# [Solved] Given an integer k, return the minimum number of Fibonacci numbers whose sum is equal to k. The same Fibonacci number can be used multiple times.

## Question

Given an integer `k`return the minimum number of Fibonacci numbers whose sum is equal to `k`. The same Fibonacci number can be used multiple times.

The Fibonacci numbers are defined as:

• `F1 = 1`
• `F2 = 1`
• `Fn = Fn-1 + Fn-2` for `n > 2.`

It is guaranteed that for the given constraints we can always find such Fibonacci numbers that sum up to `k`.

Example 1:

```Input: k = 7
Output: 2
Explanation: The Fibonacci numbers are: 1, 1, 2, 3, 5, 8, 13, ...
For k = 7 we can use 2 + 5 = 7.```

Example 2:

```Input: k = 10
Output: 2
Explanation: For k = 10 we can use 2 + 8 = 10.
```

Example 3:

```Input: k = 19
Output: 3
Explanation: For k = 19 we can use 1 + 5 + 13 = 19.
```

Constraints:

• `1 <= k <= 109`

## Python Solution

```class Solution:
def findMinFibonacciNumbers(self, k: int) -> int:
f = [1,1]
while k>f[-1]:
f.append(f[-1]+f[-2])
f = f[1:]

f.sort(reverse=True)

c = 0

for i in f:
if i<=k:
c+=1
k-=i
if i==0:
break
return c```