Package g1401_1500.s1414_find_the_minimum_number_of_fibonacci_numbers_whose_sum_is_k

Class Solution

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public final class Solution

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

    Medium

    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:

    • <code>F<sub>1</sub> = 1</code>

    • <code>F<sub>2</sub> = 1</code>

    • <code>F<sub>n</sub> = F<sub>n-1</sub> + F<sub>n-2</sub></code> for n &gt; 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:

    • <code>1 <= k <= 10<sup>9</sup></code>

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer findMinFibonacciNumbers(Integer k)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait