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

Solution: Iteration

• Time complexity: O(logk)
• Space complexity: O(logk)

 

JavaScript

/**
 * @param {number} k
 * @return {number}
 */
const findMinFibonacciNumbers = function (k) {
  const fibonacciDp = [0, 1, 1];
  const fibonacci = n => (fibonacciDp[n] = fibonacciDp[n - 1] + fibonacciDp[n - 2]);
  let current = 3;
  let result = 0;

  while (fibonacciDp.at(-1) < k) {
    fibonacci(current++);
  }
  for (let index = fibonacciDp.length - 1; index > 0; index--) {
    const value = fibonacciDp[index];

    if (k < value) continue;
    k -= value;
    result += 1;
    if (k === 0) return result;
  }
  return result;
};