Prolog Day 2

1_factorial.pl

factorial(0, 1).
factorial(X, Y) :- 
	X > 0,
	X1 is X - 1,
	factorial(X1, Z), 
	Y is Z*X.

2_reverse.pl

rev([], []).
rev([Head|Tail], Reversed) :- 
	rev(Tail, RevRest),
	append(RevRest,[Head],Reversed).

3_smallest.pl

smallest([X], X).
smallest([First,Second|Tail], Small) :-
	First =< Second,
	smallest([First|Tail], Small).
	
smallest([First,Second|Tail], Small) :-
	First > Second,
	smallest([Second|Tail], Small).
	

4_queens.pl

valid_queen([Row,Col]) :-
	Range = [1,2,3,4,5,6,7,8],
	member(Row, Range),
	member(Col, Range).

validate_queens([]).

validate_queens([Head|Tail]) :-
	valid_queen(Head),
	validate_queens(Tail).

north_west_diags([], []).

north_west_diags([[Row,Col]|Tail], Diagonals) :-
	Diag is Row - Col,
	north_west_diags(Tail, RestOfDiagonals),
	append(RestOfDiagonals,[Diag], Diagonals).

south_east_diags([],[]).

south_east_diags([[Row,Col]|Tail], Diagonals) :-
	Diag is Row + Col,
	south_east_diags(Tail, RestOfDiagonals),
	append(RestOfDiagonals,[Diag], Diagonals).

queens(List) :-
	length(List, 8),
	validate_queens(List),
	List = [[R1, C1], [R2, C2], [R3, C3], [R4, C4], [R5, C5], [R6, C6], [R7, C7], [R8, C8]],
	Rows = [R1, R2, R3, R4, R5, R6, R7, R8],
	Cols = [C1, C2, C3, C4, C5, C6, C7, C8],
	fd_all_different(Rows),
	fd_all_different(Cols),
	north_west_diags(List, NorthWestDiags),
	fd_all_different(NorthWestDiags),
	south_east_diags(List, SouthEastDiags),
	fd_all_different(SouthEastDiags).