JS gets the nth element of the Fibonacci sequence

The Fibonacci sequence can be roughly describe as a (n) = A (n-1) + A (n-2) (a >=2). Similar to this [1, 1, 2, 3, 5, 8, 13 ...].

Specific we can Baidu a bit. Let's use JS to get the nth number of Fibonacci sequence numbers:

1. Recursion

var function (n) {            if (n = = 1 | | n = = 2) {                return 1            else  { c12/>return A (n-1) + A (n-2)            }        }        console.time (' A () ')        Console.log (A ())        console.timeend (' A (44) ')

Above we can clearly see the code of thought, but this method has a fatal disadvantage: the efficiency is too poor!

Don't believe you see:

By the time the 44th was executed, it was unacceptable. Requires more than 5s. Well, let's make it a little bit better.

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2. Closures + Caching

varB = (function() {            varCache = {                1:1,                2:1            }            return function(n) {if(Cache[n]) {returnCache[n]}Else{cache[n-1] = B (n-1) Cache[n-2] = B (n-2)                    returnCache[n-1] + cache[n-2]}}) () Console.time (' B (1200) ') Console.log (b (1200)) Console.timeend (' B (1200) ')

The values calculated for each step are saved in the cache. Efficiency has improved a lot:

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3. Directly calculate the value of the array, and then take the values from the array

 var  c = function   (n) { var  arr = [1, 1]  if  (n = = 1 | | n = = 2return  1}  for  (var  i = 2; i < n; I ++ = arr[i-1] + arr[i-2]}  return  arr[n-1]} console.time ( ' C (+) ' 
     
      ) Console.log (c (
      1200 ' C (+) ') 

This efficiency has been further improved a lot:

So is there a quicker way to do that? Of course! The Fibonacci series is mathematically expressed:

Why don't we just use mathematical expressions?

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4. Direct use of mathematical expressions

var function (n) {            return (1/(Math.pow (5))) * (Math.pow ((1 + math.pow (5))/2, N)-Math.pow ((1-math.po W (5, I))/2, N)        }        console.time (' d () ')        Console.log (d ())        Console.timeend (' d (1200) ')

Now let's look at the effect:

So sum up: math is so beautiful! ^_^

JS gets the nth element of the Fibonacci sequence