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N-queens problem

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. Problem representation. N variables: Q1, …, QN

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N-queens problem

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  1. 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

  2. N-queens as a CSP Problem representation • N variables: Q1, …, QN • Domain of each variable is {1,2,…, N2} (for each possible field) • Q1 = 1, Q2 = 15, Q3 = 21, Q4 = 32 • Q5 = 34, Q6 = 44, Q7 = 54, Q8 = 59 • Representation has 648 (281 474 976 710 656) possible assignments

  3. N-queens as a CSP More compact representation • N variables: Q1, …, QN • Domain of each variable is {1,2, …, N} (i-thqueen 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 88 (16 777 216) possible assignments

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

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