Welcome to:

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Welcome to Chapel Hill UNC Computer Science
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Steve Weiss Department of Computer
Science University of North Carolina at Chapel
Hill weiss_at_cs.unc.edu
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Parallel computing
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Brute force and backtracking(or how to open your
friends lockers)
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The puzzle
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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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Brute force problem solving
Generate candidates
Filter
Solutions
Trash
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Requirements

• Candidate set must be finite.
• Must be an Oh yeah! problem.

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Example
Combination lock 606060 216,000 candidates
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Example
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Oh no!
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Oh yeah!
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Additional restrictions

• Solution is a sequence s1, s2,,sn
• Solution length, n, is known (or at least
  bounded) in advance.
• Each si is drawn from a finite pool T.

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Cavers right hand rule
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Generating the candidates
Classic backtrack algorithm At decision point,
do something new (extend something that hasnt
been added to this sequence at this place
before.) Fail Backtrack
Undo most recent decision (retract).
Fail done
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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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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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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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Faster!

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

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Richard Feynman
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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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Still more puzzles

• 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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• Solution is a sequence on known length (n) where
  each element is one of the colors.

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2
4
3
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• 2. Running a maze How can you get from start to
  finish legally in a maze?

20 x 20 grid
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• Solution is a sequence of unknown length, but
  bounded by 400, where each element is S,
  L, or R.

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• 3. Making change.
• How many ways are there to make 1.00 with coins.
  Dont forget Sacagawea.

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• 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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Lets try the 4-square puzzle

• Use pieces A, B, F, and G and try to arrange into
  a 2x2 square.

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