1414. Find the Minimum Number of Fibonacci Numbers Whose Sum Is K

Given the number k, return the minimum number of Fibonacci numbers whose sum is equal to k, whether a Fibonacci number could be used multiple times.

The Fibonacci numbers are defined as:

• F₁ = 1
• F₂ = 1
• F_n = F_n-1 + F_n-2 , for n > 2.

It is guaranteed that for the given constraints we can always find such fibonacci numbers that sum 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 <= 10^9