Find the Minimum Number of Fibonacci Numbers Whose Sum Is K

Description

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
• F_n = F_n-1 + F_n-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

Solution(javascript)

/**
 * @param {number} k
 * @return {number}
 */
const findMinFibonacciNumbers = function (k) {
  const sequence = [1, 1]
  let a = 1
  let b = 1
  while (b <= k) {
    const next = a + b
    a = b
    b = next
    sequence.push(next)
  }
  const search = (target) => {
    let left = 0
    let right = sequence.length - 1
    let result = -1
    while (left <= right) {
      const middle = Math.floor(left + (right - left) / 2)
      const num = sequence[middle]
      if (num === target) {
        return num
      } if (num < target) {
        result = num
        left = middle + 1
      } else {
        right = middle - 1
      }
    }
    return result
  }

  let count = 1
  while (search(k) < k) {
    count += 1
    k -= search(k)
  }
  return count
}