猴子摘香蕉一次可以摘1个或2个,总共50个,问有多少种摘法？

问题来自知乎

等我写完发现，知乎上都比我写的好，我快哭了！！！

等我写完之后发现不就是那啥啥函数，贴上lua代码

N很大的时候，估计是抗不住了，代码还需要优化。

function banana( n )
    local c = 1;
    if n == 0 then
        return 0
    elseif n == 1 then
        return 1
    elseif n == 2 then
        return 2
    end
    return (banana(n - 1) + banana(n - 2)) * c;
end

for i = 1,  10 do
    print(banana(i))
end

优化后的代码：

local know = {}

function banana( n )
    if know[n] then
        return know[n]
    end
    local c = 1;
    if n == 0 then
        know[n] = 0
        return 0
    elseif n == 1 then
        know[n] = 1
        return 1
    elseif n == 2 then
        know[n] = 2
        return 2
    end
    local r = (banana(n - 1) + banana(n - 2)) * c;
    know[n] = r
    return r
end

for i = 1,  50 do
    print(i, banana(i))
end