Revision as of 16:54, 20 February 2014 by Michael Leuschel (talk | contribs)

The N-Queens is a famous constraint solving benchmark puzzle. It is a generalisation of the original eight queens puzzle, where the goal is to place eight queens on a 8*8 chessboard so that no two queens attach each other.

Here is one way to encode the N-Queens puzzle in B.

MACHINE NQueens CONSTANTS n,queens PROPERTIES n = 40 & queens : 1..n >-> 1..n /* for each column the row in which the queen is in */ & !(q1,q2).(q1:1..n & q2:2..n & q2>q1 => queens(q1)+q2-q1 /= queens(q2) & queens(q1)-q2+q1 /= queens(q2)) END

ProB 1.3.7 can solve this puzzle in about 0.150 seconds (for n=40, on a 1.7 GHz Mac Book Air).

One can use graphical visualisation features to display the solution, by declaring the ANIMATION FUNCTION as follows:

MACHINE NQueens40 CONSTANTS n,queens PROPERTIES n = 40 & queens : 1..n >-> 1..n /* for each column the row in which the queen is in */ & !(q1,q2).(q1:1..n & q2:2..n & q2>q1 => queens(q1)+q2-q1 /= queens(q2) & queens(q1)-q2+q1 /= queens(q2)) DEFINITIONS ANIMATION_FUNCTION_DEFAULT == ( {r,c,i|r:1..n & c:1..n & i=(r+c) mod 2 } ); ANIMATION_FUNCTION == ( {r,c,i|c:1..n & r=queens(c) & i=2+((r+c) mod 2) } ); ANIMATION_IMG0 == "images/sm_empty_box.gif"; ANIMATION_IMG1 == "images/sm_gray_box.gif"; ANIMATION_IMG2 == "images/sm_queen_white.gif"; ANIMATION_IMG3 == "images/sm_queen_black.gif"; SET_PREF_CLPFD == TRUE; END

This will lead to ProB to show the solution graphically, as follows (the screenshot is unfortunately cropped and does not show all rows):

Instead of using ProB's standard constraint-solving backend, you can also use our Kodkod backend to solve this puzzle.
To do this, either "Enable Kodkod for Properties" in the ProB Tcl/Tk "Preferences" menu or
add the following to the DEFINITIONS in the machine file above:

SET_PREF_KODKOD == TRUE

However, using the MiniSat backend solving the N-queens puzzle for n=40 takes 57.1 seconds (on the same hardware as above).