用 SICStus Prolog 概括斐波那契数列 [英] Generalizing Fibonacci sequence with SICStus Prolog

问题描述

我正在尝试为广义斐波那契数列 (GFS) 的查询找到解决方案.问题是:是否有任何 GFS 的第 12 个数字为 885?前 2 个数字可能被限制在 1 到 10 之间.

I'm trying to find a solution for a query on a generalized Fibonacci sequence (GFS). The query is: are there any GFS that have 885 as their 12th number? The initial 2 numbers may be restricted between 1 and 10.

我已经找到了在从 (1, 1) 开始的序列中找到第 N 个数字的解决方案，其中我明确定义了初始数字.这就是我所拥有的:

I already found the solution to find the Nth number in a sequence that starts at (1, 1) in which I explicitly define the initial numbers. Here is what I have for this:

fib(1, 1).
fib(2, 1).

fib(N, X) :-
    N #> 1,
    Nmin1 #= N - 1,
    Nmin2 #= N - 2,
    fib(Nmin1, Xmin1),
    fib(Nmin2, Xmin2),
    X #= Xmin1 + Xmin2.

对于提到的查询，我认为以下方法可以解决问题，其中我重用 fib 方法而不明确定义初始数字，因为现在需要动态完成:

For the query mentioned I thought the following would do the trick, in which I reuse the fib method without defining the initial numbers explicitly since this now needs to be done dynamically:

fib(N, X) :-
    N #> 1,
    Nmin1 #= N - 1,
    Nmin2 #= N - 2,
    fib(Nmin1, Xmin1),
    fib(Nmin2, Xmin2),
    X #= Xmin1 + Xmin2.

fib2 :-
    X1 in 1..10,
    X2 in 1..10,
    fib(1, X1),
    fib(2, X2),
    fib(12, 885).

...但这似乎不起作用.

... but this does not seem to work.

这样定义初始数字是不可能的，还是我做错了什么?我不是在寻求解决方案，但任何可以帮助我解决此问题的建议将不胜感激.

Is it not possible this way to define the initial numbers, or am I doing something terribly wrong? I'm not asking for the solution, but any advice that could help me solve this would be greatly appreciated.

推荐答案

在SWI-Prolog下:

Under SWI-Prolog:

:- use_module(library(clpfd)).

fib(A,B,N,X):-
    N #> 0,
    N0 #= N-1,
    C #= A+B,
    fib(B,C,N0,X).
fib(A,B,0,A).

task(A,B):-
    A in 1..10,
    B in 1..10,
    fib(A,B,11,885).

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