Understanding the Fibonacci sequence

问题

I have an algorithm that I found online that calculates the Fibonacci sequence. I feel a bit like a fool but I have no idea how it works!

 def fib(n)

  if n == 0 || n == 1
   return n
  end

  if n >= 2
    return fib(n-1) + fib(n-2)
  end
 end

If I call the method with the argument of 10 why does it not return 18? I assume some recursion is happening here but I have no idea. Can someone help me understand this?

回答1:

Let's look at fib(4), according to your code above:

fib(4) #=> 3

It does so by using the following results:

fib(4) #calculates fib(3) + fib(2)
fib(3) #calculates fib(2) + fib(1)
fib(2) #calculates fib(1) + fib(0)
fib(1) #returns 1
fib(0) #returns 0

Crudely speaking your method uses the above results in the following fashion (note: below I am using math-notation (not code) and some dubious spacing to illustrate which bits are being substituted with the results from above):

# fib(4) =   fib(3)                       +  fib(2)
#        = ( fib(2)            + fib(1))  + (fib(1) + fib(0))
#        = ((fib(1) + fib(0))  + 1     )  + (1      + 0     )
#        = ((1      + 0     )  + 1     )  +  1
#        = ( 1                 + 1     )  +  1
#        =   2                            +  1
#        =   3

Your algorithm goes through the above steps. Similarly for fib(10), although it's hardly worth going through it manually as it can be quite cumbersome. As long as you get the basic idea, move on. And by the way you're not a fool, you're just trying to get better at something which is what many of us are trying to do as well. Good luck.

来源：https://stackoverflow.com/questions/38580523/understanding-the-fibonacci-sequence