Reputation: 1396
I am studying prolog and I am faced with a problem that I cannot deal with.
Given a number, I have to check if the sum of the factorial of each digit that composes it is equal to the number itself.
Example:
145
1! + 4! + 5! = 1 + 24 + 120
Now my problem is just how to decompose the number so that I can factorial and sum each digit.
EDIT1.
thank to @slago I understand how decompose the number, but now I have a problem to sum the factorial terms:
fact(N):-
fact(N, N, _ListNumber).
fact(N, 0, ListNumber):-
factorial(ListNumber, 1, Sum),
Sum == N.
fact(N, Number, [D|R]):-
D is Number mod 10,
Number1 is Number div 10,
fact(N, Number1, R).
factorial([], Counter, Counter).
factorial([D|R], Counter, Sum):-
print([D|R]),
checksum(D, Counter),
factorial(R, Counter, Sum).
checksum(D, Counter):-
Counter1 is Counter * D,
M is D - 1,
M >= 2, !,
checksum(M, Counter1).
I have tried like this, but I noticed [D|R] results empty, and I don't understand why.
Upvotes: 0
Views: 233
Reputation: 5509
Your code is organized in a very confusing way. It is best to code independent predicates (for more specific purposes) and, after that, use them together to get the answer you want.
Start by creating a predicate to decompose a natural number into digits.
decompose(N, [N]) :- N<10, !.
decompose(N, [D|R]) :- N>=10, D is N mod 10, M is N//10, decompose(M, R).
Example of decomposition:
?- decompose(145, D).
D = [5, 4, 1].
Then, create a predicate to compute the factorial of a natural number.
fact(N, F) :- fact(N, 1, F).
fact(0, A, A) :- !.
fact(N, A, F) :- N>0, M is N-1, B is N*A, fact(M, B, F).
Example of factorial:
?- fact(5, F).
F = 120.
After that, create a predicate to map each number of a list into its corresponding factorial (alternatively, you could use the predefined predicate maplist/3
).
map_fact([], []).
map_fact([X|Xs], [Y|Ys]) :- fact(X,Y), map_fact(Xs, Ys).
Example of mapping:
?- decompose(145, D), map_fact(D, F).
D = [5, 4, 1],
F = [120, 24, 1].
You must also create a predicate to compute the sum of the items of a list (alternatively, you could use the predefined predicate sum_list/2
).
sum(L, S) :- sum(L, 0, S).
sum([], A, A).
sum([X|Xs], A, S) :- B is A+X, sum(Xs, B, S).
Example of summation:
?- decompose(145, D), map_fact(D, F), sum(F, S).
D = [5, 4, 1],
F = [120, 24, 1],
S = 145.
Finally, create the predicate to check the desired number property.
check(N) :- decompose(N, D), map_fact(D, F), sum(F, N).
Example:
?- check(145).
true.
?- check(146).
false.
Upvotes: 1