Split Array into Fibonacci Sequence

Split Array into Fibonacci Sequence

What is this problem about?

The Split Array into Fibonacci Sequence interview question challenges you to take a string of digits and determine if it can be decomposed into a sequence of integers that follow the Fibonacci rule. In a traditional Fibonacci sequence, each number is the sum of the two preceding ones. For this coding problem, the same logic applies: you must split the given string into at least three non-negative integers such that for any three consecutive numbers $a, b,$ and $c$, the condition $a + b = c$ holds true. Additionally, each integer in the sequence must fit within a 32-bit signed integer range, and numbers cannot have leading zeros unless the number itself is zero.

Why is this asked in interviews?

This problem is a favorite at companies like Amazon and Google because it tests a candidate's ability to handle complex constraints and edge cases. It requires a deep understanding of recursion and the ability to prune search paths effectively. Interviewers look for how you manage the 32-bit integer limit and how you handle the "no leading zeros" rule. It also evaluates your skill in string manipulation and your systematic approach to exploring multiple possibilities when a simple greedy approach won't work.

Algorithmic pattern used

The primary algorithmic pattern used here is Backtracking. Since we don't know the lengths of the integers beforehand, we must explore various ways to split the string. Backtracking allows us to try one possible split, and if it doesn't lead to a valid Fibonacci sequence, we "backtrack" and try a different length for the current number. This exhaustive search, combined with early exit conditions (like when a sum exceeds the 32-bit limit), makes backtracking the most suitable Backtracking, String interview pattern for this challenge.

Example explanation (use your own example)

Imagine you are given the string "112358". To solve this Split Array into Fibonacci Sequence coding problem, you start by picking the first number. Let's say you pick "1". Then you pick the second number, also "1". Now, the third number must be "1 + 1 = 2". You check if the next part of the string starts with "2". It does. Now your sequence is [1, 1, 2]. The next number must be "1 + 2 = 3". The string continues with "3", so you add it: [1, 1, 2, 3]. The next is "2 + 3 = 5", then "3 + 5 = 8". Since you've used the entire string and have more than three numbers, [1, 1, 2, 3, 5, 8] is a valid solution.

Common mistakes candidates make

• Ignoring the 32-bit limit: Many forget that the numbers must fit in a standard integer, leading to overflow errors if using basic int types in some languages without checks.
• Leading Zeros: Candidates often fail to skip sequences where a multi-digit number starts with '0'.
• Insufficient sequence length: Forgetting that the sequence must contain at least three numbers.
• Inefficient string slicing: Repeatedly creating new string objects can slow down the solution; using indices is better.

Interview preparation tip

When practicing backtracking problems, always start by clearly defining your "base case" and your "recursive step." For this Split Array into Fibonacci Sequence interview question, your base case is reaching the end of the string with a valid sequence. Visualizing the search as a tree can help you understand how the algorithm explores different splits and where it can be optimized by pruning invalid branches early.