NQUEENS - Prolog

% This program finds a solution to the 8 queens problem. That is, the problem of placing 8

% queens on an 8x8 chessboard so that no two queens attack each other. The prototype

% board is passed in as a list with the rows instantiated from 1 to 8, and a corresponding

% variable for each column. The Prolog program instantiates those column variables as it

% finds the solution.

% Programmed by Ron Danielson, from an idea by Ivan Bratko.

% 2/17/00

queens([]). % when place queen in empty list, solution found

queens([ Row/Col | Rest]) :- % otherwise, for each row

queens(Rest), % place a queen in each higher numbered row

member(Col, [1,2,3,4,5,6,7,8]), % pick one of the possible column positions

safe( Row/Col, Rest). % and see if that is a safe position

% if not, fail back and try another column, until

% the columns are all tried, when fail back to

% previous row

safe(Anything, []). % the empty board is always safe

safe(Row/Col, [Row1/Col1 | Rest]) :- % see if attack the queen in next row down

Col =\= Col1, % same column?

Col1 - Col =\= Row1 - Row, % check diagonal

Col1 - Col =\= Row - Row1,

safe(Row/Col, Rest). % no attack on next row, try the rest of board

member(X, [X | Tail]). % member will pick successive column values

member(X, [Head | Tail]) :-

member(X, Tail).

board([1/C1, 2/C2, 3/C3, 4/C4, 5/C5, 6/C6, 7/C7, 8/C8]). % prototype board