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TO. Puzzles. ALGORITHMS. Brian Thompson [email protected]. 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 - PowerPoint PPT Presentation
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CS4HS Teacher Workshop @ Rutgers University 1
Brian [email protected]
PuzzlesTO
ALGORITHMS
August 20-21, 2012
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
Puzzles To Algorithms
CS4HS Teacher Workshop @ Rutgers University 3
Fair Cake-Splitting
Puzzles To Algorithms
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
Puzzles To Algorithms
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/.
Puzzles To Algorithms
CS4HS Teacher Workshop @ Rutgers University 6
Tower of Hanoi
Puzzles To Algorithms
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
Puzzles To Algorithms CS4HS Teacher Workshop @ Rutgers University 7
CS4HS Teacher Workshop @ Rutgers University 8
Mazes
Puzzles To Algorithms
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
Puzzles To Algorithms
CS4HS Teacher Workshop @ Rutgers University 10
The Calendar Game
Puzzles To Algorithms
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
Puzzles To Algorithms
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 winsPuzzles To Algorithms
CS4HS Teacher Workshop @ Rutgers University 13
The Calendar Game
Puzzles To Algorithms
Start
Winner!
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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
Puzzles To Algorithms
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The Calendar Game
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
JanFebMarAprMayJunJulAugSeptOctNovDec
Puzzles To Algorithms
Start
Winner!
• Let’s represent the calendar a different way• Work backwards: What happens if your opponent moves to Nov. 30?
CS4HS Teacher Workshop @ Rutgers University 16
The Calendar Game
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
JanFebMarAprMayJunJulAugSeptOctNovDec
Puzzles To Algorithms
Start
Winner!
• Discuss why the dark blue squares are “winning positions”• If both players are clever, who wins? What is the winning first move?
