JavaScript Fibonacci breakdown

Question

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Answer 1

I know the question is a bit old, and the answers are helpful. I was doing this exercise in GoLang, and thought how I would write in Javascript, and use this answer to refresh my mind as well. I see your code has a cache variable to store the value of the fib(n-2) + fib(n-1) iteration. If you're doing recursive, you don't need a variable to store the result, because each time the function is called it returns a number, and these numbers are added up to the first function call.

function fib(n) {
    if (n<=1) return n;
    return fib(n - 1) + fib(n - 2);
}

To see why you don't need the cache variable is go through each function call, and start calculate the values once n equal 1 or 0.

for example:

iteration 1)

fib(3) {
   return fib(3-1) + f(3-2)   
}
---------------------------    
iteration 2)

fib(3-1) {
   return fib(2 - 1) + fib(2-2)
}

iteration 3)

fib(3-2) {
   return 1
}    
---------------------------

iteration 4)

fib(2-1) {
   return 1
}


iteration 5)
fib(2-2) {
   return 0
}
----------------------

if you calculate it the return value backward from iteration 5)

5) 0
4) 1
3) 1
2) 1 <== 4) + 5)  = 1 + 0  
1) 2  <== 2) + 3)  = 1 + 1

so fib(3) is 2