Find the Minimum Number of Fibonacci Numbers Whose Sum Is K

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

class Solution {
    public int findMinFibonacciNumbers(int k) {
        int first = 1, second = 1;
        TreeSet<Integer> set = new TreeSet<>();
        set.add(1);
        while (second <= k) {
            int temp = first + second;
            first = second;
            second = temp;
            set.add(temp);
        }
        int count = 0;
        while (k > 0) {
            int closest = set.floor(k);
            k -= closest;
            count++;
        }
        return count;
    }
}