What is the brute force solution for Find the Minimum Number of Fibonacci Numbers Whose Sum Is K?

The brute force approach for Find the Minimum Number of Fibonacci Numbers Whose Sum Is K is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible combinations of Fibonacci numbers and checking which combinations sum up to k. This method is straightforward but inefficient as it explores many unnecessary combinations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Minimum Number of Fibonacci Numbers Whose Sum Is K?

Find the Minimum Number of Fibonacci Numbers Whose Sum Is K uses the following concepts: Math, Greedy. The recommended patterns to study are: Greedy, Dynamic Programming.

What are the interview tips for Find the Minimum Number of Fibonacci Numbers Whose Sum Is K?

Always start with a brute-force solution to demonstrate understanding, then optimize. Explain your thought process clearly to the interviewer; they value reasoning over just the final answer. Practice recognizing patterns in problems; many can be solved using similar strategies.

What are common mistakes when solving Find the Minimum Number of Fibonacci Numbers Whose Sum Is K?

Relying on brute-force without considering optimization can lead to timeouts in interviews. Not generating Fibonacci numbers efficiently can lead to unnecessary calculations.

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Find the Minimum Number of Fibonacci Numbers Whose Sum Is K

Medium

MathGreedyGreedyDynamic Programming

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Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal approach uses a greedy strategy. By always choosing the largest Fibonacci number that is less than or equal to the remaining value of k, we can minimize the number of Fibonacci numbers needed to reach k.

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Algorithm

3 steps

1Step 1: Generate all Fibonacci numbers up to k.
2Step 2: Initialize a count to 0 and iterate while k > 0.
3Step 3: For each iteration, find the largest Fibonacci number less than or equal to k, subtract it from k, and increment the count.

solution.py15 lines

1# Full working Python code
2
3def findMinFibonacciNumbers(k):
4    fib = [1, 1]
5    while fib[-1] <= k:
6        fib.append(fib[-1] + fib[-2])
7    count = 0
8    while k > 0:
9        for i in range(len(fib) - 1, -1, -1):
10            if fib[i] <= k:
11                k -= fib[i]
12                count += 1
13                break
14    return count
15

ℹ

Complexity note: The time complexity is O(n) because we are generating Fibonacci numbers up to k, and the while loop runs until k becomes 0, which is efficient due to the greedy approach.

1Greedy algorithms often yield optimal solutions for problems involving sums.
2Understanding Fibonacci sequences can help in recognizing patterns in number combinations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.