[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 kreturn 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
Abhishek Sharma
Abhishek Sharma

Started my Data Science journey in my 2nd year of college and since then continuously into it because of the magical powers of ML and continuously doing projects in almost every domain of AI like ML, DL, CV, NLP.

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