N-queens problem Original problem: How to place 8 queens on an 8x8 chessboard so that no two queens attack each other N-queen problem: Generalization for.

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N-queens problem Original problem: How to place 8 queens on an 8x8 chessboard so that no two queens attack each other N-queen problem: Generalization for N queens on NxN chessboard

N-queens as a CSP N variables: Q1, …, QN Domain of each variable is {1,2,…, N 2 } (for each possible field) Q1 = 1, Q2 = 15, Q3 = 21, Q4 = 32 Q5 = 34, Q6 = 44, Q7 = 54, Q8 = 59 Representation has 64 8 ( ) possible assignments Problem representation

N-queens as a CSP N variables: Q1, …, QN Domain of each variable is {1,2, …, N} (i-th queen is in i-th column, the domain specifies available rows) Q1 = 1, Q2 = 5, Q3 = 8, Q4 = 6 Q5 = 3, Q6 = 7, Q7 = 2, Q8 = 4 Representation has 8 8 ( ) possible assignments More compact representation

N-queens as a CSP No queen can attack any other queen: Vertically (for the compact representation explicit) Horizontally: Qi ≠ Qj Diagonally: |i-j| ≠|Qi-Qj| Constraints

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