斐波那契函数不接受0并且不显示最后一项 [英] Fibonacci function not accepting 0 and not displaying the last term only

问题描述

我写了一个函数，显示直到第n个项的斐波那契数列.该代码运行良好，但是我想进行两项更改，但不确定如何执行.

I wrote a function that displays the Fibonacci sequence up to the nth term. The code runs fine, but I want to make two changes and am not sure how to do so.

这是我的代码:

function [ F ] = get_fib( k )
    F(1) = 1;
    F(2) = 1;
    i = 3;

    while k >= i;
        F(i) = F(i-1) + F(i-2);
        i = i + 1;
    end
end

第一个问题是代码不接受0作为输入.我尝试将功能更改为:

The first problem is that the code does not accept 0 as an input. I tried changing the function to:

function [ F ] = get_fib( k )
    F(0) = 0;
    F(1) = 1;
    F(2) = 1;
    i = 3;

    while k >= i;
        F(i) = F(i-1) + F(i-2);
        i = i + 1;
    end
end

但是出现以下错误:

试图访问F(0);索引必须为正整数或逻辑.

Attempted to access F(0); index must be a positive integer or logical.

get_fib错误(第2行)
F(0)= 0;

Error in get_fib (line 2)
F(0) = 0;

我还希望代码显示序列中的最后一项，而不是整个序列.

I would also like the code to display the last term in the sequence, rather than the entire sequence.

我将功能更改为:

function [ F ] = get_fib( k );
    F(1) = 1;
    F(2) = 1;
    i = 3;

    while k >= i;
        F(i) = F(i-1) + F(i-2);
        i = i + 1;
    end

    term = F(k)
end

，但仍将其分配给ans的顺序.

but the sequence it still being assigned to ans.

如何使我的函数接受0作为参数并仅显示序列的最后一项?

How can I make my function accept 0 as an argument and only display the last term of the sequence?

推荐答案

由于其他人已经指出了如何修复代码，因此我想向您展示一种计算 nth 斐波那契数的方法无需依赖 F(n-1)和 F(n-2)项计算.

Since others already pointed out how to fix your code, I'd like to show you one approach to calculate the nth Fibonacci number without relying on the F(n-1) and F(n-2) terms calculation.

它涉及黄金比例，您可以在此处.

It involves the golden ratio, and you can read more about its relationship to the Fibonacci sequence here.

function [ F ] = get_fib( n )
    % Changed your input variable from k to n (standard notation)    
    Phi = (1+sqrt(5))/2; % Golden ratio value
    F = round((Phi^n - ((-1)^n)/(Phi^n))/sqrt(5)); %nth fibonacci number

end

由于您只对序列的最后一个值感兴趣，因此可以大大加快 n 值的计算速度.

Since you are only interested in the last value of the sequence, it could speed up the calculation for large values of n.

请注意，我已对输出(F)进行了四舍五入，以避免浮点算术错误.

Note i have rounded the output (F) to avoid floating point arithmetic errors.

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