aula2.pl

%1
% a)
factorial(0, 1).
factorial(N, F):- N>0,
    N1 is N-1,
    factorial(N1, F1),
    F is F1 * N.
%b)
somaRec(0, 0).
somaRec(N, Sum):- N > 0,
    N1 is N-1,
    somaRec(N1, Sum1),
    Sum is Sum1+N.

%c)
fib(0, 0).
fib(1, 1).
fib(N, R) :- N > 1,
	A1 is N-1,
	A2 is N-2,
	fib(A1, R1),
	fib(A2, R2),
	R is R1 + R2.

%d)
isPrime(0) :- false.
isPrime(1) :- true.
isPrime(X) :- X > 2,
    and(true, isPrime(X-1)). % not working yet

test(A, B, C) :- C is (A rem B).

and(L,R) :- L,R.
or(L,R) :- L;R.

%5
 %a)
list_size([], 0).
list_size([_ListHead | ListTail], Size):-
    %Tail is ListTail,
    %Size1 is Size + 1,
    list_size(ListTail, Size1),
    Size is Size1 + 1.

 %b)

list_sum([], 0).
list_sum([ListHead | ListTail], Size):-
    %Tail is ListTail,
    %Size1 is Size + 1,
    list_sum(ListTail, Size1),
    Size is Size1 + ListHead.

 %c)

list_prod([], 1).
list_prod([ListHead | ListTail], Prod):-
    list_prod(ListTail, Prod1),
    Prod is ListHead * Prod1.

 %d)

inner_product([], [], 0).
inner_product([List1Head | List1Tail], [List2Head | List2Tail], Result):-
    inner_product(List1Tail, List2Tail, Result1),
    Result is List1Head * List2Head + Result1.

 %e)

count(_Elem, [], 0).
count(Elem, [ListHead | ListTail], N):-
    Elem \== ListHead,
    count(Elem, ListTail, N1),
    N is N1.

count(Elem, [ListHead | ListTail], N):-
    Elem == ListHead,
    count(Elem, ListTail, N1),
    N is N1 + 1.

%6

 %a

invert([], _List).
invert([List1Head | List1Tail], List2):-
    invert(List1Tail, List21),
    append(List21, [List1Head], List2).

 %b

del_one(_Elem, [], List2):-
    List2 = [].

del_one(Elem, [List1Head | List1Tail], List2):-
    Elem \== List1Head,
    del_one(Elem, List1Tail, List21),
    append([List1Head], List21, List2).

del_one(Elem, [List1Head | List1Tail], List2):-
    Elem == List1Head,
    List2 = List1Tail.

 %c

del_all(_Elem, [], List2):-
    List2 = [].

del_all(Elem, [List1Head | List1Tail], List2):-
    Elem \== List1Head,
    del_all(Elem, List1Tail, List21),
    append([List1Head], List21, List2).

del_all(Elem, [List1Head | List1Tail], List2):-
    Elem == List1Head,
    del_all(Elem, List1Tail, List2).

 %d

del_all_list([], List1, List2):-
    List1 = List2.

del_all_list([ListElemsHead | ListElemsTail], List1, List2):-
    del_all(ListElemsHead, List1, List21),
    del_all_list(ListElemsTail, List21, List2).

 %e

del_dups([], List2):-
    List2 = [].

del_dups([List1Head | List1Tail], List2):-
    del_all(List1Head, List1Tail, List21),
    del_dups(List21, List22),
    append([List1Head], List22, List2).

 %f

find_one(Elem, [List1Head | List1Tail]):-
    Elem \== List1Head,
    find_one(Elem, List1Tail).

find_one(Elem, [List1Head | _List1Tail]):-
    Elem == List1Head.


list_perm([], []).

list_perm([List1Head | List1Tail], List2):-
    find_one(List1Head, List2),
    del_one(List1Head, List2, List21),
    list_perm(List1Tail, List21).

 %g

replicate(0, _Elem, List):-
    List = [].

replicate(Amount, Elem, List):-
    Amount > 0,
    Amount1 is Amount - 1,
    replicate(Amount1, Elem, List1),
    append([Elem], List1, List).


 %h

interperse(_Elem, [List1Last] , List2):-
    append([List1Last], [], List2).

interperse(Elem, [List1Head | List1Tail] , List2):-
    interperse(Elem, List1Tail, List21),
    append([List1Head, Elem], List21, List2).

 %i

insert_elem(0, [List1Head | List1Tail], Elem, List2):-
    append([Elem, List1Head], List1Tail, List2).

insert_elem(Index, [List1Head | List1Tail], Elem, List2):-
    Index > 0,
    Index1 is Index - 1,
    insert_elem(Index1, List1Tail, Elem, List21),
    append([List1Head], List21, List2).


 %j

delete_elem(0, [List1Head | List1Tail], Elem, List2):-
    Elem is List1Head,
    List2 = List1Tail.

delete_elem(Index, [List1Head | List1Tail], Elem, List2):-
    Index > 0,
    Index1 is Index - 1,
    delete_elem(Index1, List1Tail, Elem, List21),
    append([List1Head], List21, List2).

 %k

replace_elem([List1Head | List1Tail], 0, Old, New, List2):-
    Old is List1Head,
    append([New], List1Tail, List2).

replace_elem([List1Head | List1Tail], Index, Old, New, List2):-
    Index > 0,
    Index1 is Index - 1,
    replace_elem(List1Tail, Index1, Old, New, List21),
    append([List1Head], List21, List2).

%% THIS IS NOT PART OF THE EXERCISE

lastElem([Elem], FinalList, Elem):-
    FinalList = [].

lastElem([ListHead | ListTail], FinalList, LastElem):-
    lastElem(ListTail, FinalList2, LastElem),
    append([ListHead], FinalList2, FinalList).

list_backwards([], []).

list_backwards([List1Head | List1Tail], List2):-
    lastElem(List2, List21 ,LastElem),
    LastElem == List1Head,
    list_perm(List1Tail, List21).


%7

 %a

list_append(List1, List2, List3):-
    append(List1, List2, List3).


%8

 %a

list_to(0, List):-
    List = [].

list_to(N, List):-
    N > 0,
    N1 is N - 1,
    list_to(N1, List1),
    append(List1, [N], List).

 %b

list_from_to(Inf, Inf, List):-
    List = [Inf].

list_from_to(Inf, Sup, List):-
    Sup > Inf,
    Sup1 is Sup - 1,
    list_from_to(Inf, Sup1, List1),
    append(List1, [Sup], List).

 %c

list_from_to_step(Inf, _Step, Sup, List):-
    Inf > Sup,
    List = [].

list_from_to_step(Inf, Step, Sup, List):-
    Sup >= Inf,
    Inf1 is Inf + Step,
    list_from_to_step(Inf1, Step, Sup, List1),
    append([Inf], List1, List).

%10

 %a

is_ordered([_Single]).

is_ordered([ListA, ListB | ListTail]):-
    ListA < ListB,
    is_ordered([ListB | ListTail]).

 %b

insert_ordered(Value, [],  List2):-
    List2 = [Value].

insert_ordered(Value, [List1Head | List1Tail], List2):-
    List1Head >= Value,
    append([Value, List1Head], List1Tail, List2).

insert_ordered(Value, [List1Head | List1Tail], List2):-
    List1Head < Value,
    insert_ordered(Value, List1Tail, List21),
    append([List1Head], List21, List2).

 %c

insert_sort([], List):-
    List = [].

insert_sort([ListHead | ListTail], List):-
    insert_sort(ListTail, List1),
    insert_ordered(ListHead, List1, List).

%11

%    n!
% --------
% k!(n-k)!

pascalrow(_N, -1, Line):-
    Line = [].

pascalrow(N, K, Line):-
    K1 is K - 1,
    factorial(N, ValueN),
    factorial(K, ValueK),
    NminusK is N - K,
    factorial(NminusK, ValueNminusK),
    ValueMul is ValueK * ValueNminusK,
    Value is ValueN / ValueMul,
    pascalrow(N, K1, Line1),
    append([Value], Line1, Line).

pascal(0, Lines):-
    Lines = [[1]].

pascal(N, Lines):-
    N1 is N - 1,
    pascalrow(N, N, Line),
    pascal(N1, Lines1),
    append(Lines1, [Line], Lines).