# N queens problem in Prolog

2020-01-10

Below the N Queens problem solved in Prolog and Constraint Logic Programming over Finite Domains library

```
:- use_module(library(clpfd)).
n_queens(N, Queens) :-
length(Queens, N),
Queens ins 1..N,
all_different(Queens), %% the queens must be in different columns
different_diagonals(Queens).
different_diagonals([]).
different_diagonals([Q|Queens]) :- different_diagonals(Queens, Q, 1), different_diagonals(Queens).
different_diagonals([], _, _).
different_diagonals([Q|Queens], Q0, Distance) :-
abs(Q0 - Q) #\= Distance,
NewDistance #= Distance + 1,
different_diagonals(Queens, Q0, NewDistance).
/*
Queens is the list of columns of the queens: the corresponding rows are the position of the elements/columns in the list Queens
Examples:
?- n_queens(8, Queens), labeling([ff], Queens).
%@ Queens = [1, 5, 8, 6, 3, 7, 2, 4] ;
%@ Queens = [1, 6, 8, 3, 7, 4, 2, 5] .
The result chess cells are, for instance, [1,1], [2,5], [3,8], [4,6], [5,3], [6,7], [7,2], [8,4]
Suggestion from https://www.swi-prolog.org/pldoc/man?section=clpfd-n-queens
*/
```