---
# System prepended metadata

title: 'Fibonacci Number <img src="https://img.shields.io/badge/-easy-brightgreen">'
tags: [data_structure_python]

---

---
tags: data_structure_python
---

# Fibonacci Number <img src="https://img.shields.io/badge/-easy-brightgreen">

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

**Example 2:**

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

**Example 3:**

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

**Note:**

```0 ≤ N ≤ 30.```


# Solution

### Solution 1: Recursive + Memoization

```python=
class Solution:
    def fib(self, N: int) -> int:
        return self.__fib(N, cache = {})
        
    def __fib(self, N, cache):
        if N in [0, 1]:
            return N
        elif N in cache:
            return cache[N]
        else:
            res = self.__fib(N-1, cache) + self.__fib(N-2, cache)
            cache[N] = res
            return res
```