1414. 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) {
        TreeSet<Integer> set = new TreeSet();
        int a = 0, b = 1;
        int c = a + b;
        set.add(1);
        while(c <= k) {
            c = a + b;
            set.add(c);
            a = b;
            b = c;
        }
        int res = 0;        
        while(k > 0) {
            int cur = set.floor(k);
            res++;
            k -= cur;
        }
        return res;
    }
}

Fibonacci数的产生要三个变量，记一下

这题用TreeSet的floor方法，返回离k最近（小于等于）的key，然后继续往下即可.类似的还有ceiling方法，返回大于等于的key