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, …, QNDomain 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

Problem representation

N-queens as a CSP

N variables: Q1, …, QNDomain 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 88 (16 777 216) 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 ≠ QjDiagonally: |i-j| ≠|Qi-Qj|

Constraints