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

Problem Link

Description

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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

Solution

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Python3

class Solution:
    def findMinFibonacciNumbers(self, k: int) -> int:
        fib = [1,1]
        
        while fib[-1] < k:
            fib.append(fib[-1] + fib[-2])
        
        res = 0
        i = len(fib) - 1        
        
        while k > 0:
            res += k // fib[i]
            k %= fib[i]
            i -= 1
        
        return res