher Workshop @ Rutgers University

  16. The Calendar Game • Discuss why the dark blue squares are “winning positions” • If both players are clever, who wins? What is the winning first move? Start Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Winner! CS4HS Teacher Workshop @ Rutgers University

  17. Thank You! Brian Thompson bthom@cs.rutgers.edu CS4HS Teacher Workshop @ Rutgers University

More Related