###### tags: `Math`, `Dynamic Programming`, `Recursion`, `Memoization`

# LeetCode 509. Fibonacci Number
The Fibonacci numbers, commonly denoted ```F(n)``` form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from ```0``` and ```1```. That is,

F(0) = 0, F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n > 1.

Given ```n```, calculate ```F(n)```.

>Example 1:

Input: n = 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.

>Example 2:

Input: n = 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.

>Example 3:

Input: n = 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.

### Constraints:

- $0 <= n <= 30$
---
### Idea:
>
### Solution:

Python:

class Solution:
    def fib(self, n: int) -> int:
        sqrt5 = sqrt(5)
        return int((pow(1 + sqrt5, n) - pow(1 - sqrt5, n)) / pow(2, n) / sqrt5)

C++: