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Science1 Welcome to: Chapel Hill UNC Computer Science

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Science2 Agenda Welcome Parallel computing exercise Protein folding and origami Extended break:Meet with our students ACM Programming team First year seminar: Lego robots First year seminar: Computer animation (room 030) Deltasphere Sessions: 10:35, 11:15, 1:00, 1:40 Virtual reality demo (ticket) Russ Taylor: Visualization (sessions 1 and 2) Jan Prins: Parallel computing (sessions 1 and 2) Jack Snoeyink & Wei Wang: Protein folding (all sessions) Kevin Jeffay: Computer networking (sessions 3 and 4) Steve Weiss: Brute force (sessions 3 and 4) Round table: CS curriculum, careers, all questions answered!

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Science3 Etc. Restrooms Breaks Lunch Where are the stairs?

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Science4 Any questions ?

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Science5 Parallel computing

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Science6

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7 Brute force and backtracking (or how to open your friends’ lockers) Steve Weiss Department of Computer Science University of North Carolina at Chapel Hill weiss@cs.unc.edu

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Science8 The puzzle

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Science9 Other puzzles What two words add up to “stuff”? How many different ways to make $1.00 in change? Unscramble “eeiccns”

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Science10

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Science11 Brute force problem solving Generate candidates Filter Solutions Trash

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Science12 Requirements Candidate set must be finite. Must be an “Oh yeah!” problem.

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Science13 Example Combination lock 60*60*60 = 216,000 candidates

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Science14 Example

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Science15 Oh no!

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Science16 Oh yeah!

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Science17 Additional restrictions Solution is a sequence s 1, s 2,…,s n Solution length, n, is known (or at least bounded) in advance. Each s i is drawn from a finite pool T.

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Science18 Caver’s right hand rule

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Science19 Generating the candidates Classic backtrack algorithm: At decision point, do something new (extend something that hasn’t been added to this sequence at this place before.) Fail: Backtrack: Undo most recent decision (retract). Fail: done

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Science20 Recursive backtrack algorithm (pseudo Java) backtrack(Sequence s) { for each si in T { s.extend(si); if (s.size() == MAX) // Complete sequence display(s); else backtrack(s); s.retract(); } // End of for } // End of backtrack

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Science21 Problem solver backtrack(Sequence s) { for each si in T { s.extend(si); if (s.size() == MAX) // Complete sequence if (s.solution()) display(s); else backtrack(s); s.retract(); } // End of for } // End of backtrack

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Science22 Problems Too slow, even on very fast machines. Case study: 8-queens Example: 8-queens has more than 281,474,976,711,000 candidates.

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Science23 8-queens How can you place 8 queens on a chessboard so that no queen threatens any of the others. Queens can move left, right, up, down, and along both diagonals.

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Science24 Problems Too slow, even on very fast machines. Case study: 8-queens Example: 8-queens has more than 281,474,976,711,000 candidates.

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Science25 Faster! Reduce size of candidate set. Example: 8-queens, one per row, has only 16,777,216 candidates.

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Science26 Richard Feynman

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Science27 Faster still! Prune: reject nonviable candidates early, not just when sequence is complete. Example: 8-queens with pruning looks at about 16,000 partial and complete candidates.

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Science28 Backtrack with pruning backtrack(Sequence s) { for each si in T if (s.okToAdd(si)) // Pruning { s.extend(si); if (s.size() == MAX) // Complete solution display(s); else backtrack(s); s.retract(); } // End of if } // End of backtrack

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Science29 Still more puzzles 1.Map coloring: Given a map with n regions, and a palate of c colors, how many ways can you color the map so that no regions that share a border are the same color?

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Science30 Solution is a sequence on known length (n) where each element is one of the colors. 1 4 3 2

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Science31 2. Running a maze: How can you get from start to finish legally in a maze? 20 x 20 grid

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Science32 Solution is a sequence of unknown length, but bounded by 400, where each element is S, L, or R.

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Science33 3. Making change. How many ways are there to make $1.00 with coins. Don’t forget Sacagawea.

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Science34 4. Solving the 9 square problem. Solution is sequence of length 9 where each element is a different puzzle piece and where the touching edges sum to zero.

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Science35 Let’s try the 4-square puzzle Use pieces A, B, F, and G and try to arrange into a 2x2 square.

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Science36

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SIGCSE 20031 Nifty assignments: Brute force and backtracking Steve Weiss Department of Computer Science University of North Carolina at Chapel Hill

SIGCSE 20031 Nifty assignments: Brute force and backtracking Steve Weiss Department of Computer Science University of North Carolina at Chapel Hill

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