Find the Minimum Number of Fibonacci Numbers Whose Sum Is K

Problem

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 <= 10^9

Solution (Java)

class Solution {
    public int findMinFibonacciNumbers(int k) {
        List<Integer> list = new ArrayList<>();
        list.add(1);
        list.add(1);
        int prev = 1;
        int curr = 1;
        while (prev <= k) {
            int n = prev + curr;
            prev = curr;
            curr = n;
            list.add(n);
        }
        int count = 0;
        int num = k;
        for (int i = list.size() - 1; i >= 0; i--) {
            if (list.get(i) <= num) {
                count++;
                num = num - list.get(i);
            }
        }
        return count;
    }
}

Explain:

nope.

Complexity:

Time complexity : O(n).
Space complexity : O(n).