Reversing matrix rows in Prolog - matrix

I am trying to write a predicate which reverses all rows in a matrix using Prolog.
For instance the matrix [ [1,2,3], [4,5,6], [7,8,9] ] should become [ [3,2,1], [6,5,4], [9,8,7] ].
My attempt so far is :
reverseRows([[H|T]|_],X):-reverse([H|T],X).
which reverses only the first row. How can I change the above to work for all rows ? Any assistance is welcome.

The simplest solution is to use the predicate maplist/3.
?- maplist(reverse, [[1,2,3], [4,5,6], [7,8,9]], Reversed).
Reversed = [[3, 2, 1], [6, 5, 4], [9, 8, 7]].
Other possible solution is:
reverse_rows([], []).
reverse_rows([Xs|Xss], [Ys|Yss]) :-
reverse(Xs, Ys),
reverse_rows(Xss, Yss).
Example:
?- reverse_rows([[1,2,3], [4,5,6], [7,8,9]], Reversed).
Reversed = [[3, 2, 1], [6, 5, 4], [9, 8, 7]].

Related

Prolog: How to make a bagof fail in the middle of execution

My problem is that I have a functor with the next structure:
something(Perms, New_perms) :-
bagof(New_perm, aux_something(Perms, New_perm), <New_perms>).
aux_something(Perms, New_perm) :-
member(Perm, Perms),
take_impossible(Perm, New_perms).
take_impossible(Perm_poss, New_perm) :-
Perm_poss = [Var, Perm],
bagof(P, member(P, Perm), subsumes_term(Var, P)), New_perms),
New_perm = [Var, New_perms].
This takes a list of elements of the form:
[[A, 2, C], [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]]
It returns the list of possible permutations:
[[A, 2, C], [[1, 2, 3], [3, 2, 1]]]
But with the list containing an impossible element:
[[A, 4, C], [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]]
The functor should return false.
I need that, when it takes an element of the list which has no possible permutations, the list returns false. A forall instead of the bagof doesn't work because it doesn't change any variable bindings, and a forall before the bagof is too expensive, as I am doing the same operation to all elements of the list twice (it exceeds the limit time in the test). How can I break the execution of a bagof if the condition fails, or is there any other predicate that can do what I am looking for?
(Functor and aux_functor are not the real names of the variables, but this is college work, and so I am trying not to give too much info).
Stupid, question when I found the answer...
A bagof that fails when its objective fails is just a maplist.
Thanks for the help, anyway.
In this case, the correct answer would be:
something(Perms, New_perms) :-
maplist(take_impossible, Perms, New_perms).
take_impossible(Perm_poss, New_perm) :-
Perm_poss = [Var, Perm],
bagof(P, member(P, Perm), subsumes_term(Var, P)), New_perms),
New_perm = [Var, New_perms].

How to create a list without using findall? Prolog

I am generating permutations:
takeout(X,[X|T],T).
takeout(X,[F|R],[F|S]):-
takeout(X,R,S).
perm([],[]).
perm([X|Y],Z):-
perm(Y,W),
takeout(X,Z,W).
I want to know how to create a list of all the permutations without using findall.
Example:
?-perm([1,2,3],List).
List = [[1, 2, 3], [2, 1, 3], [2, 3, 1], [1, 3, 2], [3, 1, 2], [3, 2, 1]]
Group permutations by the element it starts with.
Take an element X and create permutations Ys1 without it in the original list.
Adding this element X as the first element of all these permutations we have the list XP of permutations starting with X.
Appending all the groups will give you all permutations.
cons(X, Xs, [X|Xs]).
perm([], [[]]).
perm(Xs, Ys) :-
dif(Xs, []),
maplist({Xs}/[X, XP]>>(select(X, Xs, Xs1),
perm(Xs1, Ys1),
maplist(cons(X), Ys1, XP)),
Xs, Yss),
append(Yss, Ys).
?- perm([1, 2, 3], X).
X = [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]] ;
false.
?- length(Y, 8), perm(Y, X), length(X, N). %8 factorial
N = 40320
The idea is to generate permutations and test if you already created this permutation. I'm using the inbuild predicate permutation/2.
perm(Ori,Out):-
perm(Ori,[],Out).
perm(Ori,Acc,Ret):-
permutation(Ori,Perm),
\+ member(Perm,Acc),
!,
perm(Ori,[Perm|Acc],Ret).
perm(_,L,L).
?- perm([1,2,3],E).
E = [[3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 3, 2], [1, 2, 3]].
The code is not the fastest one since it checks multiple times for membership.

How to permute in Prolog the elements of a list composed of sub-list and atoms

Let us consider lists such as L=[[7,3,4],9,[4,5],[1,3,5],4] where components could be lists or atoms. How to produce this type of permutation results:
R = [[7, 3, 4], 9, [4, 5], [1, 3, 5], 4]
R = [[7, 4, 3], 9, [5, 4], [1, 3, 5], 4]
R = [[7, 4, 3], 9, [4, 5], [1, 5, 3], 4]
....
In fact, we would like to have all the possible permutations of the sub-lists of L while the atom should remain unchanged.
I wrote a classical predicate permutation(OriginalList,PermutedList), and an allperm predicate that apply the maplist function to this permutation predicate:
permutation([],[]).
permutation(L,[T|Q]) :-
select(T,L,L1),
permutation(L1,Q).
/*L is the list to permute, R the result*/
allperm(L,R) :-
maplist(permutation,L,R).
It functions only in the special case where L is composed of lists and doesn't function when L is heterogeneous (atoms and lists).
Could you provide hints or elements of solution to do the right permutation?
The following modification should do:
permutation(X,X).
permutation(L,[T|Q]) :-
dif(L,[T|Q]),
select(T,L,L1),
permutation(L1,Q).
allperm(L,R) :-
maplist(permutation,L,R).
We extend the “identity” permutation to any Prolog term (first clause of permutation) and disallow it in the second clause (which can only be applied to lists anyway).

Prolog insertion sort

There is a simple Prolog insertion sort alghoritm:
sorting([A|B], Sorted) :- sorting(B, SortedTail), insert(A, SortedTail, Sorted).
sorting([], []).
insert(A, [B|C], [B|D]) :- A #> B, !, insert(A, C, D).
insert(A, C, [A|C]).
It does well on normal lists:
?- sorting([5, 4, 9, 1, 3, 8], X).
X = [1, 3, 4, 5, 8, 9].
But I also need to sort sublist of list contains any of them:
?- sorting([2, 5, [5, 4, 3], [6, 3], 4, 8], X).
X = [2, 4, 5, 8, [5, 4, 3], [6, 3]].
Is what return now. And
?- sorting([2, 5, [5, 4, 3], [6, 3], 4, 8], X).
X = [2, 4, 5, 8, [3, 4, 5], [3, 6]].
what I need to return. So how can I sort sublist too? Thanks in advance!
I offer this simple solution:
Insert element in the sorted list
insert(X, [], [X]):- !.
insert(X, [X1|L1], [X, X1|L1]):- X=<X1, !.
insert(X, [X1|L1], [X1|L]):- insert(X, L1, L).
Use principe of insertion sort algorithm
insertionSort([], []):- !.
insertionSort([X|L], S):- insertionSort(L, S1), insert(X, S1, S).

Combinatios in List of LIsts Prolog

I need to find the combinations in a list of lists.
For example give the following list,
List = [[1, 2], [1, 2, 3]]
These should be the output,
Comb = [[1,1],[1,2],[1,3],[2,1],[2,2],[2,3]]
Another example:
List = [[1,2],[1,2],[1,2,3]]
Comb = [[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[1,2,3]....etc]
I know how to do it for a list with two sublists but it needs to work for any number of sublists.
I'm new to prolog, please help.
try([],[]).
try([L|Ls],[M|Ms]):-
member(M,L),
try(Ls,Ms).
all(L,All) :- findall(M, try(L,M), All).
try returns one list composed of elements of the sublists of the first argument. all finds all such lists.
Here is your answer, cut and dry, as a fellow new prolog programmer myself.
%elementInList(input list, output answer)
answer(ListOfList, AnswerInList) :-
findall(Ans, combList(ListOfList, Ans), AnswerInList).
%combList(ListOfList, Comb) :-
combList([], []).
combList([Head|Tail], Comb) :-
combList(Tail, [Element|Tempcomb]),
elementInList(Head, Element).
%elementInList(List, Element)
elementInList([Head|_], Head).
elementInList([Head|Tail], Element) :-
elementInList(Tail, Element).
Using the definition answer(InputList, OutputResult), where e.g.
answer([[1,2],[7,8]],Comb).
Comb = [[1, 7], [2, 7], [1, 8], [2, 8]].
and e.g.
answer([[1,2],[2,8],[3,6,9]],Comb).
Comb = [[1, 2, 3], [2, 2, 3], [1, 8, 3], [2, 8, 3], [1, 2, 6], [2, 2, 6], [1, 8|...], [2|...], [...|...]|...].
and so on [X,Y,Z,..] for any number of sublists. You're welcome.

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