G52AIP Artificial Intelligence Programming

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G52AIPArtificial Intelligence Programming
Dr Rong Qu

• Modeling CSPs Case Study II

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Solving Sudoku

• Variables
• posi,j number placed at position (i,j)
• Domain
• posi,j 1, , 9

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Solving Sudoku

• Constraints
• 1, , 9 on each row
• 1, , 9 on each column
• 1, , 9 in each 3X3 square

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Solving Sudoku

• Constraints
• All different each row
• All different each column
• All different each 3X3 square
• How to model constraint 3?

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Solving Sudoku

• Constraints
• All different posi,j 1, , 9
• i 1, 2, 3 4, 5, 6 or 7, 8, 9
• j 1, 2, 3 4, 5, 6 or 7, 8, 9

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• Solving Sudoku Demo

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Data File Project in OPL

• Input data in OPL
• Project in OPL
• Add/insert model file .mod
• Add/insert data file .dat
• Data type declared in model file .mod will look
  up the data file .dat

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Solving Sudoku in OPL

• //.dat file
• input
• 0 6 0 0 5 0 0 2 00 0 0 3 0 0 0 9 07 0 0 6
  0 0 0 1 00 0 6 0 3 0 4 0 00 0 4 0 7 0 1 0
  00 0 5 0 9 0 8 0 00 4 0 0 0 1 0 0 60 3 0
  0 0 8 0 0 00 2 0 0 4 0 0 5 0

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Solving Sudoku in OPL

• //.mod file
• range dim1 1..9
• range dim2 1..9
• range bindex 0..2
• int inputdim1,dim2 ... //read in the .dat
• int setnumf in bindex x x in dim1 x lt
  (43f) x gt 3f
• var int posdim1,dim2 in 1..9

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Solving Sudoku in OPL

• solve
• forall(i in 1..9)
• forall(j in dim2 inputi,j ltgt 0)
• posi,j inputi,j

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Solving Sudoku in OPL

• solve
• forall(j in dim2)
• alldifferent(all(i in dim1) posi,j)
• forall(i in dim1)
• alldifferent(all(j in dim2) posi,j)

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Solving Sudoku in OPL

• solve
• forall(b1 in bindex)
• forall(b2 in bindex)
• alldifferent(all(i in setnumb1, j in
  setnumb2) posi,j)

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Solving Sudoku in OPL
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Exercise Coins in Bank

• You have a bag of coins to save in your bank
• Weights of coins
• If the bag of coins weighs 131g, how much in
  total?
• How about 4g? How many possible solutions?
• How can you solve this problem?