I am trying to create a function called collatz_list in Prolog. This function takes two arguments, the first one is a number and the second in a list. This list will be my output of this function. So, here's my function:
collatz_list(1,[1]).
collatz_list(N,[H|T]) :-
N > 1,
N mod 2 =:= 0,
collatz_list(N, [H|T]).
collatz_list(N,[H|T]) :-
N > 1,
N mod 2 =:= 1,
N is N*3 +1,
collatz_list(N,[H|T]).
I am struggling with creating the output list. Can anyone help me on that?
Thanks.
Assuming you want to write a collatz_list/2 predicate with parameters (int, list), where list is the collatz sequence starting with int and eventually ending with 1 (we hope so! It's an open problem so far); you just have to code the recursive definition in the declarative way.
Here's my attempt:
/* if N = 1, we just stop */
collatz_list(1, []).
/* case 1: N even
we place N / 2 in the head of the list
the tail is the collatz sequence starting from N / 2 */
collatz_list(N, [H|T]) :-
0 is N mod 2,
H is N / 2,
collatz_list(H, T), !.
/* case 2: N is odd
we place 3N + 1 in the head of the list
the tail is the collatz sequence starting from 3N + 1 */
collatz_list(N, [H|T]) :-
H is 3 * N + 1,
collatz_list(H, T).
Modified version, includes starting number
Let's test it:
full_list(N, [N|T]) :-
collatz_list(N, T).
collatz_list(1, []).
collatz_list(N, [H|T]) :-
0 is N mod 2,
H is N / 2,
collatz_list(H, T), !.
collatz_list(N, [H|T]) :-
H is 3 * N + 1,
collatz_list(H, T).
?- full_list(27, L).
L = [27, 82, 41, 124, 62, 31, 94, 47, 142|...].