# Recursion: Fibonacci Numbers

### Problem Statement :

```The Fibonacci Sequence

The Fibonacci sequence appears in nature all around us, in the arrangement of seeds in a sunflower and the spiral of a nautilus for example.

The Fibonacci sequence begins with fibonacci(0) = 0 and  fibonnaci(1) = 1 as its first and second terms. After these first two elements, each subsequent element is equal to the sum of the previous two elements.

Programmatically:

fibonacci(0) = 0
fibonacci(1) = 1
fibonacci(n) =  fibonacci( n - 1 ) + fibonacci( n - 2 )

Function Description

Complete the recursive function fibonacci in the editor below.

fibonacci has the following parameter(s):

int n: the index of the sequence to return

Returns
- int: the nth element in the Fibonacci sequence

Input Format

The integer n.

Constraints

0   <=   n   <=  30```

### Solution :

```                            ```Solution in C :

In   C :

if(n == 0)
return 0;
else if(n == 1)
return 1;
else
return fibonacci(n-1)+fibonacci(n-2);```
```

```                        ```Solution in C++ :

In   C ++   :

// Complete the function.
if(n==0)
return 0;
else if(n==1)
return 1;
else
return (fibonacci(n-1)+fibonacci(n-2));```
```

```                        ```Solution in Java :

In   Java   :

// Complete the function.
if(n == 0) return 0;
if(n == 1) return 1;
return fibonacci(n - 1) + fibonacci(n - 2);```
```

```                        ```Solution in Python :

In   Python3  :

cache = {0:0, 1:1}

def fibonacci(n):
try:
return cache[n]
except KeyError:
cache[n] = fibonacci(n - 1) + fibonacci(n - 2)
return cache[n]

n = int(input())
print(fibonacci(n))```
```

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