Find the Minimum Number of Fibonacci Numbers Whose Sum Is K Python/Java solution

Python and C++ implementations typically follow the greedy strategy: generate Fibonacci numbers, then repeatedly subtract the largest valid value while counting steps. A Java implementation can also demonstrate a dynamic programming approach similar to coin change, though the greedy method is more efficient for large inputs.

What is the best approach for Find the Minimum Number of Fibonacci Numbers Whose Sum Is K?

The greedy approach is the most efficient solution. Generate Fibonacci numbers up to k, then repeatedly subtract the largest Fibonacci number less than or equal to the remaining value. This works due to properties of Fibonacci numbers that guarantee an optimal representation. The overall time complexity is O(log k).

Is Find the Minimum Number of Fibonacci Numbers Whose Sum Is K asked at Google/Amazon/Meta?

Greedy and Fibonacci-based problems similar to this appear in interviews at large tech companies such as Google, Amazon, and Meta. The question tests understanding of greedy strategy, mathematical sequences, and recognizing when a greedy choice is provably optimal.

What data structure is used in Find the Minimum Number of Fibonacci Numbers Whose Sum Is K?

The solution mainly uses an array or list to store generated Fibonacci numbers. The greedy process then iterates through this list from largest to smallest to subtract valid values. No complex data structures are required beyond simple iteration and arithmetic operations.

What is the time complexity of Find the Minimum Number of Fibonacci Numbers Whose Sum Is K?

The optimal greedy solution runs in O(log k) time because the Fibonacci sequence grows exponentially and contains only about 45 numbers up to 1e9. Each step subtracts the largest valid Fibonacci value, and the number of iterations remains small. Space complexity is O(log k) to store the Fibonacci numbers.

Description Hints 2 Solution Video 3:54

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

Q: Is Find the Minimum Number of Fibonacci Numbers Whose Sum Is K easy or hard?

The problem is classified as Medium on LeetCode. Implementation is straightforward once you recognize the greedy pattern, but the key challenge is realizing that choosing the largest Fibonacci number at each step always leads to the optimal minimum count.

Q: How to solve Find the Minimum Number of Fibonacci Numbers Whose Sum Is K in O(log k)?

First generate all Fibonacci numbers less than or equal to k. Starting from the largest Fibonacci number, subtract it from k if it is not greater than the remaining value. Continue subtracting the largest possible Fibonacci number until k becomes zero. Each subtraction reduces the remaining value quickly, leading to O(log k) complexity.

Medium64.9% acceptance1 company

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
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 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

Asked at 1 company

Google

Topics

Greedy Math

Hints open one at a time

Hint 1

Generate all Fibonacci numbers up to the limit (they are few).

Hint 2

Use greedy solution, taking at every time the greatest Fibonacci number which is smaller than or equal to the current number. Subtract this Fibonacci number from the current number and repeat again the process.

3:54

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def findMinFibonacciNumbers(self, k: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

Your code is saved on this device.Solution