How do you solve Split Array into Fibonacci Sequence on LeetCode?

Split Array into Fibonacci Sequence (LeetCode #842) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The sequence must start with non-zero numbers unless it's a single zero.

What is the brute force solution for Split Array into Fibonacci Sequence?

The brute force approach for Split Array into Fibonacci Sequence is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible ways to split the string into parts and checking if any of these parts can form a Fibonacci-like sequence. This is straightforward but inefficient due to the exponential number of combinations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Split Array into Fibonacci Sequence?

Split Array into Fibonacci Sequence uses the following concepts: String, Backtracking. The recommended patterns to study are: Backtracking, Recursion.

What are the interview tips for Split Array into Fibonacci Sequence?

Clearly explain your thought process as you approach the problem. Consider edge cases, such as leading zeros or very large numbers. Practice backtracking problems to become familiar with the recursive approach.

What are common mistakes when solving Split Array into Fibonacci Sequence?

Forgetting to check for leading zeros in splits. Not handling large numbers correctly.

#842

Split Array into Fibonacci Sequence

Medium

StringBacktrackingBacktrackingRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

The optimal solution leverages backtracking with early stopping conditions to efficiently explore potential splits while adhering to Fibonacci sequence rules. This reduces unnecessary checks and improves performance.

⚙️

Algorithm

4 steps

1Step 1: Use a backtracking function to explore all possible splits of the string.
2Step 2: Maintain a path to store the current Fibonacci sequence being built.
3Step 3: For each split, check if the current number can be part of the Fibonacci sequence based on the last two numbers.
4Step 4: If a valid sequence is found, return it; otherwise, backtrack and try the next split.

solution.py22 lines

1# Full working Python code
2
3def splitIntoFibonacci(num):
4    def backtrack(start, path):
5        if start == len(num) and len(path) >= 3:
6            return path
7        for i in range(start + 1, len(num) + 1):
8            if num[start] == '0' and i > start + 1:
9                break
10            num1 = int(num[start:i])
11            if num1 >= 2**31:
12                break
13            if len(path) >= 2 and num1 != path[-1] + path[-2]:
14                continue
15            path.append(num1)
16            result = backtrack(i, path)
17            if result:
18                return result
19            path.pop()
20        return []
21
22    return backtrack(0, [])

ℹ

Complexity note: The optimal solution runs in O(n) time because it explores each character in the string once, and the space complexity is O(n) due to the storage of the Fibonacci sequence.

1The sequence must start with non-zero numbers unless it's a single zero.
2Each number must not exceed 2^31 - 1.

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