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

## Description

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 <= 109

## Solutions

• class Solution {

public int findMinFibonacciNumbers(int k) {
if (k < 2) {
return k;
}
int a = 1, b = 1;
while (b <= k) {
b = a + b;
a = b - a;
}
return 1 + findMinFibonacciNumbers(k - a);
}
}

• class Solution {
public:
int findMinFibonacciNumbers(int k) {
if (k < 2) return k;
int a = 1, b = 1;
while (b <= k) {
b = a + b;
a = b - a;
}
return 1 + findMinFibonacciNumbers(k - a);
}
};

• class Solution:
def findMinFibonacciNumbers(self, k: int) -> int:
def dfs(k):
if k < 2:
return k
a = b = 1
while b <= k:
a, b = b, a + b
return 1 + dfs(k - a)

return dfs(k)


• func findMinFibonacciNumbers(k int) int {
if k < 2 {
return k
}
a, b := 1, 1
for b <= k {
a, b = b, a+b
}
return 1 + findMinFibonacciNumbers(k-a)
}

• const arr = [
1836311903, 1134903170, 701408733, 433494437, 267914296, 165580141, 102334155, 63245986,
39088169, 24157817, 14930352, 9227465, 5702887, 3524578, 2178309, 1346269, 832040, 514229,
317811, 196418, 121393, 75025, 46368, 28657, 17711, 10946, 6765, 4181, 2584, 1597, 987, 610,
377, 233, 144, 89, 55, 34, 21, 13, 8, 5, 3, 2, 1,
];

function findMinFibonacciNumbers(k: number): number {
let res = 0;
for (const num of arr) {
if (k >= num) {
k -= num;
res++;
if (k === 0) {
break;
}
}
}
return res;
}


• const FIB: [i32; 45] = [
1836311903, 1134903170, 701408733, 433494437, 267914296, 165580141, 102334155, 63245986,
39088169, 24157817, 14930352, 9227465, 5702887, 3524578, 2178309, 1346269, 832040, 514229,
317811, 196418, 121393, 75025, 46368, 28657, 17711, 10946, 6765, 4181, 2584, 1597, 987, 610,
377, 233, 144, 89, 55, 34, 21, 13, 8, 5, 3, 2, 1,
];

impl Solution {
pub fn find_min_fibonacci_numbers(mut k: i32) -> i32 {
let mut res = 0;
for &i in FIB.into_iter() {
if k >= i {
k -= i;
res += 1;
if k == 0 {
break;
}
}
}
res
}
}