1414. Find the Minimum Number of Fibonacci Numbers Whose Sum Is K
Difficulty: Medium
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
- 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 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
Solution
Language: Python3
class Solution:
def findMinFibonacciNumbers(self, k: int) -> int:
cur=[1,1]
while cur[-1]+cur[-2]<=k:
cur.append(cur[-1]+cur[-2])
rep=0
while k>0:
k-=cur[-1]
rep+=1
while k>0 and cur[-1]>k:
cur.pop()
return rep
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