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Reason About Alternating Positive and Negative Values

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MediumSoftware EngineerOnsiteSoftware Engineering Fundamentals

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This problem tests your ability to manipulate array elements in-place while managing constraints on stability and the treatment of special values like zeros.

Problem Statement

Given an array arr of integers, rearrange the elements such that positive and negative numbers alternate. If there are extra elements of one sign, they should be appended to the end of the array. Zeros should be treated as neutral elements and moved to the very end of the array, maintaining their relative order if possible.

Requirements

  1. If possible, perform the operation in-place with O(1) extra space.
  2. Discuss the trade-offs between an in-place approach and a stable approach (where the relative order of elements of the same sign is preserved).

Function Signature

def rearrange_array(arr: list[int]) -> list[int]:
    # Returns the rearranged array
    pass

Examples

Example 1:

  • Input: [1, -2, 3, -4, 0, 5]
  • Output: [1, -2, 3, -4, 5, 0]
  • Explanation: The alternating sequence 1, -2, 3, -4, 5 is formed, and the zero is pushed to the end.

Example 2:

  • Input: [-1, -2, 3, 0]
  • Output: [3, -1, -2, 0]
  • Explanation: Since there are more negatives than positives, we alternate as much as possible and append the remaining negatives.

Constraints

  • 1 <= len(arr) <= 10^5
  • -10^9 <= arr[i] <= 10^9
  • Time complexity target: O(n)

Hints

Hint 1

Consider first partitioning the array into positive, negative, and zero segments using a three-pointer approach similar to the Dutch National Flag problem.

Hint 2

If you need to maintain stability, think about whether a single-pass in-place swap approach is mathematically possible without using extra buffers.

Hint 3

If in-place is required but stability isn't, you can use two pointers to move elements to their target indices, though the order of elements will be changed.

Follow-up questions

  • How would your approach change if we required the resulting array to start with a negative number instead of a positive one?
  • What is the time complexity of a stable approach that uses O(n) extra space, and how does it compare to your in-place solution?
  • If the array is extremely large (e.g., larger than RAM), how would you handle the rearrangement process?