LeetCode 1414: Find the Minimum Number of Fibonacci Numbers Whose Sum Is K Solution

Master LeetCode problem 1414 (Find the Minimum Number of Fibonacci Numbers Whose Sum Is K), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

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

Medium

Math Greedy

Problem Explanation

Explanation

To solve this problem, we can start by generating Fibonacci numbers up to the given integer k. Then, we can iterate through the Fibonacci numbers starting from the largest and greedily select the largest Fibonacci number that can be used to sum up to k. We continue this process until k becomes 0, indicating that we have found the minimum number of Fibonacci numbers whose sum is equal to the original k.

Algorithm:

Generate Fibonacci numbers up to k.
Initialize a counter to keep track of the minimum number of Fibonacci numbers.
Iterate through the Fibonacci numbers in descending order.
Check if the current Fibonacci number is less than or equal to k.
If yes, subtract the Fibonacci number from k and increment the counter.
Repeat steps 4-5 until k becomes 0.
Return the counter as the result.

Time Complexity: Generating Fibonacci numbers up to k takes O(log(k)) time. The iteration process also takes O(log(k)) time. So, the overall time complexity is O(log(k)).

Space Complexity: We only need constant space for storing variables and the Fibonacci sequence up to k, so the space complexity is O(1).

Solution Code

class Solution {
    public int findMinFibonacciNumbers(int k) {
        int a = 1, b = 1;
        List<Integer> fibonacci = new ArrayList<>();
        fibonacci.add(a);
        fibonacci.add(b);
        
        while (a + b <= k) {
            int temp = a + b;
            fibonacci.add(temp);
            a = b;
            b = temp;
        }
        
        int count = 0;
        int index = fibonacci.size() - 1;
        while (k > 0) {
            if (fibonacci.get(index) <= k) {
                k -= fibonacci.get(index);
                count++;
            }
            index--;
        }
        
        return count;
    }
}

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